Hypertree Decompositions: A Survey

This paper surveys recent results related to the concept of hypertree decomposition and the associated notion of hypertree width. A hypertree decomposition of a hypergraph (similar to a tree decomposition of a graph) is a suitable clustering of its hyperedges yielding a tree or a forest. Important NP hard problems become tractable if restricted to instances whose associated hypergraphs are of bounded hypertree width. We also review a number of complexity results on problems whose structure is described by acyclic or nearly acyclic hypergraphs.

[1]  Georg Gottlob,et al.  Hypergraphs in Model Checking: Acyclicity and Hypertree-Width versus Clique-Width , 2001, SIAM J. Comput..

[2]  Georg Gottlob,et al.  Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width , 2001, PODS '01.

[3]  Georg Gottlob,et al.  Hypertree decompositions and tractable queries , 1998, PODS '99.

[4]  Phokion G. Kolaitis,et al.  Conjunctive-query containment and constraint satisfaction , 1998, PODS.

[5]  C. R. Ramakrishnan,et al.  Subsumption Algorithms Based on Search Trees , 1996, CAAP.

[6]  H. Gaifman.  On Local and Non-Local Properties , 1982 .

[7]  Oded Shmueli,et al.  Acyclic Hypergraph Projections , 1999, J. Algorithms.

[8]  Georg Gottlob,et al.  The complexity of acyclic conjunctive queries , 2001, JACM.

[9]  Peter M. G. Apers,et al.  Parallel evaluation of multi-join queries , 1995, SIGMOD '95.

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

[11]  Egon Wanke.  Bounded Tree-Width and LOGCFL , 1993, WG.

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

[13]  Anand Rajaraman,et al.  Conjunctive query containment revisited , 2000, Theor. Comput. Sci..

[14]  YannakakisMihalis,et al.  On the Desirability of Acyclic Database Schemes , 1983 .

[15]  Peter Jeavons,et al.  A Survey of Tractable Constraint Satisfaction Problems , 1997 .

[16]  Catriel Beeri,et al.  On the Desirability of Acyclic Database Schemes , 1983, JACM.

[17]  Jörg Flum,et al.  Query evaluation via tree-decompositions , 2001, JACM.

[18]  Eugene C. Freuder.  Complexity of K-Tree Structured Constraint Satisfaction Problems , 1990, AAAI.

[19]  Philip A. Bernstein,et al.  Power of Natural Semijoins , 1981, SIAM J. Comput..

[20]  Georg Gottlob,et al.  Advanced Parallel Algorithms far Processing Acyclic Conjunctive Queries, Rules, and Constraints, , 2000 .

[21]  Anand Rajaraman,et al.  Conjunctive query containment revisited , 1997, Theor. Comput. Sci..

[22]  Georg Gottlob,et al.  On Tractable Queries and Constraints , 1999, DEXA.

[23]  Mihalis Yannakakis,et al.  Algorithms for Acyclic Database Schemes , 1981, VLDB.

[24]  Georg Gottlob,et al.  Computing LOGCFL certificates , 1999, Theor. Comput. Sci..

[25]  Christophe Lecoutre.  Constraint Networks , 1992 .

[26]  David S. Johnson,et al.  A Catalog of Complexity Classes , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[27]  Robert E. Tarjan,et al.  Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs , 1984, SIAM J. Comput..

[28]  Hans L. Bodlaender.  A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC '93.

[29]  Ronald Fagin,et al.  Degrees of acyclicity for hypergraphs and relational database schemes , 1983, JACM.

[30]  Marc Gyssens,et al.  A Decomposition Methodology for Cyclic Databases , 1982, Advances in Data Base Theory.

[31]  Ashok K. Chandra,et al.  Optimal implementation of conjunctive queries in relational data bases , 1977, STOC '77.

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

[33]  Moshe Y. Vardi.  The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.

[34]  Tomás Feder,et al.  The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory , 1999, SIAM J. Comput..

[35]  Robin Thomas,et al.  Graph Searching and a Min-Max Theorem for Tree-Width , 1993, J. Comb. Theory, Ser. B.

[36]  Paul D. Seymour,et al.  Graph Minors. II. Algorithmic Aspects of Tree-Width , 1986, J. Algorithms.

[37]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs VII: Graphs as Relational Structures , 1992, Theor. Comput. Sci..

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

[39]  Thomas Schwentick,et al.  When is the evaluation of conjunctive queries tractable? , 2001, STOC '01.

[40]  Marc Gyssens,et al.  Decomposing Constraint Satisfaction Problems Using Database Techniques , 1994, Artif. Intell..

[41]  Bruno Courcelle,et al.  Graph Rewriting: An Algebraic and Logic Approach , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[42]  Georg Gottlob,et al.  A Comparison of Structural CSP Decomposition Methods , 1999, IJCAI.

[43]  David Maier,et al.  The Theory of Relational Databases , 1983 .