[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2010.16316"}],"type":"journal_article","date_published":"2023-12-01T00:00:00Z","oa":1,"publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"language":[{"iso":"eng"}],"publication":"Algorithmica","month":"12","project":[{"grant_number":"101019564","name":"The design and evaluation of modern fully dynamic data structures","_id":"bd9ca328-d553-11ed-ba76-dc4f890cfe62","call_identifier":"H2020"},{"_id":"bd9e3a2e-d553-11ed-ba76-8aa684ce17fe","grant_number":"P33775 ","name":"Fast Algorithms for a Reactive Network Layer"}],"oa_version":"Preprint","acknowledgement":"Monika Henzinger was supported by funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme Grant agreement No. 101019564 “The Design of Modern Fully Dynamic Data Structures (MoDynStruct)” and from the Austrian Science Fund (FWF) project “Fast Algorithms for a Reactive Network Layer (ReactNet)”, P 33775-N, with additional funding from the netidee SCIENCE Stiftung, 2020–2024. Billy Jin was Supported in part by NSERC fellowship PGSD3-532673-2019 and NSF grant CCF-2007009. Richard Peng was supported in part by an NSERC Discovery Grant and NSF grant CCF-1846218. David P. Williamson was supported in part by NSF grant CCF-2007009.","volume":85,"external_id":{"isi":["001041254900002"],"arxiv":["2010.16316"]},"isi":1,"citation":{"ista":"Henzinger MH, Jin B, Peng R, Williamson DP. 2023. A combinatorial cut-toggling algorithm for solving Laplacian linear systems. Algorithmica. 85, 2680–3716.","mla":"Henzinger, Monika H., et al. “A Combinatorial Cut-Toggling Algorithm for Solving Laplacian Linear Systems.” <i>Algorithmica</i>, vol. 85, Springer Nature, 2023, pp. 2680–3716, doi:<a href=\"https://doi.org/10.1007/s00453-023-01154-8\">10.1007/s00453-023-01154-8</a>.","short":"M.H. Henzinger, B. Jin, R. Peng, D.P. Williamson, Algorithmica 85 (2023) 2680–3716.","chicago":"Henzinger, Monika H, Billy Jin, Richard Peng, and David P. Williamson. “A Combinatorial Cut-Toggling Algorithm for Solving Laplacian Linear Systems.” <i>Algorithmica</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00453-023-01154-8\">https://doi.org/10.1007/s00453-023-01154-8</a>.","ieee":"M. H. Henzinger, B. Jin, R. Peng, and D. P. Williamson, “A combinatorial cut-toggling algorithm for solving Laplacian linear systems,” <i>Algorithmica</i>, vol. 85. Springer Nature, pp. 2680–3716, 2023.","apa":"Henzinger, M. H., Jin, B., Peng, R., &#38; Williamson, D. P. (2023). A combinatorial cut-toggling algorithm for solving Laplacian linear systems. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00453-023-01154-8\">https://doi.org/10.1007/s00453-023-01154-8</a>","ama":"Henzinger MH, Jin B, Peng R, Williamson DP. A combinatorial cut-toggling algorithm for solving Laplacian linear systems. <i>Algorithmica</i>. 2023;85:2680-3716. doi:<a href=\"https://doi.org/10.1007/s00453-023-01154-8\">10.1007/s00453-023-01154-8</a>"},"year":"2023","date_updated":"2024-01-30T12:33:10Z","abstract":[{"text":"Over the last two decades, a significant line of work in theoretical algorithms has made progress in solving linear systems of the form Lx=b, where L is the Laplacian matrix of a weighted graph with weights w(i,j)>0 on the edges. The solution x of the linear system can be interpreted as the potentials of an electrical flow in which the resistance on edge (i, j) is 1/w(i, j). Kelner et al. (in: Proceedings of the 45th Annual ACM Symposium on the Theory of Computing, pp 911–920, 2013. https://doi.org/10.1145/2488608.2488724) give a combinatorial, near-linear time algorithm that maintains the Kirchoff Current Law, and gradually enforces the Kirchoff Potential Law by updating flows around cycles (cycle toggling). In this paper, we consider a dual version of the algorithm that maintains the Kirchoff Potential Law, and gradually enforces the Kirchoff Current Law by cut toggling: each iteration updates all potentials on one side of a fundamental cut of a spanning tree by the same amount. We prove that this dual algorithm also runs in a near-linear number of iterations. We show, however, that if we abstract cut toggling as a natural data structure problem, this problem can be reduced to the online vector–matrix-vector problem, which has been conjectured to be difficult for dynamic algorithms (Henzinger et al., in: Proceedings of the 47th Annual ACM Symposium on the Theory of Computing, pp 21–30, 2015. https://doi.org/10.1145/2746539.2746609). The conjecture implies that the data structure does not have an O(n1−ϵ) time algorithm for any ϵ>0, and thus a straightforward implementation of the cut-toggling algorithm requires essentially linear time per iteration. To circumvent the lower bound, we batch update steps, and perform them simultaneously instead of sequentially. An appropriate choice of batching leads to an O˜(m1.5) time cut-toggling algorithm for solving Laplacian systems. Furthermore, we show that if we sparsify the graph and call our algorithm recursively on the Laplacian system implied by batching and sparsifying, we can reduce the running time to O(m1+ϵ) for any ϵ>0. Thus, the dual cut-toggling algorithm can achieve (almost) the same running time as its primal cycle-toggling counterpart.","lang":"eng"}],"day":"01","arxiv":1,"doi":"10.1007/s00453-023-01154-8","quality_controlled":"1","ec_funded":1,"page":"2680-3716","article_type":"original","publisher":"Springer Nature","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H"},{"last_name":"Jin","first_name":"Billy","full_name":"Jin, Billy"},{"last_name":"Peng","first_name":"Richard","full_name":"Peng, Richard"},{"full_name":"Williamson, David