[{"title":"Stochastic processes with expected stopping time","date_updated":"2025-07-14T09:10:08Z","month":"07","date_published":"2021-07-07T00:00:00Z","keyword":["Computer science","Heuristic algorithms","Memory management","Automata","Markov processes","Probability distribution","Complexity theory"],"article_processing_charge":"No","ec_funded":1,"publication":"Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science","page":"1-13","_id":"10004","project":[{"name":"Formal Methods for Stochastic Models: Algorithms and Applications","_id":"0599E47C-7A3F-11EA-A408-12923DDC885E","grant_number":"863818","call_identifier":"H2020"}],"date_created":"2021-09-12T22:01:25Z","external_id":{"isi":["000947350400036"],"arxiv":["2104.07278"]},"main_file_link":[{"url":"https://arxiv.org/abs/2104.07278","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"We are grateful to the anonymous reviewers of LICS 2021 and of a previous version of this paper for insightful comments that helped improving the presentation. This research was partially supported by the grant ERC CoG 863818 (ForM-SMArt).","oa":1,"scopus_import":"1","publication_identifier":{"issn":["1043-6871"],"eisbn":["978-1-6654-4895-6"],"isbn":["978-1-6654-4896-3"]},"department":[{"_id":"KrCh"}],"isi":1,"author":[{"id":"2E5DCA20-F248-11E8-B48F-1D18A9856A87","first_name":"Krishnendu","last_name":"Chatterjee","full_name":"Chatterjee, Krishnendu","orcid":"0000-0002-4561-241X"},{"last_name":"Doyen","full_name":"Doyen, Laurent","first_name":"Laurent"}],"conference":{"location":"Rome, Italy","start_date":"2021-06-29","end_date":"2021-07-02","name":"LICS: Symposium on Logic in Computer Science"},"year":"2021","doi":"10.1109/LICS52264.2021.9470595","oa_version":"Preprint","arxiv":1,"publisher":"Institute of Electrical and Electronics Engineers","day":"07","abstract":[{"text":"Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical optimization criterion is the maximal expected total reward where the MDP stops after T steps, which can be computed by a simple dynamic programming algorithm. We consider a natural generalization of the problem where the stopping times can be chosen according to a probability distribution, such that the expected stopping time is T, to optimize the expected total reward. Quite surprisingly we establish inter-reducibility of the expected stopping-time problem for Markov chains with the Positivity problem (which is related to the well-known Skolem problem), for which establishing either decidability or undecidability would be a major breakthrough. Given the hardness of the exact problem, we consider the approximate version of the problem: we show that it can be solved in exponential time for Markov chains and in exponential space for MDPs.","lang":"eng"}],"publication_status":"published","language":[{"iso":"eng"}],"status":"public","quality_controlled":"1","citation":{"ieee":"K. Chatterjee and L. Doyen, “Stochastic processes with expected stopping time,” in <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, Rome, Italy, 2021, pp. 1–13.","short":"K. Chatterjee, L. Doyen, in:, Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13.","apa":"Chatterjee, K., &#38; Doyen, L. (2021). Stochastic processes with expected stopping time. In <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i> (pp. 1–13). Rome, Italy: Institute of Electrical and Electronics Engineers. <a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">https://doi.org/10.1109/LICS52264.2021.9470595</a>","ista":"Chatterjee K, Doyen L. 2021. Stochastic processes with expected stopping time. Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Symposium on Logic in Computer Science, 1–13.","mla":"Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected Stopping Time.” <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, Institute of Electrical and Electronics Engineers, 2021, pp. 1–13, doi:<a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">10.1109/LICS52264.2021.9470595</a>.","chicago":"Chatterjee, Krishnendu, and Laurent Doyen. “Stochastic Processes with Expected Stopping Time.” In <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>, 1–13. Institute of Electrical and Electronics Engineers, 2021. <a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">https://doi.org/10.1109/LICS52264.2021.9470595</a>.","ama":"Chatterjee K, Doyen L. Stochastic processes with expected stopping time. In: <i>Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science</i>. Institute of Electrical and Electronics Engineers; 2021:1-13. doi:<a