Related papers: On the exactness of the cavity method for Weighted…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
We study the classical weighted perfect matchings problem for bipartite graphs or sometimes referred to as the assignment problem, i.e., given a weighted bipartite graph $G = (U\cup V,E)$ with weights $w : E \rightarrow \mathcal{R}$ we are…
The graph matching problem aims to discover a latent correspondence between the vertex sets of two observed graphs. This problem has proven to be quite challenging, with few satisfying methods that are computationally tractable and widely…
The random assignment problem asks for the minimum-cost perfect matching in the complete $n\times n$ bipartite graph $\Knn$ with i.i.d. edge weights, say uniform on $[0,1]$. In a remarkable work by Aldous (2001), the optimal cost was shown…
The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…
Consider a real line equipped with a (not necessarily intrinsic) distance. We deal with the minimum-weight perfect matching problem for a complete graph whose points are located on the line and whose edges have weights equal to distances…
A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018)…
This paper addresses the Graph Matching problem, which consists of finding the best possible alignment between two input graphs, and has many applications in computer vision, network deanonymization and protein alignment. A common approach…
Belief propagation (BP) is a powerful tool to solve distributed inference problems, though it is limited by short cycles in the corresponding factor graph. Such cycles may lead to incorrect solutions or oscillatory behavior. Only for…
We investigate the question of tightness of linear programming (LP) relaxation for finding a maximum weight independent set (MWIS) in sparse random weighted graphs. We show that an edge-based LP relaxation is asymptotically tight for…
A statistical-mechanical study of the effect of constraint relaxation on the minimum vertex cover problem in Erd\H{o}s-R\'enyi random graphs is presented. Using a penalty-method formulation for constraint relaxation, typical properties of…
We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The…
In this paper we rigorously prove the validity of the cavity method for the problem of counting the number of matchings in graphs with large girth. Cavity method is an important heuristic developed by statistical physicists that has lead to…
The profile-based matching problem is the problem of finding a matching that optimizes profile from an instance $(G, r, \langle u_1, \dots, u_r \rangle)$, where $G$ is a bipartite graph $(A \cup B, E)$, $r$ is the number of utility…
Using the theory of negative association for measures and the notion of random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically…
Finding an optimal matching in a weighted graph is a standard combinatorial problem. We consider its semi-bandit version where either a pair or a full matching is sampled sequentially. We prove that it is possible to leverage a rank-1…
Given a bipartite graph $G(V= (A \cup B),E)$ with $n$ vertices and $m$ edges and a function $b \colon V \to \mathbb{Z}_+$, a $b$-matching is a subset of edges such that every vertex $v \in V$ is incident to at most $b(v)$ edges in the…
The matching problem plays a basic role in combinatorial optimization and in statistical mechanics. In its stochastic variants, optimization decisions have to be taken given only some probabilistic information about the instance. While the…
Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…