Homology flows, cohomology cuts
暂无分享,去创建一个
[1] Jianer Chen,et al. A Note on Approximating Graph Genus , 1997, Inf. Process. Lett..
[2] Yash P. Aneja,et al. Equivalence of ε -Approximate Separation and Optimization in Fixed Dimensions1 , 2001, Algorithmica.
[3] Tamal K. Dey,et al. Optimal homologous cycles, total unimodularity, and linear programming , 2010, STOC '10.
[4] P. Wright,et al. On Minimum Spanning Trees and Determinants , 2000 .
[5] Carsten Thomassen,et al. The Graph Genus Problem is NP-Complete , 1989, J. Algorithms.
[6] Pravin M. Vaidya,et al. Speeding-up linear programming using fast matrix multiplication , 1989, 30th Annual Symposium on Foundations of Computer Science.
[7] Philip N. Klein,et al. Steiner Tree in Planar Graphs: An O ( n log n ) Approximation Scheme with Singly-Exponential Dependence on Epsilon , 2007, WADS.
[8] Helmut Alt,et al. Functions Equivalent to Integer Multiplication , 1980, International Colloquium on Automata, Languages and Programming.
[9] Alon Itai,et al. Maximum Flow in Planar Networks , 1979, SIAM J. Comput..
[10] Anil N. Hirani,et al. The least spanning area of a knot and the optimal bounding chain problem , 2010, SoCG '11.
[11] E. Felten,et al. A Crystalline Approximation Theorem for Hypersurfaces , 1990 .
[12] Jeff Erickson,et al. Maximum flows and parametric shortest paths in planar graphs , 2010, SODA '10.
[13] Micha Sharir,et al. Efficient algorithms for geometric optimization , 1998, CSUR.
[14] Michael T. Goodrich,et al. Planar Separators and Parallel Polygon Triangulation , 1995, J. Comput. Syst. Sci..
[15] Chao Chen,et al. Hardness Results for Homology Localization , 2010, SODA '10.
[16] Philip N. Klein,et al. An O (n log n) algorithm for maximum st-flow in a directed planar graph , 2006, SODA '06.
[17] W. Massey. A basic course in algebraic topology , 1991 .
[18] D. R. Fulkerson,et al. Maximal Flow Through a Network , 1956 .
[19] P. Gács,et al. Khachiyan’s algorithm for linear programming , 1981 .
[20] Donald B. Johnson,et al. Partition of Planar Flow Networks (Preliminary Version) , 1983, FOCS 1983.
[21] Refael Hassin,et al. An O(n log2 n) Algorithm for Maximum Flow in Undirected Planar Networks , 1985, SIAM J. Comput..
[22] Bojan Mohar,et al. A Linear Time Algorithm for Embedding Graphs in an Arbitrary Surface , 1999, SIAM J. Discret. Math..
[23] Philip N. Klein,et al. Shortest paths in directed planar graphs with negative lengths: A linear-space O(n log2 n)-time algorithm , 2010, TALG.
[24] David Eppstein. Diameter and Treewidth in Minor-Closed Graph Families , 2000, Algorithmica.
[25] Arnold Schönhage,et al. Schnelle Multiplikation großer Zahlen , 1971, Computing.
[26] Joan P. Hutchinson. Deleting vertices to make graphs of positive genus planar , 1986 .
[27] Hristo Djidjev,et al. Linear Algorithms for Partitioning Embedded Graphs of Bounded Genus , 1996, SIAM J. Discret. Math..
[28] Hiroshi Imai,et al. Efficient Sequential and Parallel Algorithms for Planar Minimum Cost Flow , 1990, SIGAL International Symposium on Algorithms.
[29] S. Gortler,et al. A Discrete Global Minimization Algorithm for Continuous Variational Problems , 2004 .
[30] Ang Yan Sheng,et al. Discrete Differential Geometry , 2017 .
[31] Philip N. Klein,et al. Multiple-source shortest paths in planar graphs , 2005, SODA '05.
[32] Greg N. Frederickson,et al. Fast Algorithms for Shortest Paths in Planar Graphs, with Applications , 1987, SIAM J. Comput..
[33] M. Sharir,et al. An Efficient Multi-Dimensional Searching Technique and itsApplications , 1993 .
[34] Shankar M. Venkatesan. Algorithms for network flows , 1983 .
[35] Martin Grohe,et al. Isomorphism testing for embeddable graphs through definability , 2000, STOC '00.
[36] David Eppstein,et al. Dynamic generators of topologically embedded graphs , 2002, SODA '03.
[37] Éva Tardos,et al. Using separation algorithms in fixed dimension , 1990, SODA '90.
[38] Karsten Weihe,et al. Edge-Disjoint (s, t)-Paths in Undirected Planar Graphs in Linear Time , 1997, J. Algorithms.