P.","first_name":"David P.","last_name":"Williamson"}],"scopus_import":"1","_id":"14043","intvolume":"        85","title":"A combinatorial cut-toggling algorithm for solving Laplacian linear systems","department":[{"_id":"MoHe"}],"article_processing_charge":"No","date_created":"2023-08-13T22:01:13Z","publication_status":"published"},{"author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Osang","first_name":"Georg F","full_name":"Osang, Georg F","id":"464B40D6-F248-11E8-B48F-1D18A9856A87"}],"_id":"12086","scopus_import":"1","title":"A simple algorithm for higher-order Delaunay mosaics and alpha shapes","intvolume":"        85","publication_status":"published","date_created":"2022-09-11T22:01:57Z","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"HeEd"}],"file_date_updated":"2023-01-20T10:02:48Z","page":"277-295","quality_controlled":"1","ec_funded":1,"article_type":"original","publisher":"Springer Nature","isi":1,"external_id":{"isi":["000846967100001"]},"date_updated":"2023-06-27T12:53:43Z","citation":{"ama":"Edelsbrunner H, Osang GF. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. <i>Algorithmica</i>. 2023;85:277-295. doi:<a href=\"https://doi.org/10.1007/s00453-022-01027-6\">10.1007/s00453-022-01027-6</a>","apa":"Edelsbrunner, H., &#38; Osang, G. F. (2023). A simple algorithm for higher-order Delaunay mosaics and alpha shapes. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00453-022-01027-6\">https://doi.org/10.1007/s00453-022-01027-6</a>","ieee":"H. Edelsbrunner and G. F. Osang, “A simple algorithm for higher-order Delaunay mosaics and alpha shapes,” <i>Algorithmica</i>, vol. 85. Springer Nature, pp. 277–295, 2023.","chicago":"Edelsbrunner, Herbert, and Georg F Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” <i>Algorithmica</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00453-022-01027-6\">https://doi.org/10.1007/s00453-022-01027-6</a>.","short":"H. Edelsbrunner, G.F. Osang, Algorithmica 85 (2023) 277–295.","mla":"Edelsbrunner, Herbert, and Georg F. Osang. “A Simple Algorithm for Higher-Order Delaunay Mosaics and Alpha Shapes.” <i>Algorithmica</i>, vol. 85, Springer Nature, 2023, pp. 277–95, doi:<a href=\"https://doi.org/10.1007/s00453-022-01027-6\">10.1007/s00453-022-01027-6</a>.","ista":"Edelsbrunner H, Osang GF. 2023. A simple algorithm for higher-order Delaunay mosaics and alpha shapes. Algorithmica. 85, 277–295."},"year":"2023","abstract":[{"text":"We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets.","lang":"eng"}],"doi":"10.1007/s00453-022-01027-6","day":"01","ddc":["510"],"acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.","volume":85,"publication":"Algorithmica","has_accepted_license":"1","month":"01","oa_version":"Published Version","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"Z00342","name":"The Wittgenstein Prize","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"language":[{"iso":"eng"}],"date_published":"2023-01-01T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"user_id":"2EBD1598-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"access_level":"open_access","success":1,"relation":"main_file","creator":"dernst","file_id":"12322","file_size":911017,"checksum":"71685ca5121f4c837f40c3f8eb50c915","date_created":"2023-01-20T10:02:48Z","content_type":"application/pdf","file_name":"2023_Algorithmica_Edelsbrunner.pdf","date_updated":"2023-01-20T10:02:48Z"}]},{"ddc":["000"],"acknowledgement":"The authors sincerely thank Thomas Sauerwald and George Giakkoupis for insightful discussions, and Mohsen Ghaffari, Yuval Peres, and Udi Wieder for feedback on earlier versions of this draft. We also thank the ICALP anonymous reviewers for their very useful comments. Open access funding provided by Institute of Science and Technology (IST Austria). Funding was provided by European Research Council (Grant No. PR1042ERC01).","isi":1,"external_id":{"isi":["000734004600001"],"arxiv":["2003.09297"]},"date_updated":"2024-03-05T07:35:53Z","year":"2021","citation":{"apa":"Alistarh, D.-A., Nadiradze, G., &#38; Sabour, A. (2021). Dynamic averaging load balancing on cycles. <i>Algorithmica</i>. Virtual, Online; Germany: Springer Nature. <a href=\"https://doi.org/10.1007/s00453-021-00905-9\">https://doi.org/10.1007/s00453-021-00905-9</a>","ama":"Alistarh D-A, Nadiradze G, Sabour A. Dynamic averaging load balancing on cycles. <i>Algorithmica</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s00453-021-00905-9\">10.1007/s00453-021-00905-9</a>","ieee":"D.-A. Alistarh, G. Nadiradze, and A. Sabour, “Dynamic averaging load balancing on cycles,” <i>Algorithmica</i>. Springer Nature, 2021.","chicago":"Alistarh, Dan-Adrian, Giorgi Nadiradze, and Amirmojtaba Sabour. “Dynamic Averaging Load Balancing on Cycles.” <i>Algorithmica</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00453-021-00905-9\">https://doi.org/10.1007/s00453-021-00905-9</a>.","mla":"Alistarh, Dan-Adrian, et al. “Dynamic Averaging Load Balancing on Cycles.” <i>Algorithmica</i>, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00453-021-00905-9\">10.1007/s00453-021-00905-9</a>.","short":"D.-A. Alistarh, G. Nadiradze, A. Sabour, Algorithmica (2021).","ista":"Alistarh D-A, Nadiradze G, Sabour A. 2021. Dynamic averaging load balancing on cycles. Algorithmica."