Given a linear code and observations from a noisy channel, the decoding problem is to determine the most likely (ML) codeword. We describe a method for approximate ML decoding of an arbitrary binary linear code, based on a linear programming (LP) relaxation that is defined by a factor graph or parity check representation of the code. The resulting LP decoder, which generalizes our previous work...

The $p$-center problem (pCP) is a fundamental in location science, where we are given customer demand points and possible facility locations, want to choose $p$ of these locations open such that the maximum distance any point its closest minimized. State-of-the-art solution approaches pCP use connection set cover solve an iterative fashion by repeatedly solving problems. classical textbook inte...

This paper discusses the graph covering problem in which a set of edges in an edgeand nodeweighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large integrality gap of a natural linear programming (LP) relaxation, LP rounding algorithms based on the relaxation yield poor performance. Here we propose a stronger LP ...

Consider the relaxation of an integer programming (IP) problem in which the feasible region is replaced by the intersection of the linear programming (LP) feasible region and the corner polyhedron for a particular LP basis. Recently a primal-dual ascent algorithm has been given for solving this relaxation. Given an optimal solution of this relaxation, we state criteria for selecting a new LP ba...

Primal-dual algorithms have played an integral role in recent developments in approximation algorithms, and yet there has been little work on these algorithms in the context of LP relaxations that have been strengthened by the addition of more sophisticated valid inequalities. We introduce primal-dual schema based on the LP relaxations devised by Carr, Fleischer, Leung & Phillips for the minimu...

We propose a new integer-linear programming model for the delete relaxation in cost-optimal planning. While a naive formulation of the delete relaxation as IP is impractical, our model incorporates landmarks and relevance-based constraints, resulting in an IP that can be used to directly solve the delete relaxation. We show that our IP model outperforms the previous state-of-the-art solver for ...

AbstractThe Matching Augmentation Problem (MAP) has recently received significant attention as an important step towards better approximation algorithms for finding cheap 2-edge connected subgraphs. This culminated in a \(\frac{5}{3}\)-approximation algorithm. However, the algorithm and its analysis are fairly involved do not compare against problem’s well-known LP relaxation called cut LP.In t...

In this work, we prove several relations between three different energy minimization techniques. A recently proposed methods for determining a provably optimal partial assignment of variables by Ivan Kovtun (IK), the linear programming relaxation approach (LP) and the popular expansion move algorithm by Yuri Boykov. We propose a novel sufficient condition of optimal partial assignment, which is...