Approximating Semidefinite Packing Programs

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...

Approximating Quadratic Programs with Semidefinite Relaxations

Given an arbitrary matrix A in which all of the diagonal elements are zero, we would like to find x1, x2, . . . , xn ∈ {−1, 1} such that ∑n i=1 ∑n j=1 aijxixj is maximized. This problem has an important application in correlation clustering, and is also related to the well-known inequality of Grothendieck in functional analysis. While solving quadratic programs is NP-hard, we can approximate th...

Approximating Semidefinite Programs in Sublinear Time

In recent years semidefinite optimization has become a tool of major importance in various optimization and machine learning problems. In many of these problems the amount of data in practice is so large that there is a constant need for faster algorithms. In this work we present the first sublinear time approximation algorithm for semidefinite programs which we believe may be useful for such p...

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 ...