Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Tree clustering for constraint networks (research note)
Artificial Intelligence
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
A dichotomy theorem for maximum generalized satisfiability problems
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
New upper bounds for maximum satisfiability
Journal of Algorithms
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
An algorithm for counting maximum weighted independent sets and its applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
A Probabilistic Algorithm for k-SAT and Constraint Satisfaction Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Worst-case upper bounds for MAX-2-SAT with an application to MAX-CUT
Discrete Applied Mathematics - The renesse issue on satisfiability
Quasiconvex analysis of backtracking algorithms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Parameterized Complexity of Constraint Satisfaction Problems
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Polynomial Time Approximation Schemes for MAX-BISECTION on Planar and Geometric Graphs
SIAM Journal on Computing
Solving Sparse Random Instances of Max Cut and Max 2-CSP in Linear Expected Time
Combinatorics, Probability and Computing
A new approach to proving upper bounds for MAX-2-SAT
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Counting models for 2SAT and 3SAT formulae
Theoretical Computer Science
An LP-designed algorithm for constraint satisfaction
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Exact Max 2-Sat: Easier and Faster
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Pathwidth of cubic graphs and exact algorithms
Information Processing Letters
3-coloring in time O (1.3289n)
Journal of Algorithms
Algorithms based on the treewidth of sparse graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
An exact algorithm for MAX-CUT in sparse graphs
Operations Research Letters
A New Upper Bound for Max-2-SAT: A Graph-Theoretic Approach
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
ACM SIGACT News
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function
ACM Transactions on Algorithms (TALG)
A new upper bound for Max-2-SAT: A graph-theoretic approach
Journal of Discrete Algorithms
A universally fastest algorithm for Max 2-Sat, Max 2-CSP, and everything in between
Journal of Computer and System Sciences
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
New upper bounds for MAX-2-SAT and MAX-2-CSP w.r.t. the average variable degree
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
New bounds for MAX-SAT by clause learning
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
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The class Max (r,2)-CSP, or simply Max 2-CSP, consists of constraint satisfaction problems with at most two r-valued variables per clause. For instances with n variables and m binary clauses, we present an O(nr^5^+^1^9^m^/^1^0^0)-time algorithm which is the fastest polynomial-space algorithm for many problems in the class, including Max Cut. The method also proves a treewidth bound tw(G)@?(13/75+o(1))m, which gives a faster Max 2-CSP algorithm that uses exponential space: running in time O^@?(2^(^1^3^/^7^5^+^o^(^1^)^)^m), this is fastest for most problems in Max 2-CSP. Parametrizing in terms of n rather than m, for graphs of average degree d we show a simple algorithm running time O^@?(2^(^1^-^2^d^+^1^)^n), the fastest polynomial-space algorithm known. In combination with ''Polynomial CSPs'' introduced in a companion paper, these algorithms also allow (with an additional polynomial factor overhead in space and time) counting and sampling, and the solution of problems like Max Bisection that escape the usual CSP framework. Linear programming is key to the design as well as the analysis of the algorithms.