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Related papers: Maintaning maximal matching with lookahead

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In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions…

Data Structures and Algorithms · Computer Science 2019-01-29 Niklas Hjuler , Giuseppe F. Italiano , Nikos Parotsidis , David Saulpic

We present the first deterministic data structures for maintaining approximate minimum vertex cover and maximum matching in a fully dynamic graph $G = (V,E)$, with $|V| = n$ and $|E| =m$, in $o(\sqrt{m}\,)$ time per update. In particular,…

Data Structures and Algorithms · Computer Science 2014-12-04 Sayan Bhattacharya , Monika Henzinger , Giuseppe F. Italiano

We present the first data structures that maintain near optimal maximum cardinality and maximum weighted matchings on sparse graphs in sublinear time per update. Our main result is a data structure that maintains a $(1+\epsilon)$…

Data Structures and Algorithms · Computer Science 2013-04-11 Manoj Gupta , Richard Peng

Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…

Discrete Mathematics · Computer Science 2020-09-30 George B. Mertzios , Hendrik Molter , Rolf Niedermeier , Viktor Zamaraev , Philipp Zschoche

We present a randomized algorithm to maintain a maximal matching without 3 length augmenting paths in the fully dynamic setting. Consequently, we maintain a $3/2$ approximate maximum cardinality matching. Our algorithm takes expected…

Data Structures and Algorithms · Computer Science 2018-11-06 Manas Jyoti Kashyop , N. S. Narayanaswamy

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…

Data Structures and Algorithms · Computer Science 2015-08-18 Aaron Bernstein , Cliff Stein

In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees. In particular, we obtain improved dynamic algorithms that, given an unweighted and…

Data Structures and Algorithms · Computer Science 2022-09-09 Jan van den Brand , Sebastian Forster , Yasamin Nazari

We consider the problem of maintaining an approximate maximum integral matching in a dynamic graph $G$, while the adversary makes changes to the edges of the graph. The goal is to maintain a $(1+\epsilon)$-approximate maximum matching for…

Data Structures and Algorithms · Computer Science 2022-07-07 Sepehr Assadi , Aaron Bernstein , Aditi Dudeja

In this paper, we have developed a fully-dynamic algorithm for maintaining cardinality of maximum-matching in a tree using the construction of top-trees. The time complexities are as follows: 1. Initialization Time: $O(n(log(n)))$ to build…

Data Structures and Algorithms · Computer Science 2009-01-20 Manoj Gupta , Ankit Sharma

We study the maximum matching problem in fully dynamic graphs: a graph is undergoing both edge insertions and deletions, and the goal is to efficiently maintain a large matching after each edge update. This problem has received considerable…

Data Structures and Algorithms · Computer Science 2022-01-11 Soheil Behnezhad , Sanjeev Khanna

We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for $(\Delta+1)$- vertex coloring and…

Data Structures and Algorithms · Computer Science 2017-11-15 Sayan Bhattacharya , Deeparnab Chakrabarty , Monika Henzinger , Danupon Nanongkai

We present deterministic algorithms for maintaining a $(3/2 + \epsilon)$ and $(2 + \epsilon)$-approximate maximum matching in a fully dynamic graph with worst-case update times $\hat{O}(\sqrt{n})$ and $\tilde{O}(1)$ respectively. The…

Data Structures and Algorithms · Computer Science 2021-11-22 Peter Kiss

We show a fully dynamic algorithm for maintaining $(1+\epsilon)$-approximate \emph{size} of maximum matching of the graph with $n$ vertices and $m$ edges using $m^{0.5-\Omega_{\epsilon}(1)}$ update time. This is the first polynomial…

Data Structures and Algorithms · Computer Science 2024-04-30 Sayan Bhattacharya , Peter Kiss , Thatchaphol Saranurak

Given a simple $n$-vertex, $m$-edge graph $G$ undergoing edge insertions and deletions, we give two new fully dynamic algorithms for exactly maintaining the edge connectivity of $G$ in $\tilde{O}(n)$ worst-case update time and…

Data Structures and Algorithms · Computer Science 2024-03-25 Gramoz Goranci , Monika Henzinger , Danupon Nanongkai , Thatchaphol Saranurak , Mikkel Thorup , Christian Wulff-Nilsen

Despite significant research efforts, the state-of-the-art algorithm for maintaining an approximate matching in fully dynamic graphs has a polynomial {worst-case} update time, even for very poor approximation guarantees. In a recent…

Data Structures and Algorithms · Computer Science 2018-03-16 Moses Charikar , Shay Solomon

In the fully dynamic maximal matching problem, the goal is to maintain a maximal matching in a graph undergoing an online sequence of edge insertions and deletions. The problem has been studied extensively in the oblivious-adversary…

Data Structures and Algorithms · Computer Science 2026-05-04 Julia Chuzhoy , Sanjeev Khanna , Junkai Song

A dynamic bipartite matching model is given by a bipartite matching graph which determines the possible matchings between the various types of supply and demand items. Both supply and demand items arrive to the system according to a…

Discrete Mathematics · Computer Science 2020-09-11 Arnaud Cadas , Ana Bušić , Josu Doncel

Most graphs in real life keep changing with time. These changes can be in the form of insertion or deletion of edges or vertices. Such rapidly changing graphs motivate us to study dynamic graph algorithms. However, three important graph…

Data Structures and Algorithms · Computer Science 2018-08-07 Manoj Gupta , Shahbaz Khan

We present the first algorithm for maintaining a maximal independent set (MIS) of a fully dynamic graph---which undergoes both edge insertions and deletions---in polylogarithmic time. Our algorithm is randomized and, per update, takes…

Data Structures and Algorithms · Computer Science 2019-09-10 Soheil Behnezhad , Mahsa Derakhshan , MohammadTaghi Hajiaghayi , Cliff Stein , Madhu Sudan

In this paper, we consider the problem of maintaining a $(1-\varepsilon)$-approximate maximum weight matching in a dynamic graph $G$, while the adversary makes changes to the edges of the graph. In the fully dynamic setting, where both edge…

Data Structures and Algorithms · Computer Science 2023-12-15 Aditi Dudeja