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
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