3,056 research outputs found
The complexity of weighted and unweighted #CSP
We give some reductions among problems in (nonnegative) weighted #CSP which
restrict the class of functions that needs to be considered in computational
complexity studies. Our reductions can be applied to both exact and approximate
computation. In particular, we show that a recent dichotomy for unweighted #CSP
can be extended to rational-weighted #CSP.Comment: 11 page
Metric Construction, Stopping Times and Path Coupling
In this paper we examine the importance of the choice of metric in path
coupling, and the relationship of this to \emph{stopping time analysis}. We
give strong evidence that stopping time analysis is no more powerful than
standard path coupling. In particular, we prove a stronger theorem for path
coupling with stopping times, using a metric which allows us to restrict
analysis to standard one-step path coupling. This approach provides insight for
the design of non-standard metrics giving improvements in the analysis of
specific problems.
We give illustrative applications to hypergraph independent sets and SAT
instances, hypergraph colourings and colourings of bipartite graphs.Comment: 21 pages, revised version includes statement and proof of general
stopping times theorem (section 2.2), and additonal remarks in section
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