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A new way of using semidefinite programming with applications to linear equations mod p
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.ORCID iD: 0000-0002-5379-345X
2001 (English)In: Journal of Algorithms, ISSN 0196-6774, E-ISSN 1090-2678, Vol. 39, no 2, 162-204 p.Article in journal (Refereed) Published
Abstract [en]

We introduce a new method of constructing approximation algorithms for combinatorial optimization problems using semidefinite programming. It consists of expressing each combinatorial object in the original problem as a constellation of vectors in the semidefinite program. When we apply this technique to systems of linear equations mod p with at most two variables in each equation, we can show that the problem is approximable within (1 - kappa (p))p, where kappa (p)> 0 for all p. Using standard techniques we also show that it is NP-hard to approximate the problem within a constant ratio, independent of p.

Place, publisher, year, edition, pages
2001. Vol. 39, no 2, 162-204 p.
Keyword [en]
approximation algorithms, linear equations, lower bounds, NP-hard optimization problems, semidefinite programming, improved approximation algorithms, cut
Identifiers
URN: urn:nbn:se:kth:diva-20556ISI: 000168309000003OAI: oai:DiVA.org:kth-20556DiVA: diva2:339252
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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Håstad, Johan

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