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2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2007)
Providence, Rhode Island
Oct. 21, 2007 to Oct. 23, 2007
ISSN: 0272-5428
ISBN: 0-7695-3010-9
pp: 329-337
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.
Christoph Ambühl, Monaldo Mastrolilli, Ola Svensson, "Inapproximability Results for Sparsest Cut, Optimal Linear Arrangement, and Precedence Constrained Scheduling", 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, vol. 00, no. , pp. 329-337, 2007, doi:10.1109/FOCS.2007.40
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