[{"related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1016/j.jsc.2015.09.002"}]},"intvolume":"        50","date_updated":"2021-01-12T08:05:15Z","article_processing_charge":"No","year":"2013","citation":{"apa":"Hillar, C. J., &#38; Martin del Campo Sanchez, A. (2013). Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jsc.2012.06.006\">https://doi.org/10.1016/j.jsc.2012.06.006</a>","ieee":"C. J. Hillar and A. Martin del Campo Sanchez, “Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals,” <i>Journal of Symbolic Computation</i>, vol. 50. Elsevier, pp. 314–334, 2013.","ama":"Hillar CJ, Martin del Campo Sanchez A. Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals. <i>Journal of Symbolic Computation</i>. 2013;50:314-334. doi:<a href=\"https://doi.org/10.1016/j.jsc.2012.06.006\">10.1016/j.jsc.2012.06.006</a>","short":"C.J. Hillar, A. Martin del Campo Sanchez, Journal of Symbolic Computation 50 (2013) 314–334.","ista":"Hillar CJ, Martin del Campo Sanchez A. 2013. Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals. Journal of Symbolic Computation. 50, 314–334.","chicago":"Hillar, Christopher J., and Abraham Martin del Campo Sanchez. “Finiteness Theorems and Algorithms for Permutation Invariant Chains of Laurent Lattice Ideals.” <i>Journal of Symbolic Computation</i>. Elsevier, 2013. <a href=\"https://doi.org/10.1016/j.jsc.2012.06.006\">https://doi.org/10.1016/j.jsc.2012.06.006</a>.","mla":"Hillar, Christopher J., and Abraham Martin del Campo Sanchez. “Finiteness Theorems and Algorithms for Permutation Invariant Chains of Laurent Lattice Ideals.” <i>Journal of Symbolic Computation</i>, vol. 50, Elsevier, 2013, pp. 314–34, doi:<a href=\"https://doi.org/10.1016/j.jsc.2012.06.006\">10.1016/j.jsc.2012.06.006</a>."},"date_created":"2019-02-05T08:48:24Z","title":"Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals","publication":"Journal of Symbolic Computation","doi":"10.1016/j.jsc.2012.06.006","_id":"5920","article_type":"original","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0747-7171"]},"month":"03","oa_version":"None","day":"01","abstract":[{"text":"We study chains of lattice ideals that are invariant under a symmetric group action. In our setting, the ambient rings for these ideals are polynomial rings which are increasing in (Krull) dimension. Thus, these chains will fail to stabilize in the traditional commutative algebra sense. However, we prove a theorem which says that “up to the action of the group”, these chains locally stabilize. We also give an algorithm, which we have implemented in software, for explicitly constructing these stabilization generators for a family of Laurent toric ideals involved in applications to algebraic statistics. We close with several open problems and conjectures arising from our theoretical and computational investigations.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Hillar","first_name":"Christopher J.","full_name":"Hillar, Christopher J."},{"first_name":"Abraham","full_name":"Martin del Campo Sanchez, Abraham","last_name":"Martin del Campo Sanchez","id":"4CF47F6A-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","publisher":"Elsevier","status":"public","date_published":"2013-03-01T00:00:00Z","type":"journal_article","extern":"1","page":"314-334","quality_controlled":"1","volume":50},{"author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"last_name":"Preparata","first_name":"Franco","full_name":"Preparata, Franco"},{"full_name":"West, Douglas","first_name":"Douglas","last_name":"West"}],"oa_version":"Published Version","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0747717108800685?via%3Dihub","open_access":"1"}],"day":"01","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","month":"01","publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"status":"public","type":"journal_article","title":"Tetrahedrizing point sets in three dimensions","date_updated":"2022-02-23T10:10:35Z","oa":1,"article_processing_charge":"No","issue":"3-4","scopus_import":"1","intvolume":"        10","language":[{"iso":"eng"}],"publication":"Journal of Symbolic Computation","publication_status":"published","abstract":[{"text":"This paper offers combinatorial results on extremum problems concerning the number of tetrahedra in a tetrahedrization of n points in general position in three dimensions, i.e. such that no four points are co-planar, It also presents an algorithm that in O(n log n) time constructs a tetrahedrization of a set of n points consisting of at most 3n-11 tetrahedra.","lang":"eng"}],"page":"335 - 347","extern":"1","volume":10,"quality_controlled":"1","publisher":"Elsevier","date_published":"1990-01-01T00:00:00Z","citation":{"apa":"Edelsbrunner, H., Preparata, F., &#38; West, D. (1990). Tetrahedrizing point sets in three dimensions. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">https://doi.org/10.1016/S0747-7171(08)80068-5</a>","ista":"Edelsbrunner H, Preparata F, West D. 1990. Tetrahedrizing point sets in three dimensions. Journal of Symbolic Computation. 10(3–4), 335–347.","mla":"Edelsbrunner, Herbert, et al. “Tetrahedrizing Point Sets in Three Dimensions.” <i>Journal of Symbolic Computation</i>, vol. 10, no. 3–4, Elsevier, 1990, pp. 335–47, doi:<a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">10.1016/S0747-7171(08)80068-5</a>.","chicago":"Edelsbrunner, Herbert, Franco Preparata, and Douglas West. “Tetrahedrizing Point Sets in Three Dimensions.” <i>Journal of Symbolic Computation</i>. Elsevier, 1990. <a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">https://doi.org/10.1016/S0747-7171(08)80068-5</a>.","ieee":"H. Edelsbrunner, F. Preparata, and D. West, “Tetrahedrizing point sets in three dimensions,” <i>Journal of Symbolic Computation</i>, vol. 10, no. 3–4. Elsevier, pp. 335–347, 1990.","ama":"Edelsbrunner H, Preparata F, West D. Tetrahedrizing point sets in three dimensions. <i>Journal of Symbolic Computation</i>. 1990;10(3-4):335-347. doi:<a href=\"https://doi.org/10.1016/S0747-7171(08)80068-5\">10.1016/S0747-7171(08)80068-5</a>","short":"H. Edelsbrunner, F. Preparata, D. West, Journal of Symbolic Computation 10 (1990) 335–347."},"publist_id":"2061","date_created":"2018-12-11T12:06:42Z","acknowledgement":"Research of the first author is supported by Amoco Fnd. Fac. Dec. Comput. Sci. 1-6-44862, the second author is supported by NSF Grant ECS 84-10902, and research of the third author is supported in part by ONR Grant N00014-85K0570 and by NSF Grant DMS 8504322.","year":"1990","_id":"4060","article_type":"original","doi":"10.1016/S0747-7171(08)80068-5"},{"year":"1986","date_created":"2018-12-11T12:06:58Z","publist_id":"2018","citation":{"ama":"Edelsbrunner H, Waupotitsch R. Computing a ham-sandwich cut in two dimensions. <i>Journal of Symbolic Computation</i>. 1986;2(2):171-178. doi:<a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">10.1016/S0747-7171(86)80020-7</a>","ieee":"H. Edelsbrunner and R. Waupotitsch, “Computing a ham-sandwich cut in two dimensions,” <i>Journal of Symbolic Computation</i>, vol. 2, no. 2. Elsevier, pp. 171–178, 1986.","short":"H. Edelsbrunner, R. Waupotitsch, Journal of Symbolic Computation 2 (1986) 171–178.","mla":"Edelsbrunner, Herbert, and Roman Waupotitsch. “Computing a Ham-Sandwich Cut in Two Dimensions.” <i>Journal of Symbolic Computation</i>, vol. 2, no. 2, Elsevier, 1986, pp. 171–78, doi:<a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">10.1016/S0747-7171(86)80020-7</a>.","ista":"Edelsbrunner H, Waupotitsch R. 1986. Computing a ham-sandwich cut in two dimensions. Journal of Symbolic Computation. 2(2), 171–178.","chicago":"Edelsbrunner, Herbert, and Roman Waupotitsch. “Computing a Ham-Sandwich Cut in Two Dimensions.” <i>Journal of Symbolic Computation</i>. Elsevier, 1986. <a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">https://doi.org/10.1016/S0747-7171(86)80020-7</a>.","apa":"Edelsbrunner, H., &#38; Waupotitsch, R. (1986). Computing a ham-sandwich cut in two dimensions. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0747-7171(86)80020-7\">https://doi.org/10.1016/S0747-7171(86)80020-7</a>"},"article_type":"original","_id":"4106","doi":"10.1016/S0747-7171(86)80020-7","publication_status":"published","abstract":[{"lang":"eng","text":"Let B be a set of nb black points and W a set of nw, white points in the Euclidean plane. A line h is said to bisect B (or W) if, at most, half of the points of B (or W) lie on any one side of h. A line that bisects both B and W is called a ham-sandwich cut of B and W. We give an algorithm that computes a ham-sandwich cut of B and W in 0((nh+nw) log (min {nb, nw}+ 1)) time. The algorithm is considerably simpler than the previous most efficient one which takes 0((nb + nw) log (nb + nw)) time."