},"abstract":[{"text":"We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step t≥ 0, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks a random neighbor, and the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure. Variants of the above graphical balanced allocation process have been studied previously by Peres, Talwar, and Wieder [Peres et al., 2015], and by Sauerwald and Sun [Sauerwald and Sun, 2015]. These authors left as open the question of characterizing the gap in the case of cycle graphs in the dynamic case, where weights are created during the algorithm’s execution. For this case, the only known upper bound is of 𝒪(n log n), following from a majorization argument due to [Peres et al., 2015], which analyzes a related graphical allocation process. In this paper, we provide an upper bound of 𝒪 (√n log n) on the expected gap of the above process for cycles of length n. We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any k ≤ n/2. We complement this with a \"gap covering\" argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We provide analytical and experimental evidence that our upper bound on the gap is tight up to a logarithmic factor. ","lang":"eng"}],"doi":"10.1007/s00453-021-00905-9","arxiv":1,"day":"24","file_date_updated":"2021-12-27T10:36:40Z","ec_funded":1,"quality_controlled":"1","article_type":"original","publisher":"Springer Nature","author":[{"last_name":"Alistarh","first_name":"Dan-Adrian","full_name":"Alistarh, Dan-Adrian","orcid":"0000-0003-3650-940X","id":"4A899BFC-F248-11E8-B48F-1D18A9856A87"},{"id":"3279A00C-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgi","last_name":"Nadiradze","orcid":"0000-0001-5634-0731","full_name":"Nadiradze, Giorgi"},{"id":"bcc145fd-e77f-11ea-ae8b-80d661dbff67","first_name":"Amirmojtaba","last_name":"Sabour","full_name":"Sabour, Amirmojtaba"}],"_id":"8286","scopus_import":"1","title":"Dynamic averaging load balancing on cycles","publication_status":"published","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"DaAl"}],"date_created":"2020-08-24T06:24:04Z","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","related_material":{"link":[{"relation":"earlier_version","url":"https://doi.org/10.4230/LIPIcs.ICALP.2020.7"}],"record":[{"status":"public","relation":"earlier_version","id":"15077"}]},"file":[{"access_level":"open_access","success":1,"relation":"main_file","file_id":"10577","creator":"cchlebak","date_created":"2021-12-27T10:36:40Z","file_size":525950,"checksum":"21169b25b0c8e17b21e12af22bff9870","date_updated":"2021-12-27T10:36:40Z","content_type":"application/pdf","file_name":"2021_Algorithmica_Alistarh.pdf"}],"date_published":"2021-12-24T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"language":[{"iso":"eng"}],"conference":{"end_date":"2020-07-11","location":"Virtual, Online; Germany","start_date":"2020-07-08","name":"ICALP: International Colloquium on Automata, Languages, and Programming "},"publication":"Algorithmica","has_accepted_license":"1","month":"12","oa_version":"Published Version","project":[{"grant_number":"805223","name":"Elastic Coordination for Scalable Machine Learning","_id":"268A44D6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}]},{"publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"oa":1,"date_published":"2020-11-01T00:00:00Z","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1707.02577"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","oa_version":"Preprint","month":"11","publication":"Algorithmica","language":[{"iso":"eng"}],"doi":"10.1007/s00453-020-00721-7","arxiv":1,"day":"01","abstract":[{"lang":"eng","text":"In this paper, we study the problem of opening centers to cluster a set of clients in a metric space so as to minimize the sum of the costs of the centers and of the cluster radii, in a dynamic environment where clients arrive and depart, and the solution must be updated efficiently while remaining competitive with respect to the current optimal solution. We call this dynamic sum-of-radii clustering problem. We present a data structure that maintains a solution whose cost is within a constant factor of the cost of an optimal solution in metric spaces with bounded doubling dimension and whose worst-case update time is logarithmic in the parameters of the problem."}],"date_updated":"2022-09-12T08:50:14Z","year":"2020","citation":{"apa":"Henzinger, M. H., Leniowski, D., &#38; Mathieu, C. (2020). Dynamic clustering to minimize the sum of radii. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00453-020-00721-7\">https://doi.org/10.1007/s00453-020-00721-7</a>","ama":"Henzinger MH, Leniowski D, Mathieu C. Dynamic clustering to minimize the sum of radii. <i>Algorithmica</i>. 2020;82(11):3183-3194. doi:<a href=\"https://doi.org/10.1007/s00453-020-00721-7\">10.1007/s00453-020-00721-7</a>","ieee":"M. H. Henzinger, D. Leniowski, and C. Mathieu, “Dynamic clustering to minimize the sum of radii,” <i>Algorithmica</i>, vol. 82, no. 11. Springer Nature, pp. 3183–3194, 2020.","chicago":"Henzinger, Monika H, Dariusz Leniowski, and Claire Mathieu. “Dynamic Clustering to Minimize the Sum of Radii.” <i>Algorithmica</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00453-020-00721-7\">https://doi.org/10.1007/s00453-020-00721-7</a>.","short":"M.H. Henzinger, D. Leniowski, C. Mathieu, Algorithmica 82 (2020) 3183–3194.","mla":"Henzinger, Monika H., et al. “Dynamic Clustering to Minimize the Sum of Radii.” <i>Algorithmica</i>, vol. 82, no. 11, Springer Nature, 2020, pp. 3183–94, doi:<a href=\"https://doi.org/10.1007/s00453-020-00721-7\">10.1007/s00453-020-00721-7</a>.","ista":"Henzinger MH, Leniowski D, Mathieu C. 2020. Dynamic clustering to minimize the sum of radii. Algorithmica. 82(11), 3183–3194."