Results 1  10
of
139
The computational structure of monotone monadic SNP and constraint satisfaction: A study through Datalog and group theory
 SIAM J. Comput
, 1998
"... ..."
ConjunctiveQuery Containment and Constraint Satisfaction
 Journal of Computer and System Sciences
, 1998
"... Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in c ..."
Abstract

Cited by 131 (13 self)
 Add to MetaCart
Conjunctivequery containment is recognized as a fundamental problem in database query evaluation and optimization. At the same time, constraint satisfaction is recognized as a fundamental problem in artificial intelligence. What do conjunctivequery containment and constraint satisfaction have in common? Our main conceptual contribution in this paper is to point out that, despite their very different formulation, conjunctivequery containment and constraint satisfaction are essentially the same problem. The reason is that they can be recast as the following fundamental algebraic problem: given two finite relational structures A and B, is there a homomorphism h : A ! B? As formulated above, the homomorphism problem is uniform in the sense that both relational structures A and B are part of the input. By fixing the structure B, one obtains the following nonuniform problem: given a finite relational structure A, is there a homomorphism h : A ! B? In general, nonuniform tractability results do not uniformize. Thus, it is natural to ask: which tractable cases of nonuniform tractability results for constraint satisfaction and conjunctivequery containment do uniformize? Our main technical contribution in this paper is to show that several cases of tractable nonuniform constraint satisfaction problems do indeed uniformize. We exhibit three nonuniform tractability results that uniformize and, thus, give rise to polynomialtime solvable cases of constraint satisfaction and conjunctivequery containment.
Viewbased query processing and constraint satisfaction
 IN PROC. OF THE 15TH IEEE SYMP. ON LOGIC IN COMPUTER SCIENCE (LICS 2000
, 2000
"... Viewbased query processing requires to answer a query posed to a database only on the basis of the information on a set of views, which are again queries over the same database. This problem is relevant in many aspects of database management, and has been addressed by means of two basic approaches, ..."
Abstract

Cited by 46 (29 self)
 Add to MetaCart
Viewbased query processing requires to answer a query posed to a database only on the basis of the information on a set of views, which are again queries over the same database. This problem is relevant in many aspects of database management, and has been addressed by means of two basic approaches, namely, query rewriting and query answering. In the former approach, one tries to compute a rewriting of the query in terms of the views, whereas in the latter, one aims at directly answering the query based on the view extensions. We study viewbased query processing for the case of regularpath queries, which are the basic querying mechanisms for the emergent field of semistructured data. Based on recent results, we first show that a rewriting is in general a coNP function wrt to the size of view extensions. Hence, the problem arises of characterizing which instances of the problem admit a rewriting that is PTIME. A second contribution of the work is to establish a tight connection between viewbased query answering and constraintsatisfaction problems, which allows us to show that the above characterization is going to be difficult. As a third contribution of our work, we present two methods for computing PTIME rewritings of specific forms. The first method, which is based on the established connection with constraintsatisfaction problems, gives us rewritings expressed in Datalog with a fixed number of variables. The second method, based on automatatheoretic techniques, gives us rewritings that are formulated as unions of conjunctive regularpath queries with a fixed number of variables.
Constraint Satisfaction, Bounded Treewidth, and FiniteVariable Logics
, 2002
"... We systematically investigate the connections between constraint satisfaction problems, structures of bounded treewidth, and definability in logics with a finite number of variables. We first show that constraint satisfaction problems on inputs of treewidth less than k are definable using Datalog ..."
Abstract

Cited by 43 (9 self)
 Add to MetaCart
We systematically investigate the connections between constraint satisfaction problems, structures of bounded treewidth, and definability in logics with a finite number of variables. We first show that constraint satisfaction problems on inputs of treewidth less than k are definable using Datalog programs with at most k variables; this provides a new explanation for the tractability of these classes of problems. After this, we investigate constraint satisfaction on inputs that are homomorphically equivalent to structures of bounded treewidth.
Good and Semistrong Colorings of Oriented Planar Graphs
 INF. PROCESSING LETTERS 51
, 1994
"... A kcoloring of an oriented graph G = (V, A) is an assignment c of one of the colors 1; 2; : : : ; k to each vertex of the graph such that, for every arc (x; y) of G, c(x) 6= c(y). The kcoloring is good if for every arc (x; y) of G there is no arc (z; t) 2 A such that c(x) = c(t) and c(y) = c(z). ..."
Abstract

Cited by 42 (19 self)
 Add to MetaCart
A kcoloring of an oriented graph G = (V, A) is an assignment c of one of the colors 1; 2; : : : ; k to each vertex of the graph such that, for every arc (x; y) of G, c(x) 6= c(y). The kcoloring is good if for every arc (x; y) of G there is no arc (z; t) 2 A such that c(x) = c(t) and c(y) = c(z). A kcoloring is said to be semistrong if for every vertex x of G, c(z) 6= c(t) for any pair fz; tg of vertices of N \Gamma (x). We show that every oriented planar graph has a good coloring using at most 5 \Theta 2 4 colors and that every oriented planar graph G = (V; A) with d \Gamma (x) 3 for every x 2 V has a good and semistrong coloring using at most 4 \Theta 5 \Theta 2 4 colors.
Acyclic and Oriented Chromatic Numbers of Graphs
 J. Graph Theory
, 1997
"... . The oriented chromatic number o ( ~ G) of an oriented graph ~ G = (V; A) is the minimum number of vertices in an oriented graph ~ H for which there exists a homomorphism of ~ G to ~ H . The oriented chromatic number o (G) of an undirected graph G is the maximum of the oriented chromatic n ..."
Abstract

