proposing a robust designed facility location is one of the most effective ways to hedge against unexpected disruptions and failures in a transportation network system. this paper considers the combined facility location/network design problem with regard to transportation link disruptions and develops a mixed integer linear programming formulation to model it. with respect to the probability o...

A long-standing conjecture in Combinatorial Optimization is that the integrality gap of the Held-Karp LP relaxation for the Asymmetric Traveling Salesman Problem (ATSP) is a constant. In this paper, we give a simpler LP relaxation for the ASTP. The integrality gaps of this relaxation and of the Held-Karp relaxation are within a constant factor of each other. Our LP is simpler in the sense that ...

Linear programming (LP) relaxation is a common technique used to find good solutions to complex optimization problems. We present the method of “LP decoding”: applying LP relaxation to the problem of maximum-likelihood (ML) decoding. An arbitrary binary-input memoryless channel is considered. This treatment of the LP decoding method places our previous work on turbo codes [6] and low-density pa...

MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence between the LP pairwise auxiliary variables, and QP equivalent terms given b...

Correlation clustering is an exciting area of research in the fields of graphical models and image segmentation. In this article we study the linear programming (LP) relaxation corresponding to PlanarCC and the multi-cut LP relaxation which are two methods for correlation clustering. We demonstrate that they have equal value when optimized. This provides justification for the use of PlanarCC wh...

Maximum a-posteriori (MAP) estimation is an important task in many applications of probabilistic graphical models. Although finding an exact solution is generally intractable, approximations based on linear programming (LP) relaxation often provide good approximate solutions. In this paper we present an algorithm for solving the LP relaxation optimization problem. In order to overcome the lack ...

We present methods for constructing approximation algorithms to NP-hard optimization problems using linear programming (LP). We typically obtain an LP relaxation of the problem by formulating it as an integer linear program and dropping the integrality constraints. We then solve the LP relaxation exactly, and apply various rounding strategies (including randomized rounding and iterative roundin...

In lecture 19, we saw an LP relaxation based algorithm to solve the sparsest cut problem with an approximation guarantee of O(logn). In this lecture, we will show that the integrality gap of the LP relaxation is O(logn) and hence this is the best approximation factor one can get via the LP relaxation. We will also start developing an SDP relaxation based algorithm which provides an O( √ log n) ...

This paper studies how well the standard LP relaxation ap-proximates a k-ary constraint satisfaction problem (CSP) on label set[L]. We show that, assuming the Unique Games Conjecture, it achievesan approximation within O(k · logL) of the optimal approximation fac-tor. In particular we prove the following hardness result: let I be a k-aryCSP on label set [L] with constraints ...

According to [2], in this paper we discuss a new method to match two 3D shapes in a geometrically consistent way. We understand a matching as a diffemorphism and want to find the matching that minimizes the physical energy that is necessary to deform one shape into the other. Because of the fact that diffeomorphisms can be completely characterized by their graph, we propose an equivalent formul...