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Algorithms with large domination ratio Gregory Gutin
 

Summary: Algorithms with large domination ratio
Noga Alon
Gregory Gutin
Michael Krivelevich
Abstract
Let P be an optimization problem, and let A be an approximation algorithm for P.
The domination ratio domr(A, n) is the maximum real q such that the solution x(I)
obtained by A for any instance I of P of size n is not worse than at least a fraction q
of the feasible solutions of I. We describe a deterministic, polynomial time algorithm
with domination ratio 1-o(1) for the partition problem, and a deterministic, polynomial
time algorithm with domination ratio (1) for the MaxCut problem and for some far-
reaching extensions of it, including Max-r-Sat, for each fixed r. The techniques combine
combinatorial and probabilistic methods with tools from Harmonic Analysis.
Keywords: Combinatorial Optimization; Domination analysis; Approximation Algorithms
1 Introduction
Let P be an optimization problem, and let A be an approximation algorithm for P. The
domination ratio domr(A, n) is the maximum real q such that the solution x(I) obtained by
A for any instance I of P of size n is not worse than at least a fraction q of the feasible
solutions of I.
Initially, domination ratios were studied only for traveling salesman problem (TSP) heuris-

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University
Gutin, Gregory - Department of Computer Science, Royal Holloway, University of London

 

Collections: Computer Technologies and Information Sciences; Mathematics