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Providence, Rhode Island

Oct. 21, 2007 to Oct. 23, 2007

ISBN: 0-7695-3010-9

pp: 329-337

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2007.40

ABSTRACT

We consider (Uniform) Sparsest Cut, Optimal Linear Arrangement and the precedence constrained scheduling problem 1\left| {prec} \right|\sum {w_j C_j }. So far, these three notorious NPhard problems have resisted all attempts to prove inapproximability results. We show that they have no Polynomial Time Approximation Scheme (PTAS), unless NP-complete problems can be solved in randomized subexponential time. Furthermore, we prove that the scheduling problem is as hard to approximate as Vertex Cover when the so-called fixed cost, that is present in all feasible solutions, is subtracted from the objective function.

INDEX TERMS

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CITATION

Christoph Ambühl,
Monaldo Mastrolilli,
Ola Svensson,
"Inapproximability Results for Sparsest Cut, Optimal Linear Arrangement, and Precedence Constrained Scheduling",

*FOCS*, 2007, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2007, pp. 329-337, doi:10.1109/FOCS.2007.40