},"external_id":{"arxiv":["1707.02577"]},"volume":82,"extern":"1","publication_status":"published","article_processing_charge":"No","date_created":"2022-07-27T13:58:58Z","title":"Dynamic clustering to minimize the sum of radii","intvolume":"        82","_id":"11674","scopus_import":"1","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H","last_name":"Henzinger"},{"first_name":"Dariusz","last_name":"Leniowski","full_name":"Leniowski, Dariusz"},{"first_name":"Claire","last_name":"Mathieu","full_name":"Mathieu, Claire"}],"issue":"11","publisher":"Springer Nature","article_type":"original","page":"3183-3194","quality_controlled":"1"},{"keyword":["Dynamic algorithms","Data structures","Graph algorithms","Matching","Vertex cover"],"language":[{"iso":"eng"}],"oa_version":"Published Version","month":"04","publication":"Algorithmica","main_file_link":[{"url":"https://doi.org/10.1007/s00453-019-00630-4","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"oa":1,"type":"journal_article","date_published":"2020-04-01T00:00:00Z","publisher":"Springer Nature","article_type":"original","quality_controlled":"1","page":"1057-1080","date_created":"2022-07-27T14:31:06Z","article_processing_charge":"No","publication_status":"published","intvolume":"        82","title":"Deterministic dynamic matching in O(1) update time","scopus_import":"1","_id":"11675","issue":"4","author":[{"full_name":"Bhattacharya, Sayan","last_name":"Bhattacharya","first_name":"Sayan"},{"last_name":"Chakrabarty","first_name":"Deeparnab","full_name":"Chakrabarty, Deeparnab"},{"first_name":"Monika H","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"}],"volume":82,"extern":"1","day":"01","doi":"10.1007/s00453-019-00630-4","abstract":[{"lang":"eng","text":"We consider the problems of maintaining an approximate maximum matching and an approximate minimum vertex cover in a dynamic graph undergoing a sequence of edge insertions/deletions. Starting with the seminal work of Onak and Rubinfeld (in: Proceedings of the ACM symposium on theory of computing (STOC), 2010), this problem has received significant attention in recent years. Very recently, extending the framework of Baswana et al. (in: Proceedings of the IEEE symposium on foundations of computer science (FOCS), 2011) , Solomon (in: Proceedings of the IEEE symposium on foundations of computer science (FOCS), 2016) gave a randomized dynamic algorithm for this problem that has an approximation ratio of 2 and an amortized update time of O(1) with high probability. This algorithm requires the assumption of an oblivious adversary, meaning that the future sequence of edge insertions/deletions in the graph cannot depend in any way on the algorithm’s past output. A natural way to remove the assumption on oblivious adversary is to give a deterministic dynamic algorithm for the same problem in O(1) update time. In this paper, we resolve this question. We present a new deterministic fully dynamic algorithm that maintains a O(1)-approximate minimum vertex cover and maximum fractional matching, with an amortized update time of O(1). Previously, the best deterministic algorithm for this problem was due to Bhattacharya et al. (in: Proceedings of the ACM-SIAM symposium on discrete algorithms (SODA), 2015); it had an approximation ratio of (2+ε) and an amortized update time of O(logn/ε2). Our result can be generalized to give a fully dynamic O(f3)-approximate algorithm with O(f2) amortized update time for the hypergraph vertex cover and fractional hypergraph matching problem, where every hyperedge has at most f vertices."}],"citation":{"apa":"Bhattacharya, S., Chakrabarty, D., &#38; Henzinger, M. H. (2020). Deterministic dynamic matching in O(1) update time. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00453-019-00630-4\">https://doi.org/10.1007/s00453-019-00630-4</a>","ama":"Bhattacharya S, Chakrabarty D, Henzinger MH. Deterministic dynamic matching in O(1) update time. <i>Algorithmica</i>. 2020;82(4):1057-1080. doi:<a href=\"https://doi.org/10.1007/s00453-019-00630-4\">10.1007/s00453-019-00630-4</a>","chicago":"Bhattacharya, Sayan, Deeparnab Chakrabarty, and Monika H Henzinger. “Deterministic Dynamic Matching in O(1) Update Time.” <i>Algorithmica</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00453-019-00630-4\">https://doi.org/10.1007/s00453-019-00630-4</a>.","ieee":"S. Bhattacharya, D. Chakrabarty, and M. H. Henzinger, “Deterministic dynamic matching in O(1) update time,” <i>Algorithmica</i>, vol. 82, no. 4. Springer Nature, pp. 1057–1080, 2020.","short":"S. Bhattacharya, D. Chakrabarty, M.H. Henzinger, Algorithmica 82 (2020) 1057–1080.","mla":"Bhattacharya, Sayan, et al. “Deterministic Dynamic Matching in O(1) Update Time.” <i>Algorithmica</i>, vol. 82, no. 4, Springer Nature, 2020, pp. 1057–80, doi:<a href=\"https://doi.org/10.1007/s00453-019-00630-4\">10.1007/s00453-019-00630-4</a>.","ista":"Bhattacharya S, Chakrabarty D, Henzinger MH. 2020. Deterministic dynamic matching in O(1) update time. Algorithmica. 82(4), 1057–1080."},"year":"2020","date_updated":"2022-09-12T08:55:46Z"},{"issue":"1","author":[{"full_name":"Dvořák, Wolfgang","last_name":"Dvořák","first_name":"Wolfgang"},{"full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","last_name":"Henzinger","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"first_name":"David P.","last_name":"Williamson","full_name":"Williamson, David P."