SIGACT news complexity theory column 34
ACM SIGACT News
On the Hamming distance of constraint satisfaction problems
Theoretical Computer Science - Complexity and logic
Towards a Predictive Computational Complexity Theory
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Equivalence and Isomorphism for Boolean Constraint Satisfaction
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The complexity of minimal satisfiability problems
Information and Computation
New hardness results for congestion minimization and machine scheduling
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Complexity of Boolean Constraint Satisfaction Local Search Problems
Annals of Mathematics and Artificial Intelligence
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Effective bounding techniques for solving unate and binate covering problems
Proceedings of the 42nd annual Design Automation Conference
Supermodular functions and the complexity of MAX CSP
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
The NP-completeness column: The many limits on approximation
ACM Transactions on Algorithms (TALG)
The complexity of soft constraint satisfaction
Artificial Intelligence
The approximability of non-Boolean satisfiability problems and restricted integer programming
Theoretical Computer Science
Solving the minimum-cost satisfiability problem using SAT based branch-and-bound search
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
Maximum H-colourable subdigraphs and constraint optimization with arbitrary weights
Journal of Computer and System Sciences
Artificial Intelligence
High-contrast algorithm behavior: observation, hypothesis, and experimental design
Proceedings of the 2007 workshop on Experimental computer science
Performance testing of combinatorial solvers with isomorph class instances
Proceedings of the 2007 workshop on Experimental computer science
High-contrast algorithm behavior: observation, conjecture, and experimental design
ecs'07 Experimental computer science on Experimental computer science
Performance testing of combinatorial solvers with isomorph class instances
ecs'07 Experimental computer science on Experimental computer science
Sampling subproblems of heterogeneous Max-Cut problems and approximation algorithms
Random Structures & Algorithms
A dichotomy for minimum cost graph homomorphisms
European Journal of Combinatorics
The approximability of MAX CSP with fixed-value constraints
Journal of the ACM (JACM)
Non-uniform Boolean Constraint Satisfaction Problems with Cardinality Constraint
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints
Introduction to the Maximum Solution Problem
Complexity of Constraints
A note on some collapse results of valued constraints
Information Processing Letters
Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
Approximability of the Maximum Solution Problem for Certain Families of Algebras
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
A maximal tractable class of soft constraints
Journal of Artificial Intelligence Research
A maximal tractable class of soft constraints
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
The complexity of soft constraint satisfaction
Artificial Intelligence
Supermodular functions and the complexity of MAX CSP
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
On the boolean connectivity problem for horn relations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Bounded tree-width and CSP-related problems
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Minimum cost homomorphisms to reflexive digraphs
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Nonuniform Boolean constraint satisfaction problems with cardinality constraint
ACM Transactions on Computational Logic (TOCL)
Constraint satisfaction problems and global cardinality constraints
Communications of the ACM
On the Boolean connectivity problem for Horn relations
Discrete Applied Mathematics
Preprocessing of min ones problems: a dichotomy
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Parameterized complexity and kernelizability of max ones and exact ones problems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Constraint satisfaction parameterized by solution size
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Linear programming, width-1 CSPs, and robust satisfaction
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Approximability of integer programming with generalised constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
The complexity of conservative valued CSPs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
On the complexity of global constraint satisfaction
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Tight bounds on the approximability of almost-satisfiable Horn SAT and exact hitting set
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The connectivity of boolean satisfiability: computational and structural dichotomies
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Generalised integer programming based on logically defined relations
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Approximability of bounded occurrence max ones
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Tight approximability results for the maximum solution equation problem over Zp
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Quantified constraint satisfaction, maximal constraint languages, and symmetric polymorphisms
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
On the hardness of losing weight
ACM Transactions on Algorithms (TALG)
Optimization, randomized approximability, and boolean constraint satisfaction problems
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Robust satisfiability of constraint satisfaction problems
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Linear-programming design and analysis of fast algorithms for Max 2-CSP
Discrete Optimization
Approximation of the Quadratic Set Covering problem
Discrete Optimization
Unordered constraint satisfaction games
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Tractable triangles and cross-free convexity in discrete optimisation
Journal of Artificial Intelligence Research
Ruling out polynomial-time approximation schemes for hard constraint satisfaction problems
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
The complexity of finite-valued CSPs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
The complexity of three-element min-sol and conservative min-cost-hom
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Do hard SAT-related reasoning tasks become easier in the Krom fragment?
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Complexity of approximating CSP with balance / hard constraints
Proceedings of the 5th conference on Innovations in theoretical computer science
Hi-index | 0.02 |
We study optimization problems that may be expressed as "Boolean constraint satisfaction problems." An instance of a Boolean constraint satisfaction problem is given by m constraints applied to n Boolean variables. Different computational problems arise from constraint satisfaction problems depending on the nature of the "underlying" constraints as well as on the goal of the optimization task. Here we consider four possible goals: Max CSP (Min CSP) is the class of problems where the goal is to find an assignment maximizing the number of satisfied constraints (minimizing the number of unsatisfied constraints). Max Ones (Min Ones) is the class of optimization problems where the goal is to find an assignment satisfying all constraints with maximum (minimum) number of variables set to 1. Each class consists of infinitely many problems and a problem within a class is specified by a finite collection of finite Boolean functions that describe the possible constraints that may be used.Tight bounds on the approximability of every problem in Max CSP were obtained by Creignou [ J. Comput. System Sci., 51 (1995), pp. 511--522]. In this work we determine tight bounds on the "approximability" (i.e., the ratio to within which each problem may be approximated in polynomial time) of every problem in Max Ones, Min CSP, and Min Ones. Combined with the result of Creignou, this completely classifies all optimization problems derived from Boolean constraint satisfaction. Our results capture a diverse collection of optimization problems such as MAX 3-SAT, Max Cut, Max Clique, Min Cut, Nearest Codeword, etc. Our results unify recent results on the (in-)approximability of these optimization problems and yield a compact presentation of most known results. Moreover, these results provide a formal basis to many statements on the behavior of natural optimization problems that have so far been observed only empirically.