Complexity classification of exact and approximate counting problems
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[1] Jin-Yi Cai,et al. Inapproximability after Uniqueness Phase Transition in Two-Spin Systems , 2012, COCOA.
[2] Jin-Yi Cai,et al. Holographic Algorithms with Matchgates Capture Precisely Tractable Planar #CSP , 2017, SIAM J. Comput..
[3] Leslie Hogben,et al. Combinatorial Matrix Theory , 2013 .
[4] Dirk Llewellyn Vertigan. On the computational complexity of tutte, jones, homfly and kauffman invariants (tutte polynomial, jones polynomial, homfly polynomial, kauffman polynomial) , 1991 .
[5] Liang Li,et al. Approximate counting via correlation decay in spin systems , 2012, SODA.
[6] Leslie G. Valiant,et al. NP is as easy as detecting unique solutions , 1985, STOC '85.
[7] Jin-Yi Cai,et al. Computational Complexity of Holant Problems , 2011, SIAM J. Comput..
[8] J. Edmonds. Paths, Trees, and Flowers , 1965, Canadian Journal of Mathematics.
[9] Elliott H. Lleb. Residual Entropy of Square Ice , 1967 .
[10] Keisuke Fujii,et al. Quantum Commuting Circuits and Complexity of Ising Partition Functions , 2013, ArXiv.
[11] Alexander Schrijver,et al. Characterizing partition functions of the vertex model , 2011, 1102.4985.
[12] Alan D. Sokal. The multivariate Tutte polynomial (alias Potts model) for graphs and matroids , 2005, Surveys in Combinatorics.
[13] Eric Vigoda,et al. Inapproximability of the Partition Function for the Antiferromagnetic Ising and Hard-Core Models , 2012, Combinatorics, Probability and Computing.
[14] Leslie G. Valiant. Expressiveness of matchgates , 2002, Theor. Comput. Sci..
[15] W. Dur,et al. Quantum algorithms for classical lattice models , 2011, 1104.2517.
[16] Jin-Yi Cai,et al. Holographic algorithms by Fibonacci gates , 2013 .
[17] Piyush Srivastava,et al. Spatial Mixing and Approximation Algorithms for Graphs with Bounded Connective Constant , 2013, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science.
[18] Jason Morton,et al. Holographic algorithms without matchgates , 2009, ArXiv.
[19] Allan Sly,et al. The Computational Hardness of Counting in Two-Spin Models on d-Regular Graphs , 2012, 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science.
[20] Martin E. Dyer,et al. The Complexity of Weighted Boolean #CSP with Mixed Signs , 2009, Theor. Comput. Sci..
[21] Alexander Schrijver. Characterizing partition functions of the spin model by rank growth , 2012 .
[22] L. Onsager. Crystal statistics. I. A two-dimensional model with an order-disorder transition , 1944 .
[23] Leslie Ann Goldberg,et al. A Counterexample to rapid mixing of the Ge-Stefankovic Process , 2011, ArXiv.
[24] Leslie Ann Goldberg,et al. Counting Homomorphisms to Cactus Graphs Modulo 2 , 2014, STACS.
[25] Pinyan Lu,et al. FPTAS for Counting Weighted Edge Covers , 2014, ESA.
[26] Jin-Yi Cai,et al. Some Results on Matchgates and Holographic Algorithms , 2007, Int. J. Softw. Informatics.
[27] Leslie Ann Goldberg,et al. The Complexity of Approximating complex-valued Ising and Tutte partition functions , 2014, computational complexity.
[28] Leslie G. Valiant. Some observations on holographic algorithms , 2017, computational complexity.
[29] Leslie Ann Goldberg,et al. Inapproximability of the Tutte polynomial , 2006, STOC '07.
[30] Dirk L. Vertigan,et al. The Computational Complexity of Tutte Invariants for Planar Graphs , 2005, SIAM J. Comput..
[31] Martin E. Dyer,et al. The complexity of approximating conservative counting CSPs , 2012, 1208.1783.
