TY - GEN

T1 - Optimal long code test with one free bit

AU - Bansal, Nikhil

AU - Khot, Subhash

PY - 2009

Y1 - 2009

N2 - For arbitrarily small constants ε, δ > 0, we present a long code test with one free bit, completeness 1 - ε and soundness δ. Using the test, we prove the following two inapproximability results: 1) Assuming the Unique Games Conjecture of Khot [15], given an n-vertex graph that has two disjoint independent sets of size (1/2 - ε)n each, it is NP-hard to find an independent set of size δn. 2) Assuming a (new) stronger version of the Unique Games Conjecture, the scheduling problem of minimizing weighted completion time with precedence constraints is inapprox-imable within factor 2 - ε.

AB - For arbitrarily small constants ε, δ > 0, we present a long code test with one free bit, completeness 1 - ε and soundness δ. Using the test, we prove the following two inapproximability results: 1) Assuming the Unique Games Conjecture of Khot [15], given an n-vertex graph that has two disjoint independent sets of size (1/2 - ε)n each, it is NP-hard to find an independent set of size δn. 2) Assuming a (new) stronger version of the Unique Games Conjecture, the scheduling problem of minimizing weighted completion time with precedence constraints is inapprox-imable within factor 2 - ε.

UR - http://www.scopus.com/inward/record.url?scp=77952368191&partnerID=8YFLogxK

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U2 - 10.1109/FOCS.2009.23

DO - 10.1109/FOCS.2009.23

M3 - Conference contribution

AN - SCOPUS:77952368191

SN - 9780769538501

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 453

EP - 462

BT - Proceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009

T2 - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009

Y2 - 25 October 2009 through 27 October 2009

ER -