# Identifying Efficiently Solvable Cases of Max CSP

@inproceedings{Cohen2004IdentifyingES, title={Identifying Efficiently Solvable Cases of Max CSP}, author={David A. Cohen and Martin C. Cooper and Peter Jeavons and Andrei A. Krokhin}, booktitle={STACS}, year={2004} }

In this paper we study the complexity of the maximum constraint satisfaction problem (Max CSP) over an arbitrary finite domain. We describe a novel connection between this problem and the supermodular function maximization problem (which is dual to the submodular function minimization problem). Using this connection, we are able to identify large classes of efficiently solvable subproblems of Max CSP arising from certain restrictions on the constraint types. Until now, the only known polynomial…

## 9 Citations

The Approximability of Three-valued MAX CSP

- Computer Science, MathematicsSIAM J. Comput.
- 2006

This paper establishes the first step in this direction by establishing this result for MAX CSP over a three-element domain and presents a simple description of all polynomial-time solvable cases of the problem, which uses the well-known algebraic combinatorial property of supermodularity.

Supermodularity on chains and complexity of maximum constraint satisfaction problems

- Mathematics, Computer Science
- 2005

Any maximum constraint satisfaction problem with a finite set of allowed constraint types, which includes all constants, is either solvable in polynomial time or is $\mathrm{NP}$-complete.

Maximum Constraint Satisfaction on Diamonds

- Computer ScienceCP
- 2005

This paper studies the complexity of the weighted maximum constraint satisfaction problem over an arbitrary finite domain and proves several results confirming this in a special case when the lattice ordering is as loose as possible, i.e., a diamond one.

Constraint satisfaction with infinite domains

- Mathematics
- 2004

Omega-categoricity is a rather strong model-theoretic assumption on a relational structure, and it can be used to show that many techniques for constraint satisfaction with finite templates extend to omega- categorical templates.

A Linear Programming Approach to Max-Sum Problem: A Review

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2007

This work reviews a not widely known approach to the max-sum labeling problem, developed by Ukrainian researchers Schlesinger et al. in 1976, and shows how it contributes to recent results, most importantly, those on the convex combination of trees and tree-reweighted max-product.

Final Report on GR/R29598/01 Algebraic Structural Methods and Complexity of Constraint Satisfaction

- Computer Science
- 2004

This grant was designed to enable Jeavons, Bulatov and Krokhin to develop a promising new research programme concerning the use of algebraic methods in the analysis of constraint satisfaction problems, and has firmly established this field as an exciting and productive area of research on the boundary between computer science and mathematics.

Soft constraint processing

- Computer Science
- 2005

This (not so) short text presents some results I’m aware of in the field of soft constraint network processing and introduces fundamental operations on soft constraints and shows how these fundamental operations can be used to process and solve soft constraint networks.

Poly-controlled partial evaluation and its application to resource-aware program specialization = evaluacion parcial poicontrolada y su aplicacion a la especializacion de programas consiciente de los recursos

- Philosophy
- 2007

La Evaluacion Parcial es una tecnica automatica para la optimizacion de programas. Su objetivo principal es el
de especializar un programa con respecto a parte de sus datos de entrada, los que se…

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