233 research outputs found
Exact Algorithm for Graph Homomorphism and Locally Injective Graph Homomorphism
For graphs and , a homomorphism from to is a function , which maps vertices adjacent in to adjacent vertices
of . A homomorphism is locally injective if no two vertices with a common
neighbor are mapped to a single vertex in . Many cases of graph homomorphism
and locally injective graph homomorphism are NP-complete, so there is little
hope to design polynomial-time algorithms for them. In this paper we present an
algorithm for graph homomorphism and locally injective homomorphism working in
time , where is the bandwidth of the
complement of
Low-level dichotomy for Quantified Constraint Satisfaction Problems
Building on a result of Larose and Tesson for constraint satisfaction
problems (CSP s), we uncover a dichotomy for the quantified constraint
satisfaction problem QCSP(B), where B is a finite structure that is a core.
Specifically, such problems are either in ALogtime or are L-hard. This involves
demonstrating that if CSP(B) is first-order expressible, and B is a core, then
QCSP(B) is in ALogtime.
We show that the class of B such that CSP(B) is first-order expressible
(indeed, trivially true) is a microcosm for all QCSPs. Specifically, for any B
there exists a C such that CSP(C) is trivially true, yet QCSP(B) and QCSP(C)
are equivalent under logspace reductions
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