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Are Stable Instances Easy?

Published online by Cambridge University Press:  26 July 2012

YONATAN BILU  and
NATHAN LINIAL
YONATAN BILU
Affiliation:
Mobileye Vision Technologies Ltd, 13 Hartom Street, PO Box 45157, Jerusalem, 91450Israel (e-mail: [email protected])
NATHAN LINIAL
Affiliation:
Institute of Computer Science, Hebrew University, Jerusalem 91904, Israel (e-mail: [email protected])
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Abstract

We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP-hard problems are easier to solve, and in particular, whether there exist algorithms that solve in polynomial time all sufficiently stable instances of some NP-hard problem. The paper focuses on the Max-Cut problem, for which we show that this is indeed the case.

Keywords

Primary 68Q17Secondary 05C50
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 5 , September 2012 , pp. 643 - 660
Copyright
Copyright © Cambridge University Press 2012

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