Approximate fixed-rank closures of covering problems

Approximate fixed-rank closures of covering problems

Consider a 0/1 integer program min{c T x : Ax ≥ b, x ∈ {0, 1} n } where A is nonnegative. We show that if the number of minimal covers of Ax ≥ b is polynomially bounded, then there is a polynomially large lift-and-project relaxation whose value is arbitrarily close to being at least as good as that given by the rank ≤ q cuts, for any fixed q. A special case of this result is that given by set-c...

Approximate solution of nonlinear inverse problems by fixed-point iteration

In this paper we propose a derivative-free iterative method for the approximate solution of a nonlinear inverse problem Fx = y. In this method the iterations are defined as Gxk+1 = Gxk +(Sy−SFxk), where G is an easily invertible operator and S is an operator from a data space to a solution space. We give general suggestions for the choice of operators G and S and show a practically relevant exa...

Algorithms for approximate k-covering

Computing approximate patterns in strings or sequences has important applications in DNA sequence analysis, data compression, musical text analysis, and so on. In this paper, we introduce approximate k-covers and study them under various commonly used distance measures. We propose the following problem: “Given a string x of length n, a set U of m strings of length k, and a distance measure, com...

Covering Problems

Computing fixed closures in free groups

Let F be a finitely generated free group. We present an algorithm such that, given a subgroup H 6 F , decides whether H is the fixed subgroup of some family of automorphisms, or family of endomorphisms of F and, in the affirmative case, finds such a family. The algorithm combines both combinatorial and geometric methods.