Hard enumeration problems in geometry and combinatorics
SIAM Journal on Algebraic and Discrete Methods
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Polynomial-time approximation algorithms for the Ising model
SIAM Journal on Computing
Complexity of generalized satisfiability counting problems
Information and Computation
Finite fields
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
The complexity of counting graph homomorphisms
Proceedings of the ninth international conference on on Random structures and algorithms
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Universal Algebra and Applications in Theoretical Computer Science
Universal Algebra and Applications in Theoretical Computer Science
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
On Counting Independent Sets in Sparse Graphs
SIAM Journal on Computing
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
A Simple Algorithm for Mal'tsev Constraints
SIAM Journal on Computing
Counting independent sets up to the tree threshold
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The complexity of partition functions
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Towards a dichotomy theorem for the counting constraint satisfaction problem
Information and Computation
On counting homomorphisms to directed acyclic graphs
Journal of the ACM (JACM)
SIAM Journal on Computing
The Complexity of the Counting Constraint Satisfaction Problem
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Holographic Algorithms by Fibonacci Gates and Holographic Reductions for Hardness
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Holant problems and counting CSP
Proceedings of the forty-first annual ACM symposium on Theory of computing
The Complexity of Weighted Boolean CSP
SIAM Journal on Computing
Proceedings of the forty-second ACM symposium on Theory of computing
Graph homomorphisms with complex values: a dichotomy theorem
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
Holographic algorithms: From art to science
Journal of Computer and System Sciences
A Complexity Dichotomy For Hypergraph Partition Functions
Computational Complexity
Holographic Algorithms with Matchgates Capture Precisely Tractable Planar_#CSP
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Computational Transition at the Uniqueness Threshold
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A Decidable Dichotomy Theorem on Directed Graph Homomorphisms with Non-negative Weights
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A Complexity Dichotomy for Partition Functions with Mixed Signs
SIAM Journal on Computing
Non-negatively Weighted #CSP: An Effective Complexity Dichotomy
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Improved inapproximability results for counting independent sets in the hard-core model
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Computational Complexity of Holant Problems
SIAM Journal on Computing
Gadgets and anti-gadgets leading to a complexity dichotomy
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Approximate counting via correlation decay in spin systems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Dichotomy for Holant problems of Boolean domain
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The expressibility of functions on the boolean domain, with applications to counting CSPs
Journal of the ACM (JACM)
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The complexity of counting problems has been studied intensively over the years. During the past decade, significant progress has taken place and a series of successively more powerful complexity dichotomies have been discovered. Given a class of counting problems, a dichotomy states that every problem in the class is either in polynomial time or #P-hard. In this guest column, we briefly survey two threads of recent developments in counting graph homomorphisms and the counting constraint satisfaction problem.