}],"scopus_import":"1","_id":"11676","intvolume":"        77","title":"Maximizing a submodular function with viability constraints","date_created":"2022-07-27T14:37:24Z","article_processing_charge":"No","publication_status":"published","quality_controlled":"1","page":"152-172","article_type":"original","publisher":"Springer Nature","external_id":{"arxiv":["1611.05753"]},"year":"2017","citation":{"short":"W. Dvořák, M.H. Henzinger, D.P. Williamson, Algorithmica 77 (2017) 152–172.","mla":"Dvořák, Wolfgang, et al. “Maximizing a Submodular Function with Viability Constraints.” <i>Algorithmica</i>, vol. 77, no. 1, Springer Nature, 2017, pp. 152–72, doi:<a href=\"https://doi.org/10.1007/s00453-015-0066-y\">10.1007/s00453-015-0066-y</a>.","ista":"Dvořák W, Henzinger MH, Williamson DP. 2017. Maximizing a submodular function with viability constraints. Algorithmica. 77(1), 152–172.","apa":"Dvořák, W., Henzinger, M. H., &#38; Williamson, D. P. (2017). Maximizing a submodular function with viability constraints. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00453-015-0066-y\">https://doi.org/10.1007/s00453-015-0066-y</a>","ama":"Dvořák W, Henzinger MH, Williamson DP. Maximizing a submodular function with viability constraints. <i>Algorithmica</i>. 2017;77(1):152-172. doi:<a href=\"https://doi.org/10.1007/s00453-015-0066-y\">10.1007/s00453-015-0066-y</a>","chicago":"Dvořák, Wolfgang, Monika H Henzinger, and David P. Williamson. “Maximizing a Submodular Function with Viability Constraints.” <i>Algorithmica</i>. Springer Nature, 2017. <a href=\"https://doi.org/10.1007/s00453-015-0066-y\">https://doi.org/10.1007/s00453-015-0066-y</a>.","ieee":"W. Dvořák, M. H. Henzinger, and D. P. Williamson, “Maximizing a submodular function with viability constraints,” <i>Algorithmica</i>, vol. 77, no. 1. Springer Nature, pp. 152–172, 2017."},"date_updated":"2022-09-12T08:58:16Z","abstract":[{"lang":"eng","text":"We study the problem of maximizing a monotone submodular function with viability constraints. This problem originates from computational biology, where we are given a phylogenetic tree over a set of species and a directed graph, the so-called food web, encoding viability constraints between these species. These food webs usually have constant depth. The goal is to select a subset of k species that satisfies the viability constraints and has maximal phylogenetic diversity. As this problem is known to be NP-hard, we investigate approximation algorithms. We present the first constant factor approximation algorithm if the depth is constant. Its approximation ratio is (1−1e√). This algorithm not only applies to phylogenetic trees with viability constraints but for arbitrary monotone submodular set functions with viability constraints. Second, we show that there is no (1−1/e+ϵ)-approximation algorithm for our problem setting (even for additive functions) and that there is no approximation algorithm for a slight extension of this setting."}],"day":"01","doi":"10.1007/s00453-015-0066-y","arxiv":1,"extern":"1","volume":77,"acknowledgement":"The research leading to these results has received funding from the European Research\r\nCouncil under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement No. 340506.","publication":"Algorithmica","month":"01","oa_version":"Preprint","keyword":["Approximation algorithms","Submodular functions","Phylogenetic diversity","Viability constraints"],"language":[{"iso":"eng"}],"type":"journal_article","date_published":"2017-01-01T00:00:00Z","oa":1,"publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1611.05753"}]},{"article_processing_charge":"No","date_created":"2022-07-27T15:02:28Z","publication_status":"published","intvolume":"        24","title":"Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology","scopus_import":"1","_id":"11679","author":[{"last_name":"Henzinger","first_name":"Monika H","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"},{"full_name":"King, V.","last_name":"King","first_name":"V."},{"last_name":"Warnow","first_name":"T.","full_name":"Warnow, T."}],"publisher":"Springer Nature","article_type":"original","quality_controlled":"1","page":"1-13","day":"01","doi":"10.1007/pl00009268","abstract":[{"text":"We are given a set T = {T 1 ,T 2 , . . .,T k } of rooted binary trees, each T i leaf-labeled by a subset L(Ti)⊂{1,2,...,n} . If T is a tree on {1,2, . . .,n }, we let T|L denote the minimal subtree of T induced by the nodes of L and all their ancestors. The consensus tree problem asks whether there exists a tree T * such that, for every i , T∗|L(Ti) is homeomorphic to T i .\r\n\r\nWe present algorithms which test if a given set of trees has a consensus tree and if so, construct one. The deterministic algorithm takes time min{O(N n 1/2 ), O(N+ n 2 log n )}, where N=∑i|Ti| , and uses linear space. The randomized algorithm takes time O(N log3 n) and uses linear space. The previous best for this problem was a 1981 O(Nn) algorithm by Aho et al. Our faster deterministic algorithm uses a new efficient algorithm for the following interesting dynamic graph problem: Given a graph G with n nodes and m edges and a sequence of b batches of one or more edge deletions, then, after each batch, either find a new component that has just been created or determine that there is no such component. For this problem, we have a simple algorithm with running time O(n 2 log n + b 0 min{n 2 , m log n }), where b 0 is the number of batches which do not result in a new component. For our particular application, b0≤1 . If all edges are deleted, then the best previously known deterministic algorithm requires time O(mn−−√) to solve this problem. We also present two applications of these consensus tree algorithms which solve other problems in computational evolutionary biology.","lang":"eng"}],"year":"1999","citation":{"chicago":"Henzinger, Monika H, V. King, and T. Warnow. “Constructing a Tree from Homeomorphic Subtrees, with Applications to Computational Evolutionary Biology.” <i>Algorithmica</i>. Springer Nature, 1999. <a href=\"https://doi.org/10.1007/pl00009268\">https://doi.org/10.1007/pl00009268</a>.","ieee":"M. H. Henzinger, V. King, and T. Warnow, “Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology,” <i>Algorithmica</i>, vol. 24. Springer Nature, pp. 1–13, 1999.","apa":"Henzinger, M. H., King, V., &#38; Warnow, T. (1999). Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/pl00009268\">https://doi.org/10.1007/pl00009268</a>","ama":"Henzinger MH, King V, Warnow T. Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. <i>Algorithmica</i>. 1999;24:1-13. doi:<a href=\"https://doi.org/10.1007/pl00009268\">10.1007/pl00009268</a>","ista":"Henzinger MH, King V, Warnow T. 1999. Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology. Algorithmica. 24, 1–13.","mla":"Henzinger, Monika H., et al. “Constructing a Tree from Homeomorphic Subtrees, with Applications to Computational Evolutionary Biology.” <i>Algorithmica</i>, vol. 24, Springer Nature, 1999, pp. 1–13, doi:<a href=\"https://doi.org/10.1007/pl00009268\">10.1007/pl00009268</a>.","short":"M.H. Henzinger, V. King, T. Warnow, Algorithmica 24 (1999) 1–13."},"date_updated":"2023-02-21T16:33:24Z","volume":24,"extern":"1","oa_version":"None","month":"05","publication":"Algorithmica","keyword":["Algorithms","Data structures","Evolutionary biology","Theory of databases"],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"type":"journal_article","date_published":"1999-05-01T00:00:00Z","status":"public","related_material":{"record":[{"relation":"earlier_version","id":"11927","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"page":"31-60","quality_controlled":"1","publisher":"Springer Nature","article_type":"original","_id":"11680","scopus_import":"1","author":[{"last_name":"Alberts","first_name":"D.","full_name":"Alberts, D."},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H","last_name":"Henzinger"}],"publication_status":"published","date_created":"2022-07-28T06:50:51Z","article_processing_charge":"No","title":"Average-case analysis of dynamic graph algorithms","intvolume":"        20","volume":20,"acknowledgement":"The authors would like to thank Emo Welzl for helpful discussions.","extern":"1","date_updated":"2023-02-21T16:33:27Z","year":"1998","citation":{"ista":"Alberts D, Henzinger MH. 1998. Average-case analysis of dynamic graph algorithms. Algorithmica. 20, 31–60.","mla":"Alberts, D., and Monika H. Henzinger. “Average-Case Analysis of Dynamic Graph Algorithms.” <i>Algorithmica</i>, vol. 20, Springer Nature, 1998, pp. 31–60, doi:<a href=\"https://doi.org/10.1007/pl00009186\">10.1007/pl00009186</a>.","short":"D. Alberts, M.H. Henzinger, Algorithmica 20 (1998) 31–60.","ieee":"D. Alberts and M. H. Henzinger, “Average-case analysis of dynamic graph algorithms,” <i>Algorithmica</i>, vol. 20. Springer Nature, pp. 31–60, 1998.","chicago":"Alberts, D., and Monika H Henzinger. “Average-Case Analysis of Dynamic Graph Algorithms.” <i>Algorithmica</i>. Springer Nature, 1998. <a href=\"https://doi.org/10.1007/pl00009186\">https://doi.org/10.1007/pl00009186</a>.","ama":"Alberts D, Henzinger MH. Average-case analysis of dynamic graph algorithms. <i>Algorithmica</i>. 1998;20:31-60. doi:<a href=\"https://doi.org/10.1007/pl00009186\">10.1007/pl00009186</a>","apa":"Alberts, D., &#38; Henzinger, M. H. (1998). Average-case analysis of dynamic graph algorithms. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/pl00009186\">https://doi.org/10.1007/pl00009186</a>"},"doi":"10.1007/pl00009186","day":"01","abstract":[{"lang":"eng","text":"We present a model for edge updates with restricted randomness in dynamic graph algorithms and a general technique for analyzing the expected running time of an update operation. This model is able to capture the average case in many applications, since (1) it allows restrictions on the set of edges which can be used for insertions and (2) the type (insertion or deletion) of each update operation is arbitrary, i.e., not random. We use our technique to analyze existing and new dynamic algorithms for the following problems: maximum cardinality matching, minimum spanning forest, connectivity, 2-edge connectivity, k -edge connectivity, k -vertex connectivity, and bipartiteness. Given a random graph G with m 0 edges and n vertices and a sequence of l update operations such that the graph contains m i edges after operation i , the expected time for performing the updates for any l is O(llogn+∑li=1n/m−−√i) in the case of minimum spanning forests, connectivity, 2-edge connectivity, and bipartiteness. The expected time per update operation is O(n) in the case of maximum matching. We also give improved bounds for k -edge and k -vertex connectivity. Additionally we give an insertions-only algorithm for maximum cardinality matching with worst-case O(n) amortized time per insertion."