@Article{Werner-PAMI07, IS = { zkontrolovano 30 Nov 2007 }, UPDATE = { 2007-07-24 }, author = {Werner, Tom{\'a}{\v s}}, title = {A Linear Programming Approach to Max-sum Problem: {A} Review}, journal = {IEEE Trans. Pattern Analysis and Machine Intelligence}, year = {2007}, volume = {29}, number = {7}, pages = {1165--1179}, month = {July}, publisher = {IEEE Computer Society}, address = {Los Alamitos, USA}, issn = {0162-8828}, keywords = {Markov random fields, undirected graphical models, constraint satisfaction, belief propagation, linear programming relaxation, max-sum, max-plus, max-product, supermodular optimization}, annote = {The max-sum labeling problem, defined as maximizing a sum of binary (i.e., pairwise) functions of discrete variables, is a general NP-hard optimization problem with many applications, such as computing the MAP configuration of a Markov random field. We review a not widely known approach to the problem, developed by Ukrainian researchers Schlesinger et al. in 1976, and show how it contributes to recent results, most importantly, those on the convex combination of trees and tree-reweighted max-product. In particular, we review Schlesinger et al.'s upper bound on the max-sum criterion, its minimization by equivalent transformations, its relation to the constraint satisfaction problem, the fact that this minimization is dual to a linear programming relaxation of the original problem, and the three kinds of consistency necessary for optimality of the upper bound. We revisit problems with Boolean variables and supermodular problems. We describe two algorithms for decreasing the upper bound. We present an example application for structural image analysis.}, project = {IST-004176 COSPAL}, psurl = { [article pdf], [slides pdf], [www page with software and links to cited papers] }, authorship = {100}, }