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As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to…
Low-rank matrix completion is an important problem with extensive real-world applications. When observations are uniformly sampled from the underlying matrix entries, existing methods all require the matrix to be incoherent. This paper…
Point matching refers to the process of finding spatial transformation and correspondences between two sets of points. In this paper, we focus on the case that there is only partial overlap between two point sets. Following the approach of…
In $k$-hypergraph matching, we are given a collection of sets of size at most $k$, each with an associated weight, and we seek a maximum-weight subcollection whose sets are pairwise disjoint. More generally, in $k$-hypergraph $b$-matching,…
We reprove that all the matchings constructed during Edmonds' weighted perfect matching algorithm are optimal among those of the same cardinality (provided that certain mild restrictions are obeyed on the choices the algorithm makes). We…
In this paper, we study a set of combinatorial optimization problems on weighted graphs: the shortest path problem with negative weights, the weighted perfect bipartite matching problem, the unit-capacity minimum-cost maximum flow problem…
Finding large or heavy matchings in graphs is a ubiquitous combinatorial optimization problem. In this paper, we engineer the first non-trivial implementations for approximating the dynamic weighted matching problem. Our first algorithm is…
Logic programs, more specifically, Answer-set programs, can be annotated with probabilities on facts to express uncertainty. We address the problem of propagating weight annotations on facts (eg probabilities) of an ASP to its standard…
We consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. In this problem, we are given an undirected graph. Each edge is assigned a known, independent probability of existence and…
In 2016, Chandrasekaran, V\'egh, and Vempala published a method to solve the minimum-cost perfect matching problem on an arbitrary graph by solving a strictly polynomial number of linear programs. However, their method requires a strong…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…
Let G be an edge-weighted hypergraph on n vertices, m edges of size \le s, where the edges have real weights in an interval [1,W]. We show that if we can approximate a maximum weight matching in G within factor alpha in time T(n,m,W) then…
The aims of this article are two-fold. First, we give a geometric characterization of the optimal basic solutions of the general linear programming problem (no compactness assumptions) and provide a simple, self-contained proof of it…
We pursue a study of the Generalized Demand Matching problem, a common generalization of the $b$-Matching and Knapsack problems. Here, we are given a graph with vertex capacities, edge profits, and asymmetric demands on the edges. The goal…
Let $G=(V, E)$ be a given edge-weighted graph and let its {\em realization} $\mathcal{G}$ be a random subgraph of $G$ that includes each edge $e \in E$ independently with probability $p$. In the {\em stochastic matching} problem, the goal…
Two related online problems: knapsack and truthful bipartite matching are considered. For these two problems, the common theme is how to `match' an arriving left vertex in an online fashion with any of the available right vertices, if at…
Linear Programming (LP) relaxations have become powerful tools for finding the most probable (MAP) configuration in graphical models. These relaxations can be solved efficiently using message-passing algorithms such as belief propagation…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
This paper is motivated by two applications, namely i) generalizations of cuckoo hashing, a computationally simple approach to assigning keys to objects, and ii) load balancing in content distribution networks, where one is interested in…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…