Helly's Theorem: New Variations and Applications
暂无分享,去创建一个
[1] David Rolnick,et al. Quantitative (p, q) theorems in combinatorial geometry , 2017, Discret. Math..
[2] Jesús A. De Loera,et al. Random sampling in computational algebra: Helly numbers and violator spaces , 2015, J. Symb. Comput..
[3] Márton Naszódi. Proof of a Conjecture of Bárány, Katchalski and Pach , 2016, Discret. Comput. Geom..
[4] Andreas Holmsen,et al. HELLY-TYPE THEOREMS AND GEOMETRIC TRANSVERSALS , 2016 .
[5] Silouanos Brazitikos. Fractional Helly theorem for the diameter of convex sets , 2015, 1511.07779.
[6] Andreas F. Holmsen,et al. Another generalization of the colorful Carath\'eodory theorem , 2015 .
[7] P. Soberón. Helly‐type theorems for the diameter , 2015, 1509.07908.
[8] Silouanos Brazitikos. Brascamp-Lieb inequality and quantitative versions of Helly's theorem , 2015 .
[9] J. D. Loera,et al. Helly numbers of Algebraic Subsets of $\mathbb R^d$ , 2015, 1508.02380.
[10] Marco Di Summa,et al. A geometric approach to cut-generating functions , 2015, Mathematical Programming.
[11] Beyond Chance-Constrained Convex Mixed-Integer Optimization: A Generalized Calafiore-Campi Algorithm and the notion of $S$-optimization , 2015, 1504.00076.
[12] D. Rolnick,et al. Quantitative Tverberg, Helly, & Carathéodory theorems , 2015, 1503.06116.
[13] János Pach,et al. Density and regularity theorems for semi-algebraic hypergraphs , 2015, SODA.
[14] Ferenc Fodor,et al. A fractional Helly theorem for boxes , 2014, Comput. Geom..
[15] Bernd Gärtner,et al. Sampling with Removal in LP-type Problems , 2014, J. Comput. Geom..
[16] Jesús Jerónimo-Castro,et al. On a problem by Dol'nikov , 2013, Discret. Math..
[17] Xavier Goaoc,et al. Bounding Helly Numbers via Betti Numbers , 2013, SoCG.
[18] Andreas F. Holmsen,et al. A geometric Hall-type theorem , 2014, 1412.6639.
[19] Uri Zwick,et al. Random-Facet and Random-Bland require subexponential time even for shortest paths , 2014, ArXiv.
[20] Luis Pedro Montejano,et al. A New Topological Helly Theorem and Some Transversal Results , 2014, Discret. Comput. Geom..
[21] Ferenc Fodor,et al. Colourful and Fractional (p,q)-theorems , 2014, Discret. Comput. Geom..
[22] V. L. Dol'nikov,et al. On transversals of quasialgebraic families of sets , 2013, J. Comb. Theory, Ser. A.
[23] Imre B'ar'any,et al. Helly type theorems for the sum of vectors in a normed plane , 2013, 1310.0910.
[24] Sergei Sergeev,et al. Tropical convexity over max-min semiring , 2013, 1303.7451.
[25] János Pach,et al. Ramsey-type results for semi-algebraic relations , 2013, SoCG '13.
[26] Saugata Basu,et al. A Helly-Type Theorem for Semi-monotone Sets and Monotone Maps , 2012, Discret. Comput. Geom..
[27] Martin Tancer,et al. Intersection Patterns of Convex Sets via Simplicial Complexes: A Survey , 2011, 1102.0417.
[28] János Pach,et al. Geometry — Intuitive, Discrete, and Convex , 2013 .
[29] Andreas F. Holmsen. Geometric Transversal Theory: T (3)-Families in the Plane , 2013 .
[30] Luis Montejano,et al. Transversals, Topology and Colorful Geometric Results , 2013 .
[31] Marilyn Breen. Dual Helly-Type Theorems For Unions Of Sets Starshaped Via Staircase Paths , 2013, Ars Comb..
[32] Helly-type theorems for intersections of sets starshaped via orthogonally convex paths , 2012 .
[33] Xavier Goaoc,et al. Lower bounds to helly numbers of line transversals to disjoint congruent balls , 2012 .
[34] Xavier Goaoc,et al. Multinerves and helly numbers of acyclic families , 2012, SoCG '12.
[35] Wolfgang Mulzer,et al. Approximating Tverberg Points in Linear Time for Any Fixed Dimension , 2011, Discrete & Computational Geometry.
[36] Roman N. Karasev,et al. Analogues of the central point theorem for families with d-intersection property in ℝd , 2009, Comb..
[37] Jean Cardinal,et al. Helly Numbers of Polyominoes , 2011, CCCG.