}],"language":[{"iso":"eng"}],"keyword":["Dynamic graph algorithm","Average-case analysis","Minimum spanning forest","Connectivity","Bipartiteness","Maximum matching."],"publication":"Algorithmica","oa_version":"None","month":"01","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"id":"11928","relation":"earlier_version","status":"public"}]},"date_published":"1998-01-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]}},{"_id":"11681","scopus_import":"1","author":[{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H"},{"full_name":"Fredman, M. L.","first_name":"M. L.","last_name":"Fredman"}],"issue":"3","publication_status":"published","date_created":"2022-07-28T06:58:36Z","article_processing_charge":"No","title":"Lower bounds for fully dynamic connectivity problems in graphs","intvolume":"        22","page":"351-362","quality_controlled":"1","publisher":"Springer Nature","article_type":"original","date_updated":"2022-09-12T09:03:36Z","year":"1998","citation":{"ista":"Henzinger MH, Fredman ML. 1998. Lower bounds for fully dynamic connectivity problems in graphs. Algorithmica. 22(3), 351–362.","short":"M.H. Henzinger, M.L. Fredman, Algorithmica 22 (1998) 351–362.","mla":"Henzinger, Monika H., and M. L. Fredman. “Lower Bounds for Fully Dynamic Connectivity Problems in Graphs.” <i>Algorithmica</i>, vol. 22, no. 3, Springer Nature, 1998, pp. 351–62, doi:<a href=\"https://doi.org/10.1007/pl00009228\">10.1007/pl00009228</a>.","ieee":"M. H. Henzinger and M. L. Fredman, “Lower bounds for fully dynamic connectivity problems in graphs,” <i>Algorithmica</i>, vol. 22, no. 3. Springer Nature, pp. 351–362, 1998.","chicago":"Henzinger, Monika H, and M. L. Fredman. “Lower Bounds for Fully Dynamic Connectivity Problems in Graphs.” <i>Algorithmica</i>. Springer Nature, 1998. <a href=\"https://doi.org/10.1007/pl00009228\">https://doi.org/10.1007/pl00009228</a>.","apa":"Henzinger, M. H., &#38; Fredman, M. L. (1998). Lower bounds for fully dynamic connectivity problems in graphs. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/pl00009228\">https://doi.org/10.1007/pl00009228</a>","ama":"Henzinger MH, Fredman ML. Lower bounds for fully dynamic connectivity problems in graphs. <i>Algorithmica</i>. 1998;22(3):351-362. doi:<a href=\"https://doi.org/10.1007/pl00009228\">10.1007/pl00009228</a>"},"doi":"10.1007/pl00009228","day":"01","abstract":[{"lang":"eng","text":"We prove lower bounds on the complexity of maintaining fully dynamic k -edge or k -vertex connectivity in plane graphs and in (k-1) -vertex connected graphs. We show an amortized lower bound of Ω (log n / {k (log log n} + log b)) per edge insertion, deletion, or query operation in the cell probe model, where b is the word size of the machine and n is the number of vertices in G . We also show an amortized lower bound of Ω (log n /(log log n + log b)) per operation for fully dynamic planarity testing in embedded graphs. These are the first lower bounds for fully dynamic connectivity problems."}],"acknowledgement":".","volume":22,"extern":"1","publication":"Algorithmica","oa_version":"None","month":"11","language":[{"iso":"eng"}],"keyword":["Dynamic planarity testing","Dynamic connectivity testing","Lower bounds","Cell probe model"],"date_published":"1998-11-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public"},{"citation":{"ista":"Henzinger MH. 1995. Fully dynamic biconnectivity in graphs. Algorithmica. 13(6), 503–538.","short":"M.H. Henzinger, Algorithmica 13 (1995) 503–538.","mla":"Henzinger, Monika H. “Fully Dynamic Biconnectivity in Graphs.” <i>Algorithmica</i>, vol. 13, no. 6, Springer Nature, 1995, pp. 503–38, doi:<a href=\"https://doi.org/10.1007/bf01189067\">10.1007/bf01189067</a>.","ieee":"M. H. Henzinger, “Fully dynamic biconnectivity in graphs,” <i>Algorithmica</i>, vol. 13, no. 6. Springer Nature, pp. 503–538, 1995.","chicago":"Henzinger, Monika H. “Fully Dynamic Biconnectivity in Graphs.” <i>Algorithmica</i>. Springer Nature, 1995. <a href=\"https://doi.org/10.1007/bf01189067\">https://doi.org/10.1007/bf01189067</a>.","apa":"Henzinger, M. H. (1995). Fully dynamic biconnectivity in graphs. <i>Algorithmica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/bf01189067\">https://doi.org/10.1007/bf01189067</a>","ama":"Henzinger MH. Fully dynamic biconnectivity in graphs. <i>Algorithmica</i>. 1995;13(6):503-538. doi:<a href=\"https://doi.org/10.1007/bf01189067\">10.1007/bf01189067</a>"},"year":"1995","date_updated":"2022-09-12T09:00:14Z","type":"journal_article","date_published":"1995-06-01T00:00:00Z","day":"01","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"doi":"10.1007/bf01189067","abstract":[{"lang":"eng","text":"We present an algorithm for maintaining the biconnected components of a graph during a sequence of edge insertions and deletions. It requires linear storage and preprocessing time. The amortized running time for insertions and for deletions isO(m 2/3 ), wherem is the number of edges in the graph. Any query of the form ‘Are the verticesu andv biconnected?’ can be answered in timeO(1). This is the first sublinear algorithm for this problem. We can also output all articulation points separating any two vertices efficiently.\r\n\r\nIf the input is a plane graph, the amortized running time for insertions and deletions drops toO(√n logn) and the query time isO(log2 n), wheren is the number of vertices in the graph. The best previously known solution takes timeO(n 2/3 ) per update or query."