Efficient algorithms for counting parameterized list H-colorings

Algorithms to Approximately Count and Sample Conforming Colorings of Graphs

Conforming colorings naturally generalize many graph theory structures, including independent sets, vertex colorings, list colorings, H-colorings and adapted colorings. Given a multigraph G and a function F that assigns a forbidden ordered pair of colors to each edge e, we say a coloring C of the vertices is conforming to F if, for all e = (u, v), F (e) 6= (C(u), C(v)). We consider Markov chain...

Fixed Parameter Algorithms for Counting and Deciding Bounded Restrictive List H-Colorings

Improved FPTAS for Multi-spin Systems

We design deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function for a class of multi-spin systems, extending the known approximable regime by an exponential scale. As a consequence, we have an FPTAS for the Potts models with inverse temperature β up to a critical threshold |β| = O( 1 ∆ ) where ∆ is the maximum degree, confirming a conjecture in [1...

Community Structure Inspired Algorithms for SAT and #SAT

We introduce h-modularity, a structural parameter of CNF formulas, and present algorithms that render the decision problem SAT and the model counting problem #SAT fixed-parameter tractable when parameterized by h-modularity. The new parameter is defined in terms of a partition of clauses of the given CNF formula into strongly interconnected communities which are sparsely interconnected with eac...

The Complexity of Parameterized H - Colorings

We survey recent results on the complexity of several versions of the H-coloring and the list-H-coloring problems that are amenable to param-eterization.