Constraint Satisfaction Problems of Bounded Width

Abstract

We provide a full characterization of applicability of The Local Consistency Checking algorithm to solving the non-uniform Constraint Satisfaction Problems. This settles the conjecture of Larose and Zádori.

The collapse of the bounded width hierarchy

“…This paper sharpens a result of [1] that characterizes the applicability of local consistency algorithms for finite constraint languages.…”

“…All known tractable cases are solvable either by the few subpowers algorithm [16], by local consistency algorithms [1,14], or by a combination of these two. This paper sharpens a result of [1] that characterizes the applicability of local consistency algorithms for finite constraint languages.…”

Two new homomorphism dualities and lattice operations

“…. , 9}, one unary relation R 1 = {2, 3}, one binary relation R 2 = {(1, 2), (2,3), (3,4), (4,8)} and one ternary relation R 3 = {(3, 6, 7), (4, 5, 9)}. The graph Inc(B) is shown on Fig.…”

“…For example in the caterpillar from Fig. 1, the extreme non-leaves are 2 and 4, the extreme pendant blocks are R 2 (1, 2), R 1 (2), R 2 (4,8), and R 3 (4,5,9), and the terminal elements are 1,2,4,5,8,9.…”

“…The most important duality probably is bounded treewidth duality which is equivalent to definability in Datalog (see [6,16]). Structures with this duality have been recently characterised in algebraic terms (see [2], also [5]). Two other well-understood dualities are finite duality [28,32,33] and tree duality [11,16].…”