Near Unanimity Constraints Have Bounded Pathwidth Duality

We show that if a finite relational structure has a near unanimity polymorphism, then the constraint satisfaction problem with that structure as its fixed template has bounded pathwidth duality, putting the problem in nondeterministic logspace. This generalizes the analogous result of Dalmau and Krokhin for majority polymorphisms and lends further support to a conjecture suggested by Larose and Tesson.

[1]  Neil Immerman,et al.  The Complexity of Satisfiability Problems: Refining Schaefer's Theorem , 2005, MFCS.

[2]  Paul D. Seymour,et al.  Graph minors. I. Excluding a forest , 1983, J. Comb. Theory, Ser. B.

[3]  Xuding Zhu,et al.  Duality and Polynomial Testing of Tree Homomorphisms , 1996 .

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

[5]  L. A. Kaluzhnin,et al.  Galois theory for post algebras. I , 1969 .

[6]  Peter Jeavons,et al.  Classifying the Complexity of Constraints Using Finite Algebras , 2005, SIAM J. Comput..

[7]  B. Larose,et al.  Bounded width problems and algebras , 2007 .

[8]  Andrei A. Bulatov.  A graph of a relational structure and constraint satisfaction problems , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

[9]  Libor Barto,et al.  Congruence Distributivity Implies Bounded Width , 2009, SIAM J. Comput..

[10]  B. Mohar,et al.  Graph Minors , 2009 .

[11]  Pascal Tesson,et al.  Universal algebra and hardness results for constraint satisfaction problems , 2009, Theor. Comput. Sci..

[12]  Ivan Hal Sudborough,et al.  The Vertex Separation and Search Number of a Graph , 1994, Inf. Comput..

[13]  Stanley Burris,et al.  A course in universal algebra , 1981, Graduate texts in mathematics.

[14]  D. Hobby,et al.  The structure of finite algebras , 1988 .

[15]  Víctor Dalmau,et al.  Linear datalog and bounded path duality of relational structures , 2005, Log. Methods Comput. Sci..

[16]  Libor Barto,et al.  Constraint Satisfaction Problems of Bounded Width , 2009, 2009 50th Annual IEEE Symposium on Foundations of Computer Science.

[17]  Jeffrey D. Uuman.  Principles of database and knowledge- base systems , 1989 .

[18]  Desmond Fearnley-Sander,et al.  Universal Algebra , 1982 .

[19]  K. A. Baker,et al.  Polynomial interpolation and the Chinese Remainder Theorem for algebraic systems , 1975 .

[20]  Jaroslav Nesetril,et al.  Complexity of Tree Homomorphisms , 1996, Discret. Appl. Math..

[21]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[22]  Víctor Dalmau,et al.  Constraint Satisfaction Problems in Non-deterministic Logarithmic Space , 2002, ICALP.

[23]  D. Geiger.  CLOSED SYSTEMS OF FUNCTIONS AND PREDICATES , 1968 .

[24]  M. Maróti,et al.  Existence theorems for weakly symmetric operations , 2008 .

[25]  Andrei A. Krokhin,et al.  Solving Order Constraints in Logarithmic Space , 2003, STACS.

[26]  Marc Gyssens,et al.  How to Determine the Expressive Power of Constraints , 1999, Constraints.

[27]  Andrei A. Krokhin,et al.  Majority constraints have bounded pathwidth duality , 2008, Eur. J. Comb..

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

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

[30]  Libor Barto,et al.  Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem , 2012, Log. Methods Comput. Sci..

[31]  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..

[32]  Phokion G. Kolaitis,et al.  Conjunctive-Query Containment and Constraint Satisfaction , 2000, J. Comput. Syst. Sci..

[33]  Jeffrey D. Ullman,et al.  Principles of Database and Knowledge-Base Systems, Volume II , 1988, Principles of computer science series.

[34]  Jaroslav Nesetril,et al.  Graphs and homomorphisms , 2004, Oxford lecture series in mathematics and its applications.

[35]  Stephen A. Cook,et al.  Storage Requirements for Deterministic Polynomial Time Recognizable Languages , 1976, J. Comput. Syst. Sci..

[36]  L. Barto.  Finitely Related Algebras in Congruence Distributive Varieties Have Near Unanimity Terms , 2013, Canadian Journal of Mathematics.

[37]  Benoît Larose,et al.  Omitting Types, Bounded Width and the Ability to Count , 2009, Int. J. Algebra Comput..