[38] Gennadiy Averkov,et al. A proof of Lovász’s theorem on maximal lattice-free sets , 2011 .
[39] Luis Pedro Montejano,et al. Piercing Numbers for Balanced and Unbalanced Families , 2011, Discret. Comput. Geom..
[40] Luis Pedro Montejano,et al. Tolerance in Helly-Type Theorems , 2011, Discret. Comput. Geom..
[41] Javier Bracho,et al. A Helly Type Theorem for Abstract Projective Geometries , 2011, Discret. Comput. Geom..
[42] Xavier Goaoc,et al. Helly numbers of acyclic families , 2011, ArXiv.
[43] Endre Szabó,et al. Helly dimension of algebraic groups , 2009, J. Lond. Math. Soc..
[44] Gunnar Floystad. The colorful Helly theorem and colorful resolutions of ideals , 2011 .
[45] Zsolt Tuza,et al. Optimal guard sets and the Helly property , 2011, Eur. J. Comb..
[46] Hans Raj Tiwary,et al. On the computational complexity of Ham-Sandwich cuts, Helly sets, and related problems , 2011, STACS.
[47] Santanu S. Dey,et al. On Maximal S-Free Convex Sets , 2011, SIAM J. Discret. Math..
[48] Jie Gao,et al. Clustering lines in high-dimensional space: Classification of incomplete data , 2010, TALG.
[49] Gérard Cornuéjols,et al. Maximal Lattice-Free Convex Sets in Linear Subspaces , 2010, Math. Oper. Res..
[50] Robert Weismantel,et al. Transversal numbers over subsets of linear spaces , 2010, 1002.0948.
[51] Kent Andersen,et al. An Analysis of Mixed Integer Linear Sets Based on Lattice Point Free Convex Sets , 2009, Math. Oper. Res..
[52] Paul Wollan,et al. Voting in Agreeable Societies , 2008, Am. Math. Mon..
[53] S. Gaubert,et al. Carathéodory, Helly and the Others in the Max-Plus World , 2008, Discret. Comput. Geom..
[54] Ralph E. Gomory,et al. Outline of an Algorithm for Integer Solutions to Linear Programs and An Algorithm for the Mixed Integer Problem , 2010, 50 Years of Integer Programming.
[55] J. Matousek,et al. Geometric Discrepancy: An Illustrated Guide , 2009 .
[56] Jirí Matousek,et al. Dimension Gaps between Representability and Collapsibility , 2009, Discret. Comput. Geom..
[57] Jürgen Eckhoff,et al. Morris's pigeonhole principle and the Helly theorem for unions of convex sets , 2009 .
[58] Gérard Cornuéjols,et al. Minimal Valid Inequalities for Integer Constraints , 2009, Math. Oper. Res..
[59] Gary L. Miller,et al. Approximate center points with proofs , 2009, SCG '09.
[60] Ruy Fabila Monroy,et al. Very Colorful Theorems , 2009, Discret. Comput. Geom..
[61] Xavier Goaoc,et al. Some Discrete Properties of the Space of Line Transversals to Disjoint Balls , 2009 .
[62] János Pach,et al. Points surrounding the origin , 2008, Comb..
[63] Jürgen Eckhoff. Common transversals in the plane: The fractional perspective , 2008, Eur. J. Comb..
[64] E. Bronstein. Approximation of convex sets by polytopes , 2008 .
[65] Luis Pedro Montejano,et al. Colourful transversal theorems , 2008, Contributions Discret. Math..
[66] Luis Pedro Montejano,et al. A colorful theorem on transversal lines to plane convex sets , 2008, Comb..
[67] Nir Halman,et al. Discrete and Lexicographic Helly-Type Theorems , 2008, Discret. Comput. Geom..
[68] Benson Farb,et al. Group actions and Helly's theorem , 2008, 0806.1692.
[69] Xavier Goaoc,et al. Helly-Type Theorems for Approximate Covering , 2008, SCG '08.
[70] Alicia Nieto-Reyes,et al. The random Tukey depth , 2007, Comput. Stat. Data Anal..
[71] Xavier Goaoc,et al. Helly-Type Theorems for Line Transversals to Disjoint Unit Balls , 2008, Discret. Comput. Geom..
[72] Nir Halman,et al. Simple Stochastic Games, Parity Games, Mean Payoff Games and Discounted Payoff Games Are All LP-Type Problems , 2007, Algorithmica.
[73] Gil Kalai,et al. Leray numbers of projections and a topological Helly type theorem , 2007 .
[74] Jesús Jerónimo-Castro. Line Transversals to Translates of Unit Discs , 2007, Discret. Comput. Geom..
[75] M. Bálek,et al. Abstract Models of Optimization Problems , 2007 .
[76] Stephan Hell. Tverberg-type theorems and the Fractional Helly property , 2006 .
