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A New Rounding Procedure for the Assignment Problem with Applications to Dense Graph
 

Summary: A New Rounding Procedure for the Assignment
Problem with Applications to Dense Graph
Arrangement Problems #
Sanjeev Arora + Alan Frieze # Haim Kaplan §
June 6, 2002
Abstract
We present a randomized procedure for rounding fractional perfect matchings
to (integral) matchings. If the original fractional matching satisfies any linear in­
equality, then with high probability, the new matching satisfies that linear inequal­
ity in an approximate sense. This extends the well­known LP rounding procedure
of Raghavan and Thompson, which is usually used to round fractional solutions
of linear programs.
We use our rounding procedure to design an additive approximation algorithm
to the Quadratic Assignment Problem. The approximation error of the algorithm
is #n 2 and it runs in n O(log n/# 2 ) time.
We also describe Polynomial Time Approximation Schemes (PTASs) for dense
subcases of many well­known NP­hard arrangement problems, including mini­
mum linear arrangement, minimum cut linear arrangement, maximum
acyclic subgraph, and betweenness.
# Preliminary version of this paper appeared in the proceedings of the IEEE Symposium on Founda­

  

Source: Arora, Sanjeev - Department of Computer Science, Princeton University

 

Collections: Computer Technologies and Information Sciences