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Matching in Dynamic Graphs [chapter]

Surender Baswana, Manoj Gupta, Sandeep Sen
2016 Encyclopedia of Algorithms  
Key Result We address the problem of maintaining maximal matching in a fully dynamic environment -allowing updates in form of both insertion and deletion of edges.  ...  In order to maintain a maximal matching, it suffices to ensure that there is no edge (u, v) in the graph such that both u and v are free with respect to the matching M.  ... 
doi:10.1007/978-1-4939-2864-4_567 fatcat:dxszn4g6ejaxjmegitkp7pbmcu

Fully Dynamic Matching in Bipartite Graphs [article]

Aaron Bernstein, Cliff Stein
2015 arXiv   pre-print
Maximum cardinality matching in bipartite graphs is an important and well-studied problem.  ...  Existing algorithms for dynamic matching (in general graphs) seem to fall into two groups: there are fast (mostly randomized) algorithms that do not achieve a better than 2-approximation, and there slow  ...  Acknowledgements We would like to thank Tsvi Kopelowitz for very helpful pointers about dynamic orientations.  ... 
arXiv:1506.07076v2 fatcat:dfu2nrg3yncwffu6srf5bhts5m

Maintaining Approximate Maximum Weighted Matching in Fully Dynamic Graphs [article]

Abhash Anand and Surender Baswana and Manoj Gupta and Sandeep Sen
2012 arXiv   pre-print
We present a fully dynamic algorithm for maintaining approximate maximum weight matching in general weighted graphs.  ...  The algorithm achieves an expected amortized O( n C) time per edge insertion or deletion, where C is the ratio of the weights of the highest weight edge to the smallest weight edge in the given graph.  ...  In this paper, we address the problem of maintaining approximate weighted matching in a fully dynamic graph.  ... 
arXiv:1207.3976v3 fatcat:cxsdkqzukreybmybrcaykjocvm

Maximum Matching on Trees in the Online Preemptive and the Incremental Dynamic Graph Models [article]

Sumedh Tirodkar, Sundar Vishwanathan
2018 arXiv   pre-print
We study the Maximum Cardinality Matching (MCM) and the Maximum Weight Matching (MWM) problems, on trees and on some special classes of graphs, in the Online Preemptive and the Incremental Dynamic Graph  ...  In the Online Preemptive model, the edges of a graph are revealed one by one and the algorithm is required to always maintain a valid matching.  ...  Incremental Dynamic Graph model.  ... 
arXiv:1612.05419v3 fatcat:lqk75cwwh5afxnqncw5yo35wwi

Optimal Lower Bounds for Matching and Vertex Cover in Dynamic Graph Streams [article]

Jacques Dark, Christian Konrad
2020 arXiv   pre-print
in n, the number of vertices of the input graph; (2) are able to process multi-graphs; and (3) never output edges that do not exist in the input graph when the randomized algorithm errs.  ...  Bob holds a set of edge deletions, which form a subset of Alice's edges, and needs to report a large matching or a small vertex cover in the graph spanned by the edges that are not deleted.  ...  Bob holds a set of edge deletions D ⊆ E and outputs a large matching in the graph spanned by the edges E \ D.  ... 
arXiv:2005.11116v1 fatcat:ftmesaopxregvokon4gwq56b4i

Graph-based many-to-one dynamic ride-matching for shared mobility services in congested networks [article]

Seyed Mehdi Meshkani, Bilal Farooq
2021 arXiv   pre-print
We propose a novel graph-based algorithm (GMO- Match) for dynamic many-to-one matching problem in the presence of traffic congestion.  ...  GMOMatch starts with a one-to-one matching in step 1 and is followed by solving a maximum weight matching problem is step 2 to combine the travel requests.  ...  as on the implementation of our ride-matching algorithms in the micro-simulator.  ... 
arXiv:2101.08657v2 fatcat:japyjdyhyrbjlhld2eljqalmqe

Core Maintenance in Dynamic Graphs: A Parallel Approach based on Matching [article]

Na Wang, Dongxiao Yu, Hai Jin, Qiang-Sheng Hua, Xuanhua Shi, Xia Xie
2017 arXiv   pre-print
In this paper, we study the update of core numbers of vertices in dynamic graphs with edge insertions/deletions, which is known as the core maintenance problem.  ...  The core number of a vertex is a basic index depicting cohesiveness of a graph, and has been widely used in large-scale graph analytics.  ...  In this work, we aim at maintaining the core numbers of vertices in dynamic graphs.  ... 
arXiv:1703.03900v1 fatcat:sunptgqxyrdxbnpvumcnmb6hym

Bond graphs in model matching control

D. Vink, D. Ballance, P. Gawthrop
2006 Mathematical and Computer Modelling of Dynamical Systems  
Bond graphs are primarily used in the network modelling of lumped parameter physical systems, but controller design with this graphical technique is relatively unexplored.  ...  The adopted bond graph approach is presented through a detailed example, which shows that the obtained controller induces port-Hamiltonian error dynamics.  ...  The shortage of literature on bond graph based control has compelled us to contribute bond graph tools for certain model matching problems.  ... 
doi:10.1080/13873950500068278 fatcat:nwd5l4hpvze4vm2zgdfok7khxm

