 
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 1o(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 MaxrSat, 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
