Probabilistic construction of deterministic algorithms: Approximating packing integer programs

Approximation algorithms for covering/packing integer programs

Given matrices A and B and vectors a, b, c and d, all with non-negative entries, we consider the problem of computing min{cx : x ∈ Z+, Ax ≥ a, Bx ≤ b, x ≤ d}. We give a bicriteria-approximation algorithm that, given ε ∈ (0, 1], finds a solution of cost O(ln(m)/ε) times optimal, meeting the covering constraints (Ax ≥ a) and multiplicity constraints (x ≤ d), and satisfying Bx ≤ (1 + ε)b + β, wher...

Approximating disjoint-path problems using packing integer programs

Truthful Unification Framework for Approximating Packing Integer Programs with Choices∗

One of the most interesting research directions within the field of algorithmic mechanism design revolves the study of hard combinatorial optimization problems. In this setting, many common techniques, which are broadly used by approximation algorithms, cannot be utilized as they violate certain monotonicity properties that are imperative for truthfulness. Consequently, it seems of the essence ...

Approximating Disjoint-Path Problems Using Greedy Algorithms and Packing Integer Programs

The edge and vertex-disjoint path problems together with their unsplittable flow generalization are NP-hard problems with a multitude of applications in areas such as routing, scheduling and bin packing. Given the hardness of the problems, we study polynomial-time approximation algorithms with bounded performance guarantees. We introduce techniques which yield new algorithms for a wide range of...

Approximating Semidefinite Packing Programs

In this paper we define semidefinite packing programs and describe an algorithm to approximately solve these problems. Semidefinite packing programs arise in many applications such as semidefinite programming relaxations for combinatorial optimization problems, sparse principal component analysis, and sparse variance unfolding techniques for dimension reduction. Our algorithm exploits the struc...