[39] Martin Grötschel,et al. The ellipsoid method and its consequences in combinatorial optimization , 1981, Comb..
[40] Bruce A. Reed,et al. A Simpler Linear Time Algorithm for Embedding Graphs into an Arbitrary Surface and the Genus of Graphs of Bounded Tree-Width , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.
[41] Yiying Tong,et al. Discrete differential forms for computational modeling , 2005, SIGGRAPH Courses.
[42] Edith Cohen. Efficient Parallel Shortest-Paths in Digraphs with a Separator Decomposition , 1996, J. Algorithms.
[43] Kenneth Steiglitz,et al. Combinatorial Optimization: Algorithms and Complexity , 1981 .
[44] K. Weihe. Maximum (s,t)-Flows in Planar Networks in O( , 1997 .
[45] Nimrod Megiddo,et al. Applying parallel computation algorithms in the design of serial algorithms , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).
[46] Santosh N. Kabadi,et al. ε-Approximation minimization of convex functions in fixed dimension , 1996, Oper. Res. Lett..
[47] Martin Mareš. Two linear time algorithms for MST on minor closed graph classes , 2002 .
[48] R. Ho. Algebraic Topology , 2022 .
[49] A. Schrijver. On the History of Combinatorial Optimization (Till 1960) , 2005 .
[50] David Eppstein,et al. The Polyhedral Approach to the Maximum Planar Subgraph Problem: New Chances for Related Problems , 1994, GD.
[51] Samuel I. Daitch,et al. Faster Lossy Generalized Flow via Interior Point Algorithms , 2008 .
[52] Jeff Erickson,et al. Greedy optimal homotopy and homology generators , 2005, SODA '05.
[53] Karsten Weihe. Maximum (s,t)-flows in planar networks in O(|V|log|V|) time , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.
[54] Joan P. Hutchinson,et al. On Short Noncontractible Cycles in Embedded Graphs , 1988, SIAM J. Discret. Math..
[55] Philip N. Klein,et al. Faster Shortest-Path Algorithms for Planar Graphs , 1997, J. Comput. Syst. Sci..
[56] Alexander Schrijver,et al. Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.
[57] John R Gilbert,et al. A Separator Theorem for Graphs of Bounded Genus , 1984, J. Algorithms.
[58] N. Z. Shor. Cut-off method with space extension in convex programming problems , 1977, Cybernetics.
[59] Erin W. Chambers,et al. Minimum cuts and shortest homologous cycles , 2009, SCG '09.
[60] Michael J. Todd,et al. The Ellipsoid Method: A Survey , 1980 .
[61] Matthias Müller-Hannemann,et al. Shortest paths in linear time on minor-closed graph classes, with an application to Steiner tree approximation , 2009, Discret. Appl. Math..
[62] L. G. H. Cijan. A polynomial algorithm in linear programming , 1979 .
[63] Anil N. Hirani,et al. Discrete exterior calculus , 2005, math/0508341.
[64] David Fernández-Baca,et al. Weighted Multidimensional Search and Its Application to Convex Optimization , 1996, SIAM J. Comput..
[65] Jonathan L. Gross,et al. Topological Graph Theory , 1987, Handbook of Graph Theory.
[66] Alexander Schrijver,et al. Combinatorial optimization. Polyhedra and efficiency. , 2003 .
[67] Gary L. Miller,et al. Finding Small Simple Cycle Separators for 2-Connected Planar Graphs , 1986, J. Comput. Syst. Sci..
[68] David K. Smith. Network Flows: Theory, Algorithms, and Applications , 1994 .
[69] Leo Grady,et al. Computing Exact Discrete Minimal Surfaces: Extending and Solving the Shortest Path Problem in 3D with Application to Segmentation , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).
[70] Hristo Djidjev,et al. Planarization of Graphs Embedded on Surfaces , 1995, WG.
[71] E. Cohen,et al. Combinatorial algorithms for optimization problems , 1991 .
[72] Amir Nayyeri,et al. Minimum cuts and shortest non-separating cycles via homology covers , 2011, SODA '11.
[73] Michael F. Cohen,et al. Minimal Surfaces for Stereo , 2002, ECCV.
[74] Amin Saberi,et al. The asymmetric traveling salesman problem on graphs with bounded genus , 2009, SODA '11.
[75] Erin W. Chambers,et al. Splitting (complicated) surfaces is hard , 2008, Comput. Geom..
[76] Robert E. Tarjan,et al. A data structure for dynamic trees , 1981, STOC '81.
[77] Andrew V. Goldberg,et al. A new approach to the maximum flow problem , 1986, STOC '86.
[78] Therese C. Biedl,et al. Simplifying Flow Networks , 2000, MFCS.
[79] Henri Poincaré,et al. Second Complément à l'Analysis Situs , 1900 .
