Related papers: Revisiting the Auction Algorithm for Weighted Bipa…
In 1982 Papadimitriou and Yannakakis introduced the Exact Matching problem, in which given a red and blue edge-colored graph $G$ and an integer $k$ one has to decide whether there exists a perfect matching in $G$ with exactly $k$ red edges.…
Bipartite matching, where agents on one side of a market are matched to agents or items on the other, is a classical problem in computer science and economics, with widespread application in healthcare, education, advertising, and general…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
Let G=(V,E) be a graph with f:V\to Z_+ a function assigning degree bounds to vertices. We present the first efficient algebraic algorithm to find an f-factor. The time is \tilde{O}(f(V)^{\omega}). More generally for graphs with integral…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
We present a deterministic way of assigning small (log bit) weights to the edges of a bipartite planar graph so that the minimum weight perfect matching becomes unique. The isolation lemma as described in (Mulmuley et al. 1987) achieves the…
This paper explores combinatorial optimization for problems of max-weight graph matching on multi-partite graphs, which arise in integrating multiple data sources. Entity resolution-the data integration problem of performing noisy joins on…
Bipartite b-matching is fundamental in algorithm design, and has been widely applied into economic markets, labor markets, etc. These practical problems usually exhibit two distinct features: large-scale and dynamic, which requires the…
Maximum cardinality matching in bipartite graphs is an important and well-studied problem. The fully dynamic version, in which edges are inserted and deleted over time has also been the subject of much attention. Existing algorithms for…
We consider the classical linear assignment problem, and we introduce new auction algorithms for its optimal and suboptimal solution. The algorithms are founded on duality theory, and are related to ideas of competitive bidding by persons…
In this paper a new method for checking the subsumption relation for the optimal-size sorting network problem is described. The new approach is based on creating a bipartite graph and modelling the subsumption test as the problem of…
Dominating set problems are among the most important class of combinatorial problems in graph optimization, from a theoretical as well as from a practical point of view. In this paper, we address the recently introduced (minimum) weighted…
We study the greedy-based online algorithm for edge-weighted matching with (one-sided) vertex arrivals in bipartite graphs, and edge arrivals in general graphs. This algorithm was first studied more than a decade ago by Korula and P\'al for…
We consider the weighted $k$-set packing problem, in which we are given a collection of weighted sets, each with at most $k$ elements and must return a collection of pairwise disjoint sets with maximum total weight. For $k = 3$, this…
Optimal transportation theory is an area of mathematics with real-world applications in fields ranging from economics to optimal control to machine learning. We propose a new algorithm for solving discrete transport (network flow) problems,…
We consider the problem of determining the maximal $\alpha \in (0,1]$ such that every matching $M$ of size $k$ (or at most $k$) in a bipartite graph $G$ contains an induced matching of size at least $\alpha |M|$. This measure was recently…
In this paper, we consider distributed optimization design for resource allocation problems over weight-balanced graphs. With the help of singular perturbation analysis, we propose a simple sub-optimal continuous-time optimization…
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…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
Let $\Ga$ be the collection of all weighted bipartite graphs each having $\sigma$ and $m$, as the size of a vertex partition and the total weight, respectively. We give a tight lower bound $\lceil \frac{m-\sigma}{\sigma} \rceil+1$ for the…