Benoit Larose

Stable sets of maximal size in Kneser-type graphs

We introduce a family of vertex-transitive graphs with specified subgroups of automorphisms which generalise Kneser graphs, powers of complete graphs and Cayley graphs of permutations. We compute the stability ratio for a wide class of these. Under certain conditions we characterise their stable sets of maximal size.

Dualities for Constraint Satisfaction Problems

In a nutshell, a duality for a constraint satisfaction problem equates the existence of one homomorphism to the non-existence of other homomorphisms. In this survey paper, we give an overview of logical, combinatorial, and algebraic aspects of the following forms of duality for constraint satisfaction problems: finite duality, bounded pathwidth duality, and bounded treewidth duality.

TAYLOR TERMS, CONSTRAINT SATISFACTION AND THE COMPLEXITY OF POLYNOMIAL EQUATIONS OVER FINITE ALGEBRAS

We study the algorithmic complexity of determining whether a system of polynomial equations over a finite algebra admits a solution. We characterize, within various families of algebras, which of them give rise to an NP-complete problem and which yield a problem solvable in polynomial time. In particular, we prove a dichotomy result which encompasses the cases of lattices, rings, modules, quasigroups and also generalizes a result of Goldmann and Russell for groups [15].

Maximizing Supermodular Functions on Product Lattices, with Application to Maximum Constraint Satisfaction

Recently, a strong link has been discovered between supermodularity on lattices and tractability of optimization problems known as maximum constraint satisfaction problems. This paper strengthens this link. We study the problem of maximizing a supermodular function which is defined on a product of

Projectivity and independent sets in powers of graphs

n

Symmetric Datalog and Constraint Satisfaction Problems in Logspace

copies of a fixed finite lattice and given by an oracle. We exhibit a large class of finite lattices for which this problem can be solved in oracle-polynomial time in

The Complexity of the Extendibility Problem for Finite Posets

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On Normal Cayley Graphs and Hom-idempotent Graphs

. We also obtain new large classes of tractable maximum constraint satisfaction problems.

A Characterisation of First-Order Constraint Satisfaction Problems

We investigate the relationship between projectivity and the structure of maximal independent sets in powers of circular graphs, Kneser graphs and truncated simplices. 2002 Wiley Periodicals, Inc. J Graph Theory 40: 162– 171, 2002

The Complexity of the List Homomorphism Problem for Graphs

We introduce symmetric Datalog, a syntactic restriction of linear Datalog and show that its expressive power is exactly that of restricted symmetric Krom monotone SNP. The deep result of Reingold [17] on the complexity of undirected connectivity suffices to show that symmetric Datalog queries can be evaluated in logarithmic space. We show that for a number of constraint languages Gamma, the complement of the constraint satisfaction problem CSP(Gamma) can be expressed in symmetric Datalog. In particular, we show that if CSP(Gamma) is first-order definable and Lambda is a finite subset of the relational clone generated by Gamma then notCSP(Lambda) is definable in symmetric Datalog. Over the two-element domain and under standard complexity-theoretic assumptions, expressibility of notCSP(Gamma) in symmetric Datalog corresponds exactly to the class of CSPs computable in logarithmic space. Finally, we describe a fairly general subclass of implicational (or 0/1/all) constraints for which the complement of the corresponding CSP is also definable in symmetric Datalog. Our results provide preliminary evidence that symmetric Datalog may be a unifying explanation for families of CSPs lying in L.