Computer Science Colloquia: Sun, Jan 22 at 11:00 - Eden Chlamtac
Niv Buchbinder
Dear all,
Next week we are happy to have Eden Chlamtac from Computer Science department, Tel-Aviv University.
You can view the upcoming talks of the seminar at:
See you,
Niv Buchbinder.
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Computer Science Colloquia - Open University of Israel
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Time: Sunday, January 22, at 11:00-12:00
Place: Visitor center 194, Open University.
Speaker: Eden Chlamtac, Computer Science department, Tel-Aviv University.-------
Title: Convex Programming Hierarchies: Trading Time for Approximation.
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Abstract:
Linear programming (LP) and semidefinite programming (SDP) are powerful convex optimization tools which have become ubiquitous in the field of approximation algorithms in the last few decades. Given a combinatorial optimization problem (e.g. Maximum Independent Set), a standard approach to obtain an approximation algorithm is as follows:
formulate the problem as an integer program (IP), relax this formulation to an LP or SDP, solve the relaxation, and then "round" the solution back to an integer solution.
This approach is limited by how well the convex program (LP or SDP) approximates the original IP formulation, i.e. the integrality gap. One way to circumvent this limitation is through hierarchies of convex programs, which give a systematic way of iteratively strengthening any relaxation (at the cost of increased running time to solve it), so that the integrality gap gradually decreases.
While initially, most of the literature on hierarchies in the context of approximation algorithms had focused on impossibility results, there has been a surprising surge of recent positive results. I will survey this recent development, by describing a number of combinatorial optimization problems for which we have been able to achieve improved approximations using hierarchies.