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Inapproximability Results for Sparsest Cut, Optimal Linear Arrangement, and Precedence Constrained Scheduling

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3 Author(s)
Christoph Ambuhl ; Liverpool Univ., Liverpool ; Monaldo Mastrolilli ; Ola Svensson

We consider (uniform) sparsest cut, optimal linear arrangement and the precedence constrained scheduling problem 1 |prec| SigmawjCj-So far, these three notorious NP-hard problems have resisted all attempts to prove inapproximability results. We show that they have no polynomial time approximation scheme (PTAS), unless NP-complete pmblems 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.

Published in:

Foundations of Computer Science, 2007. FOCS '07. 48th Annual IEEE Symposium on

Date of Conference:

21-23 Oct. 2007