[77] Jirí Matousek,et al. Berge's theorem, fractional Helly, and art galleries , 2006, Discret. Math..
[78] Jirí Matousek,et al. Violator spaces: Structure and algorithms , 2006, Discret. Appl. Math..
[79] Giuseppe Carlo Calafiore,et al. The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.
[80] Ferenc Fodor,et al. A Helly-type transversal theorem for n-dimensional unit balls , 2006 .
[81] V. Boltyanski,et al. Jung's theorem for a pair of Minkowski spaces , 2006 .
[82] Noga Alon,et al. Crossing patterns of semi-algebraic sets , 2005, J. Comb. Theory, Ser. A.
[83] Gil Kalai,et al. A topological colorful Helly theorem , 2005 .
[84] Charles Fefferman,et al. A sharp form of Whitney's extension theorem , 2005 .
[85] Giuseppe Carlo Calafiore,et al. Uncertain convex programs: randomized solutions and confidence levels , 2005, Math. Program..
[86] Andreas F. Holmsen,et al. Cremona convexity, frame convexity and a theorem of Santaló , 2004, math/0409219.
[87] Jirí Matousek,et al. Bounded VC-Dimension Implies a Fractional Helly Theorem , 2004, Discret. Comput. Geom..
[88] Timothy M. Chan. An optimal randomized algorithm for maximum Tukey depth , 2004, SODA '04.
[89] Friedrich Eisenbrand,et al. Fast Integer Programming in Fixed Dimension , 2003, ESA.
[90] Jiří Matoušek,et al. A fractional Helly theorem for convex lattice sets , 2003 .
[91] Henrik Björklund,et al. A Discrete Subexponential Algorithm for Parity Games , 2003, STACS.
[92] Jürgen Eckhoff,et al. A Survey of the Hadwiger-Debrunner (p, q)-problem , 2003 .
[93] Ted G. Lewis,et al. A Helly-Type Theorem for Line Transversals to Disjoint Unit Balls , 2003, Discret. Comput. Geom..
[94] Konrad J. Swanepoel,et al. Helly-type theorems for homothets of planar convex curves , 2002 .
[95] Noga Alon,et al. Transversal numbers for hypergraphs arising in geometry , 2002, Adv. Appl. Math..
[96] Jiří Matoušek. Intersection Patterns of Convex Sets , 2002 .
[97] Luis Pedro Montejano,et al. Helly-Type Theorems on the Homology of the Space of Transversals , 2002, Discret. Comput. Geom..
[98] José L. Balcázar,et al. Provably Fast Training Algorithms for Support Vector Machines , 2001, Proceedings 2001 IEEE International Conference on Data Mining.
[99] Géza Tóth,et al. Convex Sets in the Plane with Three of Every Four Meeting , 2001, Comb..
[100] David Eppstein,et al. Optimal Möbius Transformations for Information Visualization and Meshing , 2001, WADS.
[101] Shlomo Reisner,et al. Dropping a vertex or a facet from a convex polytope , 2001 .
[102] Roman N. Karasev,et al. Transversals for Families of Translates of a Two-Dimensional Convex Compact Set , 2000, Discret. Comput. Geom..
[103] Alexander Schrijver,et al. Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.
[104] Imre Bárány,et al. Colourful Linear Programming and its Relatives , 1997, Math. Oper. Res..
[105] Noga Alon,et al. A purely combinatorial proof of the Hadwiger Debrunner (p, q) Conjecture , 1997, Electron. J. Comb..
[106] Imre Bárány,et al. Caratheodory's theorem, colourful and applicable , 1997 .
[107] Nina Amenta,et al. A short proof of an interesting helly-type theorem , 1996, Discret. Comput. Geom..
[108] David Eppstein,et al. Approximating center points with iterative Radon points , 1996, Int. J. Comput. Geom. Appl..
[109] Jirí Matousek,et al. A Helly-Type Theorem for Unions of Convex Sets , 1995, SCG '95.
[110] Ronen Basri,et al. Recognition Using Region Correspondences , 1995, Proceedings of IEEE International Conference on Computer Vision.
[111] Noga Alon,et al. Bounding the piercing number , 1995, Discret. Comput. Geom..
[112] Kenneth L. Clarkson,et al. Las Vegas algorithms for linear and integer programming when the dimension is small , 1995, JACM.
[113] Bernd Gärtner. A Subexponential Algorithm for Abstract Optimization Problems , 1992, FOCS.
[114] Jiří Matoušek,et al. Lower Bounds for a Subexponential Optimization Algorithm , 1994, Random Struct. Algorithms.
[115] Nina Amenta,et al. Helly-type theorems and Generalized Linear Programming , 1994, Discret. Comput. Geom..
[116] Nina Amenta,et al. Bounded boxes, Hausdorff distance, and a new proof of an interesting Helly-type theorem , 1994, SCG '94.
