A linear time approximation algorithm for permutation flow shop scheduling
In the last 40 years, the permutation flow shop scheduling (PFS) problem with makespan minimization has been a central problem, known for its intractability, that has been well studied from both theoretical and practical aspects. The currently best performance ratio of a deterministic approximation algorithm for the PFS was recently presented by Nagarajan and Sviridenko, using a connection between the PI'S and the longest increasing subsequence problem. In a different and independent way, this paper employs monotone subsequences in the approximation analysis techniques. To do this, an extension of the Erdos-Szekeres theorem to weighted monotone subsequences is presented. The result is a simple deterministic algorithm for the PFS with a similar approximation guarantee, but a much lower time complexity. (C) 2011 Elsevier B.V. All rights reserved.
approximation algorithms permutation flow shop scheduling erdos-szekeres theorem