}],"volume":13,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","extern":"1","scopus_import":"1","_id":"11677","publication":"Algorithmica","issue":"6","author":[{"first_name":"Monika H","last_name":"Henzinger","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630"}],"article_processing_charge":"No","date_created":"2022-07-27T14:50:46Z","oa_version":"None","publication_status":"published","intvolume":"        13","title":"Fully dynamic biconnectivity in graphs","month":"06","quality_controlled":"1","page":"503-538","language":[{"iso":"eng"}],"publisher":"Springer Nature","article_type":"original"},{"publist_id":"2049","publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"type":"journal_article","date_published":"1990-06-01T00:00:00Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","status":"public","main_file_link":[{"url":"https://link.springer.com/article/10.1007/BF01840404"}],"month":"06","oa_version":"None","publication":"Algorithmica","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem of determining pairs of vertices that see each other in a star-shaped polygon. A linear-time algorithm for this problem which is of independent interest yields an optimal algorithm for finding all empty triangles. This result is then extended to an algorithm for finding empty convex r-gons (r&gt; 3) and for determining a largest empty convex subset. Finally, extensions to higher dimensions are mentioned."}],"day":"01","doi":"10.1007/BF01840404","year":"1990","citation":{"ieee":"D. Dobkin, H. Edelsbrunner, and M. Overmars, “Searching for empty convex polygons,” <i>Algorithmica</i>, vol. 5, no. 4. Springer, pp. 561–571, 1990.","chicago":"Dobkin, David, Herbert Edelsbrunner, and Mark Overmars. “Searching for Empty Convex Polygons.” <i>Algorithmica</i>. Springer, 1990. <a href=\"https://doi.org/10.1007/BF01840404\">https://doi.org/10.1007/BF01840404</a>.","apa":"Dobkin, D., Edelsbrunner, H., &#38; Overmars, M. (1990). Searching for empty convex polygons. <i>Algorithmica</i>. Springer. <a href=\"https://doi.org/10.1007/BF01840404\">https://doi.org/10.1007/BF01840404</a>","ama":"Dobkin D, Edelsbrunner H, Overmars M. Searching for empty convex polygons. <i>Algorithmica</i>. 1990;5(4):561-571. doi:<a href=\"https://doi.org/10.1007/BF01840404\">10.1007/BF01840404</a>","ista":"Dobkin D, Edelsbrunner H, Overmars M. 1990. Searching for empty convex polygons. Algorithmica. 5(4), 561–571.","mla":"Dobkin, David, et al. “Searching for Empty Convex Polygons.” <i>Algorithmica</i>, vol. 5, no. 4, Springer, 1990, pp. 561–71, doi:<a href=\"https://doi.org/10.1007/BF01840404\">10.1007/BF01840404</a>.","short":"D. Dobkin, H. Edelsbrunner, M. Overmars, Algorithmica 5 (1990) 561–571."},"date_updated":"2022-02-21T10:55:13Z","extern":"1","acknowledgement":"The first author is pleased to acknowledge support by the National Science Foundation under Grant CCR-8700917. The research of the second author was supported by Amoco Foundation Faculty Development Grant CS 1-6-44862 and by the National Science Foundatio","volume":5,"intvolume":"         5","title":"Searching for empty convex polygons","date_created":"2018-12-11T12:06:47Z","article_processing_charge":"No","publication_status":"published","issue":"4","author":[{"full_name":"Dobkin, David","last_name":"Dobkin","first_name":"David"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Mark","last_name":"Overmars","full_name":"Overmars, Mark"}],"scopus_import":"1","_id":"4075","article_type":"original","publisher":"Springer","quality_controlled":"1","page":"561 - 571"},{"extern":"1","volume":1,"abstract":[{"lang":"eng","text":"An edge-skeleton in an arrangementA(H) of a finite set of planes inE 3 is a connected collection of edges inA(H). We give a method that constructs a skeleton inO(√n logn) time per edge. This method implies new and more efficient algorithms for a number of structures in computational geometry including order-k power diagrams inE 2 and space cutting trees inE 3.\r\nWe also give a novel method for handling special cases which has the potential to substantially decrease the amount of effort needed to implement geometric algorithms."}],"day":"01","doi":"10.1007/BF01840438","year":"1986","citation":{"chicago":"Edelsbrunner, Herbert. “Edge-Skeletons in Arrangements with Applications.” <i>Algorithmica</i>. Springer, 1986. <a href=\"https://doi.org/10.1007/BF01840438\">https://doi.org/10.1007/BF01840438</a>.","ieee":"H. Edelsbrunner, “Edge-skeletons in arrangements with applications,” <i>Algorithmica</i>, vol. 1, no. 1–4. Springer, pp. 93–109, 1986.","ama":"Edelsbrunner H. Edge-skeletons in arrangements with applications. <i>Algorithmica</i>. 1986;1(1-4):93-109. doi:<a href=\"https://doi.org/10.1007/BF01840438\">10.1007/BF01840438</a>","apa":"Edelsbrunner, H. (1986). Edge-skeletons in arrangements with applications. <i>Algorithmica</i>. Springer. <a href=\"https://doi.org/10.1007/BF01840438\">https://doi.org/10.1007/BF01840438</a>","ista":"Edelsbrunner H. 1986. Edge-skeletons in arrangements with applications. Algorithmica. 1(1–4), 93–109.","mla":"Edelsbrunner, Herbert. “Edge-Skeletons in Arrangements with Applications.” <i>Algorithmica</i>, vol. 1, no. 1–4, Springer, 1986, pp. 93–109, doi:<a href=\"https://doi.org/10.1007/BF01840438\">10.1007/BF01840438</a>.","short":"H. Edelsbrunner, Algorithmica 1 (1986) 93–109."},"date_updated":"2022-02-02T09:36:32Z","article_type":"original","publisher":"Springer","quality_controlled":"1","page":"93 - 109","intvolume":"         1","title":"Edge-skeletons in arrangements with applications","article_processing_charge":"No","date_created":"2018-12-11T12:04:04Z","publication_status":"published","issue":"1-4","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"3580","status":"public","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publist_id":"2805","publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"type":"journal_article","date_published":"1986-11-01T00:00:00Z","language":[{"iso":"eng"}],"month":"11","oa_version":"None","publication":"Algorithmica"}]