New Tractable Classes from Old

Many combinatorial problems can be naturally expressed as "constraint satisfaction problems". This class of problems is known to be NP-hard in general, but a number of restrictions of the general problem have been identified which ensure tractability. This paper introduces a method of combining two or more tractable classes over disjoint domains, in order to synthesise larger, more expressive tractable classes. We demonstrate that the classes so obtained are genuinely novel, and have not been previously identified. In addition, we use algebraic techniques to extend the tractable classes which we identify, and to show that the algorithms for solving these extended classes can be less than obvious.

[1]  Martin C. Cooper,et al.  Characterising Tractable Constraints , 1994, Artif. Intell..

[2]  Henri Cohen,et al.  Algorithmic Number Theory , 1996, Lecture Notes in Computer Science.

[3]  Thomas J. Schaefer,et al.  The complexity of satisfiability problems , 1978, STOC.

[4]  Eugene C. Freuder.  A sufficient condition for backtrack-bounded search , 1985, JACM.

[5]  Bernhard Nebel,et al.  Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra , 1994, JACM.

[6]  Martin C. Cooper,et al.  Tractable Constraints on Ordered Domains , 1995, Artif. Intell..

[7]  Marc Gyssens,et al.  A Unifying Framework for Tractable Constraints , 1995, CP.

[8]  Peter Jeavons,et al.  On the Algebraic Structure of Combinatorial Problems , 1998, Theor. Comput. Sci..

[9]  Lefteris M. Kirousis,et al.  Fast Parallel Constraint Satisfaction , 1993, Artif. Intell..

[10]  Justin Pearson,et al.  Closure Functions and Width 1 Problems , 1999, CP.

[11]  Peter Jeavons,et al.  An Algebraic Characterization of Tractable Constraints , 1995, COCOON.

[12]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[13]  Peter B. Ladkin,et al.  On binary constraint problems , 1994, JACM.

[14]  Peter Jeavons,et al.  Constraint Satisfaction Problems and Finite Algebras , 2000, ICALP.

[15]  Rina Dechter,et al.  Tree Clustering for Constraint Networks , 1989, Artif. Intell..

[16]  Marc Gyssens,et al.  Closure properties of constraints , 1997, JACM.

[17]  Alan K. Mackworth.  Consistency in Networks of Relations , 1977, Artif. Intell..

[18]  Peter Jeavons,et al.  Tractable Disjunctive Constraints , 1997, CP.

[19]  Peter van Beek,et al.  On the minimality and global consistency of row-convex constraint networks , 1995, JACM.

[20]  Peter Jonsson,et al.  Exploiting Bipartiteness to Identify Yet Another Tractable Subclass of CSP , 1999, CP.

[21]  Ugo Montanari,et al.  Networks of constraints: Fundamental properties and applications to picture processing , 1974, Inf. Sci..

[22]  George Gratzer,et al.  Universal Algebra , 1979 .

[23]  Marc Gyssens,et al.  A test for Tractability , 1996, CP.