Orienting Dynamic Graphs, with Applications to Maximal Matchings and Adjacency Queries [chapter]

Meng He, Ganggui Tang, Norbert Zeh
2014 Lecture Notes in Computer Science  
Recently, Neiman and Solomon [13] found that edge orientation also has applications in maintaining a maximal matching of a dynamic graph.  ...  Graph matching is a fundamental problem in graph theory, and it has many applications in combinatorial optimization [10] .  ...  Neiman and Solomon [13] made use of the algorithm of Brodal and Fagerberg [2] to maintain maximal matchings in dynamic settings.  ... 
doi:10.1007/978-3-319-13075-0_11 fatcat:fxi3jjkturadhlw7yjf2fwkzky

Maximum Matching on Trees in the Online Preemptive and the Incremental Dynamic Graph Models [chapter]

Sumedh Tirodkar, Sundar Vishwanathan
2017 Lecture Notes in Computer Science  
We study the Maximum Cardinality Matching (MCM) and the Maximum Weight Matching (MWM) problems, on trees and on some special classes of graphs, in the Online Preemptive and the Incremental Dynamic Graph  ...  In an Incremental Dynamic Graph, at each update step an edge is added to the graph.  ...  Incremental Dynamic Graph model.  ... 
doi:10.1007/978-3-319-62389-4_42 fatcat:k5niwesxa5bcfk23cxxkx6kazq

Optimal Lower Bounds for Matching and Vertex Cover in Dynamic Graph Streams

Jacques Dark, Christian Konrad, Shubhangi Saraf
2020 Computational Complexity Conference  
in n, the number of vertices of the input graph; (2) are able to process multi-graphs; and (3) never output edges that do not exist in the input graph when the randomized algorithm errs.  ...  Bob holds a set of edge deletions, which form a subset of Alice's edges, and needs to report a large matching or a small vertex cover in the graph spanned by the edges that are not deleted.  ...  C C C 2 0 2 0 30:12 Optimal Lower Bounds for Matching and Vertex Cover in Dynamic Graph Streams C C 2 0 2 0 30:4 Optimal Lower Bounds for Matching and Vertex Cover in Dynamic Graph Streams will denote  ... 
doi:10.4230/lipics.ccc.2020.30 dblp:conf/coco/DarkK20 fatcat:wdnnzaful5avfb7pexxkts3gqq

Maximum Matchings in Dynamic Graph Streams and the Simultaneous Communication Model

Sepehr Assadi, Sanjeev Khanna, Yang Li, Grigory Yaroslavtsev
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
Weighted matching in the semi-streaming model. Algorithmica, 62(1-2):1-20, 2012. Conclusion and Open Problems Streaming model: Tight bounds for matchings in dynamic graph streams.  ...  Dynamic graph stream algorithms and linear sketches are (essentially) equivalent [LNW14, AHW15].  ... 
doi:10.1137/1.9781611974331.ch93 dblp:conf/soda/AssadiKLY16 fatcat:55eczykltbb6hi3qliocglme34

Dynamic Summarization of Video Using Minimum Edge Weight Matching in Bipartite Graphs

Shanmukhappa Angadi, Vilas Naik
2016 International Journal of Image Graphics and Signal Processing  
Then the minimum edge weight maximal matching in every bipartite graph (a set of pair wise non-adjacent edges) is found using Hungarian method.  ...  This paper describes an algorithm for constructing the dynamic summary of a video by modeling every 40 consecutive frames of video as a bipartite graph.  ...  Minimum Edge weight Matching in Bipartite graph based Algorithm for Dynamic summarization A graph G = (V,E) consists of a set V of vertices and a set E of pairs of vertices called edges.  ... 
doi:10.5815/ijigsp.2016.03.02 fatcat:tmxlcpducfcmpfmbzxkojucnae

Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams

Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, Sofya Vorotnikova
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
Algorithm for Dynamic Graph Streams. In the dynamic graph stream model, it is not possible to construct a maximal matching.  ...  We prove the following results for computing a matching in the dynamic model.  ... 
doi:10.1137/1.9781611974331.ch92 dblp:conf/soda/ChitnisCEHMMV16 fatcat:3jul55k3u5alboeeoughpqk6w4

Dynamic Matchings in Convex Bipartite Graphs [chapter]

Gerth Stølting Brodal, Loukas Georgiadis, Kristoffer Arnsfelt Hansen, Irit Katriel
Lecture Notes in Computer Science  
We consider the problem of maintaining a maximum matching in a convex bipartite graph G = (V, E) under a set of update operations which includes insertions and deletions of vertices and edges.  ...  (matched or unmatched) in constant worst-case time.  ...  In this paper we study the problem of maintaining a maximum matching in a dynamic convex bipartite graph.  ... 
doi:10.1007/978-3-540-74456-6_37 fatcat:w3jjjenj7bhmlo73gsj6gjjyui
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