Cited by 39 (13 self)
 Add to MetaCart
. The oriented chromatic number o ( ~ G) of an oriented graph ~ G = (V; A) is the minimum number of vertices in an oriented graph ~ H for which there exists a homomorphism of ~ G to ~ H . The oriented chromatic number o (G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the orientations of G. This paper discusses the relations between the oriented chromatic number and the acyclic chromatic number and some other parameters of a graph. We shall give a lower bound for o (G) in terms of a (G). An upper bound for o (G) in terms of a (G) was given by Raspaud and Sopena. We also give an upper bound for o (G) in terms of the maximum degree of G. We shall show that this upper bound is not far from being optimal. Keywords. Oriented chromatic number, Acyclic chromatic number. 1
Constraint Satisfaction with Countable Homogeneous Templates
 IN PROCEEDINGS OF CSL’03
, 2003
"... For a fixed countable homogeneous structure we study the computational problem whether a given finite structure of the same relational signature homomorphically maps to . This problem is known as the constraint satisfaction problem CSP( ) for and was intensively studied for finite . We show that ..."
Abstract

Cited by 33 (15 self)
 Add to MetaCart
For a fixed countable homogeneous structure we study the computational problem whether a given finite structure of the same relational signature homomorphically maps to . This problem is known as the constraint satisfaction problem CSP( ) for and was intensively studied for finite . We show that  as in the case of finite  the computational complexity of CSP( ) for countable homogeneous is determinded by the clone of polymorphisms of . To this end we prove the following theorem which is of independent interest: The primitive positive definable relations over an !categorical structure are precisely the relations that are invariant under the polymorphisms of .
Datalog and constraint satisfaction with infinite templates
 In Proceedings of the 23rd International Symposium on Theoretical Aspects of Computer Science (STACS’06), LNCS 3884
, 2006
"... Abstract. On finite structures, there is a wellknown connection between the expressive power of Datalog, finite variable logics, the existential pebble game, and bounded hypertree duality. We study this connection for infinite structures. This has applications for constraint satisfaction with infin ..."
Abstract

Cited by 32 (18 self)
 Add to MetaCart
Abstract. On finite structures, there is a wellknown connection between the expressive power of Datalog, finite variable logics, the existential pebble game, and bounded hypertree duality. We study this connection for infinite structures. This has applications for constraint satisfaction with infinite templates, i.e., for all computational problems that are closed under disjoint unions and whose complement is closed under homomorphisms. If the template Γ is ωcategorical, we obtain alternative characterizations of bounded Datalog width. We also show that CSP(Γ) can be solved in polynomial time if Γ is ωcategorical and the input is restricted to instances of bounded treewidth. Finally, we prove algebraic characterisations of those ωcategorical templates whose CSP has Datalog width (1, k), and for those whose CSP has strict Datalog width k.
On the Maximum Average Degree and the Oriented Chromatic Number of a Graph
 Discrete Math
, 1995
"... The oriented chromatic number o(H) of an oriented graph H is defined as the minimum order of an oriented graph H 0 such that H has a homomorphism to H 0 . The oriented chromatic number o(G) of an undirected graph G is then defined as the maximum oriented chromatic number of its orientations. In ..."
Abstract

Cited by 30 (15 self)
 Add to MetaCart
The oriented chromatic number o(H) of an oriented graph H is defined as the minimum order of an oriented graph H 0 such that H has a homomorphism to H 0 . The oriented chromatic number o(G) of an undirected graph G is then defined as the maximum oriented chromatic number of its orientations. In this paper we study the links between o(G) and mad(G) defined as the maximum average degree of the subgraphs of G. 1 Introduction and statement of results For every graph G we denote by V (G), with vG = jV (G)j, its set of vertices and by E(G), with e G = jE(G)j, its set of arcs or edges. A homomorphism from a graph G to a graph On leave of absence from the Institute of Mathematics, Novosibirsk, 630090, Russia. With support from Engineering and Physical Sciences Research Council, UK, grant GR/K00561, and from the International Science Foundation, grant NQ4000. y This work was partially supported by the Network DIMANET of the European Union and by the grant 960101614 of the Russian F...
Reasoning About Temporal Relations: The Tractable Subalgebras Of Allen's Interval Algebra
 Journal of the ACM
, 2001
"... Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra c ..."
Abstract

Cited by 29 (2 self)
 Add to MetaCart
Allen's interval algebra is one of the best established formalisms for temporal reasoning. This paper is the final step in the classification of complexity in Allen's algebra. We show that the current knowledge about tractability in the interval algebra is complete, that is, this algebra contains exactly eighteen maximal tractable subalgebras, and reasoning in any fragment not entirely contained in one of these subalgebras is NPcomplete. We obtain this result by giving a new uniform description of the known maximal tractable subalgebras and then systematically using an algebraic technique for identifying maximal subalgebras with a given property.