[80] Sergio Cabello,et al. Finding Cycles with Topological Properties in Embedded Graphs , 2011, SIAM J. Discret. Math..
[81] Piotr Sankowski,et al. Improved Minimum Cuts and Maximum Flows in Undirected Planar Graphs , 2010, ArXiv.
[82] Gary L. Miller,et al. Isomorphism testing for graphs of bounded genus , 1980, STOC '80.
[83] Andrew Chi-Chih Yao,et al. On the complexity of comparison problems using linear functions , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).
[84] Philip N. Klein,et al. A polynomial-time approximation scheme for Steiner tree in planar graphs , 2007, SODA '07.
[85] Satish Rao,et al. Planar graphs, negative weight edges, shortest paths, and near linear time , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.
[86] Daniel A. Spielman,et al. Faster approximate lossy generalized flow via interior point algorithms , 2008, STOC.
[87] Shankar M. Venkatesan,et al. Partition of planar flow networks , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).
[88] Richard J. Lipton,et al. On the Complexity of Computations under Varying Sets of Primitives , 1975, J. Comput. Syst. Sci..
[89] N. Megiddo,et al. Maximizing Concave Functions in Fixed Dimension , 1993 .
[90] Edith Cohen,et al. Strongly polynomial-time and NC algorithms for detecting cycles in periodic graphs , 1993, JACM.
[91] Gary L. Miller,et al. Flow in Planar Graphs with Multiple Sources and Sinks , 1995, SIAM J. Comput..
[92] John H. Reif,et al. Minimum s-t Cut of a Planar Undirected Network in O(n log2(n)) Time , 1983, SIAM J. Comput..
[93] Daniel J. Kleitman,et al. An Almost Linear Time Algorithm for Generalized Matrix Searching , 1990, SIAM J. Discret. Math..
[94] Leo Grady,et al. Minimal Surfaces Extend Shortest Path Segmentation Methods to 3D , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.
[95] James B. Orlin. A Faster Strongly Polynomial Minimum Cost Flow Algorithm , 1993, Oper. Res..
[96] Sivan Toledo,et al. Maximizing non-linear concave functions in fixed dimension , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.
[97] Jeff Erickson,et al. Optimally Cutting a Surface into a Disk , 2002, SCG '02.
[98] Andrew V. Goldberg,et al. Beyond the flow decomposition barrier , 1998, JACM.
[99] Samir Khuller,et al. The Lattice Structure of Flow in Planar Graphs , 1993, SIAM J. Discret. Math..
[100] Carsten Thomassen,et al. Graphs on Surfaces , 2001, Johns Hopkins series in the mathematical sciences.
[101] T. E. Harris,et al. Fundamentals of a Method for Evaluating Rail Net Capacities , 1955 .
[102] Karsten Weihe,et al. Maximum s-t-flow with k crossings in O(k3n log n) time , 2007, SODA '07.
[103] Christian Wulff-Nilsen,et al. Shortest Paths in Planar Graphs with Real Lengths in O(nlog2n/loglogn) Time , 2009, ESA.
[104] Erik D. Demaine,et al. Approximation algorithms via contraction decomposition , 2007, SODA '07.
[105] Edith Cohen,et al. Algorithms and complexity analysis for some flow problems , 1991, SODA '91.
[106] Refael Hassin,et al. Maximum Flow in (s, t) Planar Networks , 1981, Inf. Process. Lett..
[107] D. Rose,et al. Generalized nested dissection , 1977 .
[108] L. Lovász,et al. Geometric Algorithms and Combinatorial Optimization , 1981 .
[109] Donald B. Johnson,et al. Efficient Algorithms for Shortest Paths in Sparse Networks , 1977, J. ACM.
[110] Naomi Nishimura,et al. Characterizing Multiterminal Flow Networks and Computing Flows in Networks of Small Treewidth , 1998, J. Comput. Syst. Sci..
[111] L. Khachiyan. Polynomial algorithms in linear programming , 1980 .
[112] John E. Hopcroft,et al. Linear time algorithm for isomorphism of planar graphs (Preliminary Report) , 1974, STOC '74.
[113] Brenda S. Baker,et al. Approximation algorithms for NP-complete problems on planar graphs , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).
[114] Steven J. Gortler,et al. Minimal discrete curves and surfaces , 2004 .
[115] G. Borradaile,et al. Exploiting Planarity for Network Flow and Connectivity Problems , 2008 .
[116] Martin Kutz,et al. Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time , 2005, SCG '06.
[117] Erin W. Chambers,et al. Multiple source shortest paths in a genus g graph , 2007, SODA '07.
[118] Victor Y. Pan,et al. Fast and Efficient Parallel Solution of Sparse Linear Systems , 1993, SIAM J. Comput..
[119] Philip N. Klein,et al. An O(n log n) approximation scheme for Steiner tree in planar graphs , 2009, TALG.