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### Paper:

TR03-051 | 20th June 2003 00:00

#### The Relative Complexity of Local Search Heuristics and the Iteration Principle

TR03-051
Authors: Tsuyoshi Morioka
Publication: 30th June 2003 18:14
Keywords:

Abstract:

Johnson, Papadimitriou and Yannakakis introduce the class $\PLS$
consisting of optimization problems for which efficient local-
search heuristics exist. We formulate a type-2 problem $\iter$
that characterizes $\PLS$ in style of Beame et al., and prove
a criterion for type-2 problems to be nonreducible to $\iter$.
As a corollary, we obtain the first relative separation of $\PLS$
from Papadimitriou's classes $\PPA$, $\PPAD$, $\PPADS$, and
$\PPP$. Based on the criterion, we derive a special case of Riis's
\emph{independence criterion} for the Bounded Arithmetic theory
$S^2_2(L)$. We also prove that $\PLS$ is closed under Turing
reducibility.

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