href=\"https://doi.org/10.1109/LICS52264.2021.9470595\">10.1109/LICS52264.2021.9470595</a>"},"type":"conference"},{"publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"author":[{"first_name":"Sayan","full_name":"Bhattacharya, Sayan","last_name":"Bhattacharya"},{"first_name":"Deeparnab","full_name":"Chakrabarty, Deeparnab","last_name":"Chakrabarty"},{"first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530","last_name":"Henzinger"}],"year":"2020","oa_version":"Published Version","doi":"10.1007/s00453-019-00630-4","day":"01","publisher":"Springer Nature","language":[{"iso":"eng"}],"status":"public","publication_status":"published","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","citation":{"short":"S. Bhattacharya, D. Chakrabarty, M.H. Henzinger, Algorithmica 82 (2020) 1057–1080.","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>","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.","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>.","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>","ista":"Bhattacharya S, Chakrabarty D, Henzinger MH. 2020. Deterministic dynamic matching in O(1) update time. Algorithmica. 82(4), 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>."},"type":"journal_article","article_type":"original","month":"04","date_updated":"2022-09-12T08:55:46Z","title":"Deterministic dynamic matching in O(1) update time","date_published":"2020-04-01T00:00:00Z","article_processing_charge":"No","keyword":["Dynamic algorithms","Data structures","Graph algorithms","Matching","Vertex cover"],"page":"1057-1080","publication":"Algorithmica","date_created":"2022-07-27T14:31:06Z","_id":"11675","volume":82,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00453-019-00630-4"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"4","intvolume":"        82","oa":1,"scopus_import":"1","extern":"1"},{"extern":"1","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1611.05753"}],"volume":77,"oa":1,"intvolume":"        77","issue":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","page":"152-172","publication":"Algorithmica","external_id":{"arxiv":["1611.05753"]},"date_created":"2022-07-27T14:37:24Z","_id":"11676","month":"01","title":"Maximizing a submodular function with viability constraints","date_updated":"2022-09-12T08:58:16Z","article_processing_charge":"No","keyword":["Approximation algorithms","Submodular functions","Phylogenetic diversity","Viability constraints"],"date_published":"2017-01-01T00:00:00Z","citation":{"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.","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.","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>","short":"W. Dvořák, M.H. Henzinger, D.P. Williamson, Algorithmica 77 (2017) 152–172."},"type":"journal_article","article_type":"original","status":"public","language":[{"iso":"eng"}],"publication_status":"published","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","oa_version":"Preprint","arxiv":1,"doi":"10.1007/s00453-015-0066-y","day":"01","publisher":"Springer Nature","publication_identifier":{"eissn":["1432-0541"],"issn":["0178-4617"]},"year":"2017","author":[{"first_name":"Wolfgang","full_name":"Dvořák, Wolfgang","last_name":"Dvořák"},{"id":"540c9bbd-f2de-11ec-812d-d04a5be85630","first_name":"Monika H","last_name":"Henzinger","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530"},{"first_name":"David P.","full_name":"Williamson, David P.","last_name":"Williamson"}]},{"article_type":"original","citation":{"mla":"Colini-Baldeschi, Riccardo, et al. “On Multiple Keyword Sponsored Search Auctions with Budgets.” <i>ACM Transactions on Economics and Computation</i>, vol. 4, no. 1, 2, Association for Computing Machinery, 2015, doi:<a href=\"https://doi.org/10.1145/2818357\">10.1145/2818357</a>.","ista":"Colini-Baldeschi R, Leonardi S, Henzinger MH, Starnberger M. 2015. On multiple keyword sponsored search auctions with budgets. ACM Transactions on Economics and Computation. 4(1), 2.","ama":"Colini-Baldeschi R, Leonardi S, Henzinger MH, Starnberger M. On multiple keyword sponsored search auctions with budgets. <i>ACM Transactions on Economics and Computation</i>. 