169,331 research outputs found
Distance Constraint Satisfaction Problems
We study the complexity of constraint satisfaction problems for templates
that are first-order definable in , the integers with
the successor relation. Assuming a widely believed conjecture from finite
domain constraint satisfaction (we require the tractability conjecture by
Bulatov, Jeavons and Krokhin in the special case of transitive finite
templates), we provide a full classification for the case that Gamma is locally
finite (i.e., the Gaifman graph of has finite degree). We show that
one of the following is true: The structure Gamma is homomorphically equivalent
to a structure with a d-modular maximum or minimum polymorphism and
can be solved in polynomial time, or is
homomorphically equivalent to a finite transitive structure, or
is NP-complete.Comment: 35 pages, 2 figure
Random Constraint Satisfaction Problems
Random instances of constraint satisfaction problems such as k-SAT provide
challenging benchmarks. If there are m constraints over n variables there is
typically a large range of densities r=m/n where solutions are known to exist
with probability close to one due to non-constructive arguments. However, no
algorithms are known to find solutions efficiently with a non-vanishing
probability at even much lower densities. This fact appears to be related to a
phase transition in the set of all solutions. The goal of this extended
abstract is to provide a perspective on this phenomenon, and on the
computational challenge that it poses
Robustly Solvable Constraint Satisfaction Problems
An algorithm for a constraint satisfaction problem is called robust if it
outputs an assignment satisfying at least -fraction of the
constraints given a -satisfiable instance, where
as . Guruswami and
Zhou conjectured a characterization of constraint languages for which the
corresponding constraint satisfaction problem admits an efficient robust
algorithm. This paper confirms their conjecture
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