Can you beat treewidth?

: It is well-known that constraint satisfaction problems (CSP) over an unbounded domain can be solved in time nO(k) if the treewidth of the primal graph of the instance is at most k and n is the size of the input. We show that no algorithm can be significantly better than this treewidth-based algorithm, even if we restrict the problem to some special class of primal graphs. Formally, let G be a recursively enumerable class of graphs and assume that there is an algorithm A solving binary CSP (i. e., CSP where every constraint involves two variables) for instances whose primal graph is in G. We prove that if the running time of A is f(G)no(k/logk), where k is the treewidth of the primal graph G and f is an arbitrary function, then the Exponential Time Hypothesis (ETH) fails. We prove the result also in the more general framework of the homomorphism problem for bounded-arity relational structures. For this problem, the treewidth of the core of the left-hand side structure plays the same ...

• Type: Conference
• Year: 2007
• Where: FOCS
• Authors: Dániel Marx
• Keywords: Constraint Satisfaction Problems, FOCS 2007, Primal Graph, Theoretical Computer Science, Treewidth