[117] J. Eckhoff. Helly, Radon, and Carathéodory Type Theorems , 1993 .
[118] P. Gruber. Aspects of Approximation of Convex Bodies , 1993 .
[119] N. Alon,et al. Piercing convex sets and the hadwiger-debrunner (p , 1992 .
[120] Noga Alon,et al. Point Selections and Weak ε-Nets for Convex Hulls , 1992, Combinatorics, Probability and Computing.
[121] Micha Sharir,et al. A subexponential bound for linear programming , 1992, SCG '92.
[122] Micha Sharir,et al. A Combinatorial Bound for Linear Programming and Related Problems , 1992, STACS.
[123] Raimund Seidel,et al. Small-dimensional linear programming and convex hulls made easy , 1991, Discret. Comput. Geom..
[124] Marilyn Breen,et al. Starshaped unions and nonempty intersections of convex sets in , 1990 .
[125] H. P. Williams. THEORY OF LINEAR AND INTEGER PROGRAMMING (Wiley-Interscience Series in Discrete Mathematics and Optimization) , 1989 .
[126] Zsolt Tuza. Minimum number of elements representing a set system of given rank , 1989, J. Comb. Theory, Ser. A.
[127] Rephael Wenger,et al. Necessary and sufficient conditions for hyperplane transversals , 1989, SCG '89.
[128] Peter Frankl. Helly-type Theorems for Varieties , 1989, Eur. J. Comb..
[129] Helge Tverberg,et al. Proof of grünbaum's conjecture on common transversals for translates , 1989, Discret. Comput. Geom..
[130] Peter Frankl,et al. A helly type theorem for hypersurfaces , 1987, J. Comb. Theory, Ser. A.
[131] Jürgen Eckhoff,et al. An Upper-Bound theorem for families of convex sets , 1985 .
[132] J. Pach,et al. Helly"s theorem with volumes , 1984 .
[133] Hendrik W. Lenstra,et al. Integer Programming with a Fixed Number of Variables , 1983, Math. Oper. Res..
[134] Imre Bárány,et al. A generalization of carathéodory's theorem , 1982, Discret. Math..
[135] J. Pach,et al. Quantitative Helly-type theorems , 1982 .
[136] Gerard Sierksma,et al. A Tverberg-type generalization of the Helly number of a convexity space , 1981 .
[137] Robert E. Jamison-Waldner. PARTITION NUMBERS FOR TREES AND ORDERED SETS , 1981 .
[138] M. Katchalski,et al. A Problem of Geometry in R n , 1979 .
[139] A. J. Hoffman. BINDING CONSTRAINTS AND HELLY NUMBERS , 1979 .
[140] H. Scarf. An observation on the structure of production sets with indivisibilities. , 1977, Proceedings of the National Academy of Sciences of the United States of America.
[141] David E. Bell. A Theorem Concerning the Integer Lattice , 1977 .
[142] G. Wegner,et al. d-Collapsing and nerves of families of convex sets , 1975 .
[143] Jean-Paul Doignon,et al. Convexity in cristallographical lattices , 1973 .
[144] G. Nemhauser,et al. Integer Programming , 2020 .
[145] D. C. Kay,et al. Axiomatic convexity theory and relationships between the Carathéodory, Helly, and Radon numbers , 1971 .
[146] C. A. Rogers,et al. The directions of the line segments and of the r -dimensional balls on the boundary of a convex body in Euclidean space , 1970 .
[147] H. Debrunner,et al. Helly Type Theorems Derived from Basic Singular Homology , 1970 .
[148] Tom C. Brown. Common Transversals , 1976, J. Comb. Theory, Ser. A.
[149] H. Tverberg. A Generalization of Radon's Theorem , 1966 .
[150] V. Klee,et al. Helly's theorem and its relatives , 1963 .
[151] T. Motzkin,et al. On components in some families of sets , 1961 .
[152] H. Hadwiger,et al. Über eine Variante zum Hellyschen Satz , 1957 .
[153] H. Hadwiger. Ueber Eibereiche mit gemeinsamer Treffgeraden , 1957 .
[154] T. Motzkin. A proof of Hilbert's Nullstellensatz , 1955 .
[155] R. Rado. A Theorem on General Measure , 1946 .
[156] B. H. Neumann,et al. On An Invariant of Plane Regions and Mass Distributions , 1945 .
[157] E. Helly,et al. Über Systeme von abgeschlossenen Mengen mit gemeinschaftlichen Punkten , 1930 .
[158] E. Helly. Über Mengen konvexer Körper mit gemeinschaftlichen Punkte. , 1923 .
[159] J. Radon. Mengen konvexer Körper, die einen gemeinsamen Punkt enthalten , 1921 .