2015;4(1). doi:<a href=\"https://doi.org/10.1145/2818357\">10.1145/2818357</a>","chicago":"Colini-Baldeschi, Riccardo, Stefano Leonardi, Monika H Henzinger, and Martin Starnberger. “On Multiple Keyword Sponsored Search Auctions with Budgets.” <i>ACM Transactions on Economics and Computation</i>. Association for Computing Machinery, 2015. <a href=\"https://doi.org/10.1145/2818357\">https://doi.org/10.1145/2818357</a>.","ieee":"R. Colini-Baldeschi, S. Leonardi, M. H. Henzinger, and M. Starnberger, “On multiple keyword sponsored search auctions with budgets,” <i>ACM Transactions on Economics and Computation</i>, vol. 4, no. 1. Association for Computing Machinery, 2015.","short":"R. Colini-Baldeschi, S. Leonardi, M.H. Henzinger, M. Starnberger, ACM Transactions on Economics and Computation 4 (2015).","apa":"Colini-Baldeschi, R., Leonardi, S., Henzinger, M. H., &#38; Starnberger, M. (2015). On multiple keyword sponsored search auctions with budgets. <i>ACM Transactions on Economics and Computation</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/2818357\">https://doi.org/10.1145/2818357</a>"},"type":"journal_article","quality_controlled":"1","publication_status":"published","abstract":[{"text":"We study multiple keyword sponsored search auctions with budgets. Each keyword has multiple ad slots with a click-through rate. The bidders have additive valuations, which are linear in the click-through rates, and budgets, which are restricting their overall payments. Additionally, the number of slots per keyword assigned to a bidder is bounded.\r\n\r\nWe show the following results: (1) We give the first mechanism for multiple keywords, where click-through rates differ among slots. Our mechanism is incentive compatible in expectation, individually rational in expectation, and Pareto optimal. (2) We study the combinatorial setting, where each bidder is only interested in a subset of the keywords. We give an incentive compatible, individually rational, Pareto-optimal, and deterministic mechanism for identical click-through rates. (3) We give an impossibility result for incentive compatible, individually rational, Pareto-optimal, and deterministic mechanisms for bidders with diminishing marginal valuations.","lang":"eng"}],"language":[{"iso":"eng"}],"status":"public","publisher":"Association for Computing Machinery","day":"05","doi":"10.1145/2818357","oa_version":"Submitted Version","author":[{"first_name":"Riccardo","last_name":"Colini-Baldeschi","full_name":"Colini-Baldeschi, Riccardo"},{"full_name":"Leonardi, Stefano","last_name":"Leonardi","first_name":"Stefano"},{"first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530"},{"first_name":"Martin","last_name":"Starnberger","full_name":"Starnberger, Martin"}],"year":"2015","publication_identifier":{"issn":["2167-8375"],"eissn":["2167-8383"]},"scopus_import":"1","extern":"1","article_number":"2","issue":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"intvolume":"         4","volume":4,"main_file_link":[{"open_access":"1","url":"http://eprints.cs.univie.ac.at/3510/"}],"_id":"11668","date_created":"2022-07-27T11:54:56Z","publication":"ACM Transactions on Economics and Computation","date_published":"2015-12-05T00:00:00Z","keyword":["Algorithms","Economics","Clinching ascending auction","auctions with budgets","Sponsored search auctions"],"article_processing_charge":"No","date_updated":"2023-02-09T10:03:35Z","title":"On multiple keyword sponsored search auctions with budgets","month":"12"},{"citation":{"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.","short":"M.H. Henzinger, V. King, T. Warnow, Algorithmica 24 (1999) 1–13.","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>","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>.","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>","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>."},"type":"journal_article","article_type":"original","publication_status":"published","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"}],"status":"public","language":[{"iso":"eng"}],"quality_controlled":"1","doi":"10.1007/pl00009268","oa_version":"None","publisher":"Springer Nature","day":"01","publication_identifier":{"issn":["0178-4617"],"eissn":["1432-0541"]},"year":"1999","author":[{"first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","full_name":"Henzinger, Monika H","orcid":"0000-0002-5008-6530"},{"full_name":"King, V.","last_name":"King","first_name":"V."},{"last_name":"Warnow","full_name":"Warnow, T.","first_name":"T."}],"extern":"1","scopus_import":"1","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"11927"}]},"volume":24,"intvolume":"        24","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Algorithmica","page":"1-13","_id":"11679","date_created":"2022-07-27T15:02:28Z","date_updated":"2023-02-21T16:33:24Z","title":"Constructing a tree from homeomorphic subtrees, with applications to computational evolutionary biology","month":"05","article_processing_charge":"No","keyword":["Algorithms","Data structures","Evolutionary biology","Theory of databases"],"date_published":"1999-05-01T00:00:00Z"}]