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Given two graphs, the graph matching problem is to align the two vertex sets so as to minimize the number of adjacency disagreements between the two graphs. The seeded graph matching problem is the graph matching problem when we are first…

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…

Data Structures and Algorithms · Computer Science 2016-07-15 Michael B. Cohen , Aleksander Madry , Piotr Sankowski , Adrian Vladu

We consider a dynamic situation in the weighted bipartite matching problem: edge weights in the input graph are repeatedly updated and we are asked to maintain an optimal matching at any moment. A trivial approach is to compute an optimal…

Data Structures and Algorithms · Computer Science 2023-08-01 Kohei Morita , Shinya Shiroshita , Yutaro Yamaguchi , Yu Yokoi

We consider stable and popular matching problems in arbitrary graphs, which are referred to as stable roommates instances. We extend the 3/2-approximation algorithm for the maximum size weakly stable matching problem to the roommates case,…

Data Structures and Algorithms · Computer Science 2025-10-07 Gergely Csáji

We reduce the problem of finding an augmenting path in a general graph to a reachability problem in a directed bipartite graph. A slight modification of depth-first search leads to an algorithm for finding such paths. Although this setting…

Data Structures and Algorithms · Computer Science 2015-09-17 Norbert Blum

Given a bipartite graph $G=(U\cup V,E)$, a left-perfect many-to-one matching is a subset $M \subseteq E$ such that each vertex in $U$ is incident with exactly one edge in $M$. If $U$ is partitioned into some groups, the matching is called…

Computational Complexity · Computer Science 2024-11-28 Ramin Javadi , Hossein Shokouhi

Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment,…

Data Structures and Algorithms · Computer Science 2024-03-13 Ziao Wang , Ning Zhang , Weina Wang , Lele Wang

Given a simple connected graph $G = (V, E)$, we seek to partition the vertex set $V$ into $k$ non-empty parts such that the subgraph induced by each part is connected, and the partition is maximally balanced in the way that the maximum…

Data Structures and Algorithms · Computer Science 2019-10-08 Yong Chen , Zhi-Zhong Chen , Guohui Lin , Yao Xu , An Zhang

In this paper we study the generalized version of weighted matching in bipartite networks. Consider a weighted matching in a bipartite network in which the nodes derive value from the split of the matching edge assigned to them if they are…

Optimization and Control · Mathematics 2010-11-16 Ankur Mani , Asuman Ozdaglar , Alex , Pentland

The graph packing problem is a well-known area in graph theory. We consider a bipartite version and give almost tight conditions on the packability of two bipartite sequences.

Combinatorics · Mathematics 2017-05-03 Bálint Vásárhelyi

We consider the problem of finding a low-cost allocation and ordering of tasks between a team of robots in a d-dimensional, uncertain, landscape, and the sensitivity of this solution to changes in the cost function. Various algorithms have…

Optimization and Control · Mathematics 2023-06-29 Katie Clinch , Tony A. Wood , Chris Manzie

The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…

Data Structures and Algorithms · Computer Science 2021-08-31 Sen Huang , Mingyu Xiao , Xiaoyu Chen

Most recent papers addressing the algorithmic problem of allocating advertisement space for keywords in sponsored search auctions assume that pricing is done via a first-price auction, which does not realistically model the Generalized…

Data Structures and Algorithms · Computer Science 2009-08-21 Yossi Azar , Benjamin Birnbaum , Anna R. Karlin , C. Thach Nguyen

We present an algorithm for computing pure-strategy epsilon-perfect Bayesian equilibria in sequential auctions with continuous action and value spaces. Importantly, our algorithm includes a verification phase that computes an upper bound on…

Computer Science and Game Theory · Computer Science 2025-02-19 Vinzenz Thoma , Vitor Bosshard , Sven Seuken

Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…

Data Structures and Algorithms · Computer Science 2023-03-20 Pasin Manurangsi , Erel Segal-Halevi , Warut Suksompong

We consider the {\em stochastic matching} problem. An edge-weighted general (i.e., not necessarily bipartite) graph $G(V, E)$ is given in the input, where each edge in $E$ is {\em realized} independently with probability $p$; the…

Data Structures and Algorithms · Computer Science 2018-05-24 Soheil Behnezhad , Nima Reyhani

The \textsc{Bipartite Contraction} problem is to decide, given a graph $G$ and a parameter $k$, whether we can can obtain a bipartite graph from $G$ by at most $k$ edge contractions. The fixed-parameter tractability of the problem was shown…

Data Structures and Algorithms · Computer Science 2013-09-05 Sylvain Guillemot , Dániel Marx

The perfect matching problem has a randomized NC algorithm, using the celebrated Isolation Lemma of Mulmuley, Vazirani and Vazirani. The Isolation Lemma states that giving a random weight assignment to the edges of a graph, ensures that it…

Computational Complexity · Computer Science 2014-12-01 Rahul Arora , Ashu Gupta , Rohit Gurjar , Raghunath Tewari

In this paper, we present a new exact algorithm for counting perfect matchings, which relies on neither inclusion-exclusion principle nor tree-decompositions. For any bipartite graph of $2n$ nodes and $\Delta n$ edges such that $\Delta \geq…

Data Structures and Algorithms · Computer Science 2012-08-14 Taisuke Izumi , Tadashi Wadayama

Constructing the maximum spanning tree $T$ of an edge-weighted connected graph $G$ is one of the important research topics in computer science and optimization, and the related research results have played an active role in practical…

Combinatorics · Mathematics 2024-12-30 Hui Lei , Mei Lu , Yongtang Shi , Jian Sun , Xiamiao Zhao