[32] Jin-Yi Cai,et al. Gadgets and anti-gadgets leading to a complexity dichotomy , 2012, ITCS '12.
[33] G. Forney,et al. Codes on graphs: normal realizations , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).
[34] Jin-Yi Cai,et al. From Holant to #CSP and Back: Dichotomy for Holantc Problems , 2012, Algorithmica.
[35] Pinyan Lu,et al. A Simple FPTAS for Counting Edge Covers , 2013, SODA.
[36] Frank Kelly,et al. Stochastic Models of Computer Communication Systems , 1985 .
[37] Pinyan Lu,et al. The Complexity of Ferromagnetic Two-spin Systems with External Fields , 2014, APPROX-RANDOM.
[38] L. Lovasz,et al. Reflection positivity, rank connectivity, and homomorphism of graphs , 2004, math/0404468.
[39] M. .. Moore. Exactly Solved Models in Statistical Mechanics , 1983 .
[40] Elchanan Mossel,et al. On the hardness of sampling independent sets beyond the tree threshold , 2007, math/0701471.
[41] Martin E. Dyer,et al. A Random Polynomial Time Algorithm for Approximating the Volume of Convex Bodies , 1989, STOC.
[42] Allan Sly,et al. Computational Transition at the Uniqueness Threshold , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.
[43] Martin E. Dyer,et al. An approximation trichotomy for Boolean #CSP , 2010, J. Comput. Syst. Sci..
[44] Eric Vigoda,et al. Ferromagnetic Potts Model: Refined #BIS-hardness and Related Results , 2014, APPROX-RANDOM.
[45] Liang Li,et al. Correlation Decay up to Uniqueness in Spin Systems , 2013, SODA.
[46] D. Welsh,et al. On the computational complexity of the Jones and Tutte polynomials , 1990, Mathematical Proceedings of the Cambridge Philosophical Society.
[47] Richard J. Lipton,et al. On Tractable Exponential Sums , 2010, FAW.
[48] Martin E. Dyer,et al. The complexity of counting graph homomorphisms , 2000, Random Struct. Algorithms.
[49] Martin E. Dyer,et al. On counting independent sets in sparse graphs , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).
[50] Leslie G. Valiant,et al. Holographic Algorithms (Extended Abstract) , 2004, FOCS.
[51] S. Margulies,et al. Polynomial-time solvable #CSP problems via algebraic models and Pfaffian circuits , 2013, J. Symb. Comput..
[52] Pinyan Lu,et al. A Dichotomy for Real Weighted Holant Problems , 2012, 2012 IEEE 27th Conference on Computational Complexity.
[53] A. Sinclair,et al. Spatial mixing and the connective constant: optimal bounds , 2015, SODA 2015.
[54] T. D. Lee,et al. Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model , 1952 .
[55] Richard E. Ladner,et al. On the Structure of Polynomial Time Reducibility , 1975, JACM.
[56] Eric Vigoda,et al. A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries , 2004, JACM.
[57] Mark Jerrum,et al. Approximating the Permanent , 1989, SIAM J. Comput..
[58] M. Bremner,et al. Temporally unstructured quantum computation , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[59] Michel Las Vergnas,et al. On the evaluation at (3, 3) of the Tutte polynomial of a graph , 1988, J. Comb. Theory, Ser. B.
[60] Dror Weitz,et al. Counting independent sets up to the tree threshold , 2006, STOC '06.
[61] David Gamarnik,et al. Simple deterministic approximation algorithms for counting matchings , 2007, STOC '07.
[62] Eric Vigoda,et al. Improved Mixing Condition on the Grid for Counting and Sampling Independent Sets , 2011, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.
[63] P. W. Kasteleyn. The Statistics of Dimers on a Lattice , 1961 .
[64] Dan J. Shepherd,et al. Binary Matroids and Quantum Probability Distributions , 2010, ArXiv.
[65] Leslie Ann Goldberg,et al. The computational complexity of two‐state spin systems , 2003, Random Struct. Algorithms.