}],"publisher":"Elsevier","date_published":"1986-01-01T00:00:00Z","extern":"1","page":"171 - 178","volume":2,"quality_controlled":"1","date_updated":"2022-02-01T11:22:59Z","article_processing_charge":"No","issue":"2","title":"Computing a ham-sandwich cut in two dimensions","scopus_import":"1","intvolume":"         2","language":[{"iso":"eng"}],"publication":"Journal of Symbolic Computation","author":[{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert"},{"last_name":"Waupotitsch","full_name":"Waupotitsch, Roman","first_name":"Roman"}],"month":"01","publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"oa_version":"None","day":"01","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","type":"journal_article","status":"public"},{"year":"1985","acknowledgement":"The first author was supported i~1 part by NSF grants MCS 83-03925 and the Office of Naval Research and the Defense Advanced Research Projects Agency under contract N00014-g3-K-0146 and ARPA Order No. 4786.","citation":{"short":"B. Chazelle, H. Edelsbrunner, Journal of Symbolic Computation 1 (1985) 47–56.","ama":"Chazelle B, Edelsbrunner H. Optimal solutions for a class of point retrieval problems. <i>Journal of Symbolic Computation</i>. 1985;1(1):47-56. doi:<a href=\"https://doi.org/10.1016/S0747-7171(85)80028-6\">10.1016/S0747-7171(85)80028-6</a>","ieee":"B. Chazelle and H. Edelsbrunner, “Optimal solutions for a class of point retrieval problems,” <i>Journal of Symbolic Computation</i>, vol. 1, no. 1. Elsevier, pp. 47–56, 1985.","mla":"Chazelle, Bernard, and Herbert Edelsbrunner. “Optimal Solutions for a Class of Point Retrieval Problems.” <i>Journal of Symbolic Computation</i>, vol. 1, no. 1, Elsevier, 1985, pp. 47–56, doi:<a href=\"https://doi.org/10.1016/S0747-7171(85)80028-6\">10.1016/S0747-7171(85)80028-6</a>.","chicago":"Chazelle, Bernard, and Herbert Edelsbrunner. “Optimal Solutions for a Class of Point Retrieval Problems.” <i>Journal of Symbolic Computation</i>. Elsevier, 1985. <a href=\"https://doi.org/10.1016/S0747-7171(85)80028-6\">https://doi.org/10.1016/S0747-7171(85)80028-6</a>.","ista":"Chazelle B, Edelsbrunner H. 1985. Optimal solutions for a class of point retrieval problems. Journal of Symbolic Computation. 1(1), 47–56.","apa":"Chazelle, B., &#38; Edelsbrunner, H. (1985). Optimal solutions for a class of point retrieval problems. <i>Journal of Symbolic Computation</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0747-7171(85)80028-6\">https://doi.org/10.1016/S0747-7171(85)80028-6</a>"},"publist_id":"2004","date_created":"2018-12-11T12:07:03Z","doi":"10.1016/S0747-7171(85)80028-6","_id":"4120","article_type":"original","abstract":[{"text":"Let P be a set of n points in the Euclidean plane and let C be a convex figure. We study the problem of preprocessing P so that for any query point q, the points of P in C+q can be retrieved efficiently. If constant time sumces for deciding the inclusion of a point in C, we then demonstrate the existence of an optimal solution: the algorithm requires O(n) space and O(k + log n) time for a query with output size k. If C is a disk, the problem becomes the wellknown fixed-radius neighbour problem, to which we thus provide the first known optimal solution.","lang":"eng"}],"publication_status":"published","date_published":"1985-03-01T00:00:00Z","publisher":"Elsevier","volume":1,"quality_controlled":"1","page":"47 - 56","extern":"1","intvolume":"         1","article_processing_charge":"No","issue":"1","date_updated":"2022-01-31T09:20:18Z","oa":1,"title":"Optimal solutions for a class of point retrieval problems","publication":"Journal of Symbolic Computation","language":[{"iso":"eng"}],"month":"03","publication_identifier":{"issn":["0747-7171"],"eissn":["1095-855X"]},"user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0747717185800286?via%3Dihub","open_access":"1"}],"oa_version":"Published Version","day":"01","author":[{"first_name":"Bernard","full_name":"Chazelle, Bernard","last_name":"Chazelle"},{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"type":"journal_article","status":"public"}]