The problem of obtaining the maximum a posteriori estimate of a general discrete Markov random field (i.e., a Markov random field defined using a discrete set of labels) is known to be NP-hard. However, due to its central importance in many applications, several approximation algorithms have been proposed in the literature. In this paper, we present an analysis of three such algorithms based on...

We study the problem of hierarchical clustering on planar graphs. We formulate this in terms of an LP relaxation of ultrametric rounding. To solve this LP efficiently we introduce a dual cutting plane scheme that uses minimum cost perfect matching as a subroutine in order to efficiently explore the space of planar partitions. We apply our algorithm to the problem of hierarchical image segmentat...

We study techniques, approximation algorithms, structural properties and lower bounds related to applications of linear programs in combinatorial optimization. The following Steiner tree problem is central: given a graph with a distinguished subset of required vertices, and costs for each edge, find a minimum-cost subgraph that connects the required vertices. We also investigate the areas of ne...

We study the metric s-t path Traveling Salesman Problem (TSP). [An, Kleinberg, and Shmoys, STOC 2012] improved on the long standing 5 3 -approximation factor and presented an algorithm that achieves an approximation factor of 1+ √ 5 2 ≈ 1.61803. Later [Sebő, IPCO 2013] further improved the approximation factor to 85 . We present a simple, self-contained analysis that unifies both results; our m...

Many recent planning heuristics are based on LP optimization. However, planning experts mostly use LP solvers as a black box and it is often not obvious to them which LP techniques would be most suitable for their specific applications. To foster the communication between the planning and the optimization community, this paper gives an easily accessible overview over these recent LP-based heuri...

We consider an LP relaxation for ATSP. We introduce concepts of high-value and high-flow cycles in LP basic solutions and show that the existence of this kind of cycles would lead to constant-factor approximation algorithms for ATSP. The existence of high-flow cycles is motivated by computational results and theoretical observations. (

Approximating integer linear programs by solving a relaxation to a linear program (LP) and afterwards reconstructing an integer solution from the fractional one is a standard technique in a non-distributed scenario. Surprisingly, the method has not often been applied for distributed algorithms. In this paper, we show that LP relaxation is a powerful technique also to obtain fast distributed app...

Typical behavior of the linear programming problem (LP) is studied as a relaxation of the minimum vertex cover problem, which is a type of the integer programming problem (IP). To deal with the LP and IP by statistical mechanics, a lattice-gas model on the Erdös-Rényi random graphs is analyzed by a replica method. It is found that the LP optimal solution is typically equal to that of the IP bel...

The lift-and-project closure is the relaxation obtained by computing all lift-and-project cuts from the initial formulation of a mixed integer linear program or equivalently by computing all mixed integer Gomory cuts read from all tableau’s corresponding to feasible and infeasible bases. In this paper, we present an algorithm for approximating the value of the lift-and-project closure. The orig...