Results 1  10
of
176
The computational structure of monotone monadic SNP and constraint satisfaction: A study through Datalog and group theory
 SIAM J. Comput
, 1998
"... ..."
(Show Context)
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 170 (15 self)
 Add to MetaCart
(Show Context)
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.
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 71 (12 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.
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 53 (30 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.
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 53 (20 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.
The complexity of partition functions
, 2005
"... We give a complexity theoretic classification of the counting versions of socalled Hcolouring problems for graphs H that may have multiple edges between the same pair of vertices. More generally, we study the problem of computing a weighted sum of homomorphisms to a weighted graph H. The problem h ..."
Abstract

Cited by 53 (7 self)
 Add to MetaCart
We give a complexity theoretic classification of the counting versions of socalled Hcolouring problems for graphs H that may have multiple edges between the same pair of vertices. More generally, we study the problem of computing a weighted sum of homomorphisms to a weighted graph H. The problem has two interesting alternative formulations: First, it is equivalent to computing the partition function of a spin system as studied in statistical physics. And second, it is equivalent to counting the solutions to a constraint satisfaction problem whose constraint language consists of two equivalence relations. In a nutshell, our result says that the problem is in polynomial time if the adjacency matrix of H has row rank 1, and #Phard otherwise.
Towards a Dichotomy Theorem for the Counting Constraint Satisfaction Problem
, 2006
"... The Counting Constraint Satisfaction Problem (#CSP) can be expressed as follows: given a set of variables, a set of values that can be taken by the variables, and a set of constraints specifying some restrictions on the values that can be taken simultaneously by some variables, determine the number ..."
Abstract

Cited by 51 (9 self)
 Add to MetaCart
The Counting Constraint Satisfaction Problem (#CSP) can be expressed as follows: given a set of variables, a set of values that can be taken by the variables, and a set of constraints specifying some restrictions on the values that can be taken simultaneously by some variables, determine the number of assignments of values to variables that satisfy all the constraints. The #CSP provides a general framework for numerous counting combinatorial problems including counting satisfying assignments to a propositional formula, counting graph homomorphisms, graph reliability and many others. This problem can be parametrized by the set of relations that may appear in a constraint. In this paper we start a systematic study of subclasses of the #CSP restricted in this way. The ultimate goal of this investigation is to distinguish those restricted subclasses of the #CSP which are solvable in polynomial time from those which are not. We show that the complexity of any restricted #CSP class on a finite domain can be deduced from the properties of polymorphisms of the allowed constraints, similar to that for the decision constraint satisfaction problem. Then we prove that if a subclass of the #CSP is solvable in polynomial time, then constraints allowed by the class satisfy some very restrictive condition: they need to have a Mal’tsev polymorphism, that is a ternary operation m(x, y, z) such that m(x, y, y) = m(y, y, x) = x. This condition uniformly explains many existing complexity results for particular cases of the #CSP, including the dichotomy results for the problem of counting graph homomorphisms, and it allows us to obtain new results.
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 49 (15 self)
 Add to MetaCart
(Show Context)
. 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
The complexity of the counting constraint satisfaction problem
 In ICALP (1
, 2008
"... The Counting Constraint Satisfaction Problem (#CSP(H)) over a finite relational structureH can be expressed as follows: given a relational structure G over the same vocabulary, determine the number of homomorphisms from G toH. In this paper we characterize relational structuresH for which#CSP(H) can ..."
Abstract

Cited by 45 (7 self)
 Add to MetaCart
(Show Context)
The Counting Constraint Satisfaction Problem (#CSP(H)) over a finite relational structureH can be expressed as follows: given a relational structure G over the same vocabulary, determine the number of homomorphisms from G toH. In this paper we characterize relational structuresH for which#CSP(H) can be solved in polynomial time and prove that for all other structures the problem is #Pcomplete. 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 42 (19 self)
 Add to MetaCart
(Show Context)
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 .