TY - GEN

T1 - Computer assisted proof of optimal approximability results

AU - Zwick, Uri

PY - 2002

Y1 - 2002

N2 - We obtain computer assisted proofs of several spherical volume inequalities that appear in the analysis of semidennite programrning based approximation algorithms for Boolean constraint satisfaction problems. These inequalities imply, in particular, that the performance ratio achieved by the MAX 3-SAT approximation algorithm of Karloff and Zwick is indeed 7/8, as conjectured by them, and that the performance ratio of the MAX 3-CSP algorithm of the author is indeed 1/2. Other results are also implied. The computer assisted proofs are obtained using a system called Real Search, written by the author. This system uses interval arithmetic to produce rigorous proofs that certain collections of constraints in real variables have no real solution.

AB - We obtain computer assisted proofs of several spherical volume inequalities that appear in the analysis of semidennite programrning based approximation algorithms for Boolean constraint satisfaction problems. These inequalities imply, in particular, that the performance ratio achieved by the MAX 3-SAT approximation algorithm of Karloff and Zwick is indeed 7/8, as conjectured by them, and that the performance ratio of the MAX 3-CSP algorithm of the author is indeed 1/2. Other results are also implied. The computer assisted proofs are obtained using a system called Real Search, written by the author. This system uses interval arithmetic to produce rigorous proofs that certain collections of constraints in real variables have no real solution.

UR - http://www.scopus.com/inward/record.url?scp=79955718215&partnerID=8YFLogxK

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AN - SCOPUS:79955718215

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 496

EP - 505

BT - Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002

PB - Association for Computing Machinery

T2 - 13th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2002

Y2 - 6 January 2002 through 8 January 2002

ER -