[66] Eric Vigoda,et al. Improved Inapproximability Results for Counting Independent Sets in the Hard-Core Model , 2011, APPROX-RANDOM.
[67] Mingji Xia. Holographic Reduction: A Domain Changed Application and its Partial Converse Theorems , 2011, Int. J. Softw. Informatics.
[68] Leslie G. Valiant,et al. Quantum Circuits That Can Be Simulated Classically in Polynomial Time , 2002, SIAM J. Comput..
[69] Leslie Ann Goldberg,et al. A Complexity Dichotomy for Partition Functions with Mixed Signs , 2008, SIAM J. Comput..
[70] Elliott H. Lieb,et al. A general Lee-Yang theorem for one-component and multicomponent ferromagnets , 1981 .
[71] Y. Bugeaud. Approximation by Algebraic Numbers , 2004 .
[72] Jin-Yi Cai,et al. Holographic reduction, interpolation and hardness , 2012, computational complexity.
[73] Dmitriy Katz,et al. Correlation decay and deterministic FPTAS for counting list-colorings of a graph , 2007, SODA '07.
[74] Leslie Ann Goldberg,et al. Approximating the Partition Function of the Ferromagnetic Potts Model , 2010, ICALP.
[75] Eric Vigoda,et al. #BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Non-uniqueness Region , 2014, APPROX-RANDOM.
[76] Andrei A. Bulatov,et al. The complexity of partition functions , 2005, Theor. Comput. Sci..
[77] Martin E. Dyer,et al. The Relative Complexity of Approximate Counting Problems , 2000, Algorithmica.
[78] Jin-Yi Cai,et al. Spin systems on k-regular graphs with complex edge functions , 2012, Theor. Comput. Sci..
[79] Jin-Yi Cai,et al. Dichotomy for Holant problems of Boolean domain , 2011, SODA '11.
[80] Jin-Yi Cai,et al. A complete dichotomy rises from the capture of vanishing signatures: extended abstract , 2013, STOC '13.
[81] Ding‐Zhu Du,et al. Wiley Series in Discrete Mathematics and Optimization , 2014 .
[82] Heng Guo,et al. The Complexity of Planar Boolean #CSP with Complex Weights , 2012, ICALP.
[83] Jin-Yi Cai,et al. Holographic Algorithms Beyond Matchgates , 2014, ICALP.
[84] Martin E. Dyer,et al. The expressibility of functions on the boolean domain, with applications to counting CSPs , 2011, JACM.
[85] Richard Jozsa,et al. Classical simulation complexity of extended Clifford circuits , 2013, Quantum Inf. Comput..
[86] Leslie Ann Goldberg,et al. The Complexity of Computing the Sign of the Tutte Polynomial , 2012, SIAM J. Comput..
[87] Jin-Yi Cai,et al. Dichotomy theorems for holant problems , 2010 .
[88] J. Scott Provan,et al. The Complexity of Counting Cuts and of Computing the Probability that a Graph is Connected , 1983, SIAM J. Comput..
[89] John Faben. The complexity of counting solutions to Generalised Satisfiability Problems modulo k , 2008, ArXiv.
[90] D. Welsh. Complexity: Knots, Colourings and Counting: Link polynomials and the Tait conjectures , 1993 .
[91] Martin E. Dyer,et al. The Complexity of Weighted Boolean #CSP , 2009, SIAM J. Comput..
[92] Eric Vigoda,et al. Improved bounds for sampling colorings , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).
[93] D. Gamarnik,et al. Counting without sampling: Asymptotics of the log-partition function for certain statistical physics models , 2008 .
[94] Leslie Ann Goldberg,et al. The Complexity of Ferromagnetic Ising with Local Fields , 2006, Combinatorics, Probability and Computing.
[95] M. Fisher,et al. Dimer problem in statistical mechanics-an exact result , 1961 .
[96] Jin-Yi Cai,et al. Partition functions on kk-regular graphs with {0, 1}{0, 1}-vertex assignments and real edge functions , 2013, Theor. Comput. Sci..
[97] Leslie G. Valiant,et al. The Complexity of Symmetric Boolean Parity Holant Problems , 2013, SIAM J. Comput..
[98] Mark Jerrum,et al. Polynomial-Time Approximation Algorithms for the Ising Model , 1990, SIAM J. Comput..
[99] Mark Jerrum,et al. The Complexity of Parity Graph Homomorphism: An Initial Investigation , 2013, Theory Comput..
[100] E. Ising. Beitrag zur Theorie des Ferromagnetismus , 1925 .
[101] Michael I. Jordan,et al. Graphical Models, Exponential Families, and Variational Inference , 2008, Found. Trends Mach. Learn..
[102] R. Jozsa,et al. Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[103] Jin-Yi Cai,et al. Holographic algorithms: From art to science , 2011, J. Comput. Syst. Sci..
[104] Piyush Srivastava,et al. Approximation Algorithms for Two-State Anti-Ferromagnetic Spin Systems on Bounded Degree Graphs , 2011, Journal of Statistical Physics.
[105] Leslie G. Valiant,et al. The Complexity of Enumeration and Reliability Problems , 1979, SIAM J. Comput..
[106] Pinyan Lu,et al. Improved FPTAS for Multi-spin Systems , 2013, APPROX-RANDOM.
[107] Chen Ning Yang,et al. The Spontaneous Magnetization of a Two-Dimensional Ising Model , 1952 .
[108] Martin E. Dyer,et al. On Markov Chains for Independent Sets , 2000, J. Algorithms.
[109] Tom Brylawski,et al. Matroid Applications: The Tutte Polynomial and Its Applications , 1992 .
[110] A. Ziv. Relative distance—an error measure in round-off error analysis , 1982 .
[111] Heng Guo,et al. Uniqueness, Spatial Mixing, and Approximation for Ferromagnetic 2-Spin Systems , 2016, APPROX-RANDOM.
[112] Jin-Yi Cai,et al. The complexity of complex weighted Boolean #CSP , 2014, J. Comput. Syst. Sci..
[113] Leslie G. Valiant,et al. The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..
[114] Elchanan Mossel,et al. Exact thresholds for Ising–Gibbs samplers on general graphs , 2009, The Annals of Probability.
[115] Mingji Xia,et al. The Complexity of Weighted Boolean #CSP Modulo k , 2011, STACS.
[116] Qi Ge,et al. A Graph Polynomial for Independent Sets of Bipartite Graphs , 2009, Combinatorics, Probability and Computing.
[117] Jin-Yi Cai,et al. Graph Homomorphisms with Complex Values: A Dichotomy Theorem , 2013, SIAM J. Comput..
[118] Pinyan Lu,et al. FPTAS for Weighted Fibonacci Gates and Its Applications , 2014, ICALP.
[119] Leslie Ann Goldberg,et al. Approximating the partition function of planar two-state spin systems , 2012, J. Comput. Syst. Sci..
[120] A. Sinclair,et al. Fast mixing for independent sets, colorings, and other models on trees , 2007 .
[121] Pinyan Lu,et al. FPTAS for Counting Monotone CNF , 2015, SODA.
[122] Jin-Yi Cai,et al. On the Theory of Matchgate Computations , 2007, Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07).
[123] Leslie Ann Goldberg,et al. Counting Homomorphisms to Square-Free Graphs, Modulo 2 , 2016, TOCT.
[124] Leslie G. Valiant,et al. Random Generation of Combinatorial Structures from a Uniform Distribution , 1986, Theor. Comput. Sci..
[125] Jin-Yi Cai,et al. On Symmetric Signatures in Holographic Algorithms , 2007, STACS.
[126] Eric Vigoda,et al. Inapproximability for antiferromagnetic spin systems in the tree non-uniqueness region , 2013, STOC.
[127] Jin-Yi Cai,et al. A Holant Dichotomy: Is the FKT Algorithm Universal? , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.