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We present a new approach for finding matchings in dense graphs by building on Szemer\'edi's celebrated Regularity Lemma. This allows us to obtain non-trivial albeit slight improvements over longstanding bounds for matchings in streaming…

Data Structures and Algorithms · Computer Science 2022-07-20 Sepehr Assadi , Soheil Behnezhad , Sanjeev Khanna , Huan Li

Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of Dyck reachability problems in directed and undirected graphs, where updates may add or delete…

Computational Complexity · Computer Science 2017-04-18 Patricia Bouyer , Vincent Jugé

This study considers the (soft) capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing…

Data Structures and Algorithms · Computer Science 2018-02-21 Hao-Ting Wei , Wing-Kai Hon , Paul Horn , Chung-Shou Liao , Kunihiko Sadakane

We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that handles updates in…

Data Structures and Algorithms · Computer Science 2019-07-05 Adam Karczmarz , Jakub Łącki

The Glauber dynamics on the colourings of a graph is a random process which consists in recolouring at each step a random vertex of a graph with a new colour chosen uniformly at random among the colours not already present in its…

Combinatorics · Mathematics 2020-11-04 Marc Heinrich

Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the…

Data Structures and Algorithms · Computer Science 2016-12-13 Monika Henzinger , Sebastian Krinninger , Danupon Nanongkai

In this work, we propose, analyze and empirically validate a lazy-update approach to maintain accurate approximations of the $2$-hop neighborhoods of dynamic graphs resulting from sequences of edge insertions. We first show that under…

Data Structures and Algorithms · Computer Science 2025-07-08 Luca Becchetti , Andrea Clementi , Luciano Gualà , Luca Pepè Sciarria , Alessandro Straziota , Matteo Stromieri

Given a directed weighted graph $G=(V,E)$ undergoing vertex insertions \emph{and} deletions, the All-Pairs Shortest Paths (APSP) problem asks to maintain a data structure that processes updates efficiently and returns after each update the…

Data Structures and Algorithms · Computer Science 2020-02-20 Maximilian Probst Gutenberg , Christian Wulff-Nilsen

We prove an optimal mixing time bound on the single-site update Markov chain known as the Glauber dynamics or Gibbs sampling in a variety of settings. Our work presents an improved version of the spectral independence approach of Anari et…

Discrete Mathematics · Computer Science 2023-03-24 Zongchen Chen , Kuikui Liu , Eric Vigoda

Graph coloring is a fundamental problem in computer science. We study the fully dynamic version of the problem in which the graph is undergoing edge insertions and deletions and we wish to maintain a vertex-coloring with small update time…

Data Structures and Algorithms · Computer Science 2020-02-25 Monika Henzinger , Stefan Neumann , Andreas Wiese

We address the problem of testing whether a dynamic graph is temporally connected, i.e. a temporal path ({\em journey}) exists between all pairs of vertices. We consider a discrete version of the problem, where the topology is given as an…

Data Structures and Algorithms · Computer Science 2014-05-02 Matthieu Barjon , Arnaud Casteigts , Serge Chaumette , Colette Johnen , Yessin M. Neggaz

Graph burning is a discrete-time process that models the propagation of information in a network. Initially, we have an undirected graph of unburned vertices. At each time step, an unburned vertex is chosen to burn; additionally, unburned…

Combinatorics · Mathematics 2026-03-17 Dhanyamol Antony , L. Sunil Chandran , Anita Das , Shirish Gosavi , Dalu Jacob , Shashanka Kulamarva

Sequential change-point detection for graphs is a fundamental problem for streaming network data types and has wide applications in social networks and power systems. Given fixed vertices and a sequence of random graphs, the objective is to…

Statistics Theory · Mathematics 2021-02-12 Liyan Xie , Yao Xie

In (fully) dynamic set cover, the goal is to maintain an approximately optimal solution to a dynamically evolving instance of set cover, where in each step either an element is added to or removed from the instance. The two main desiderata…

Data Structures and Algorithms · Computer Science 2025-11-12 Sayan Bhattacharya , Ruoxu Cen , Debmalya Panigrahi

An edge-weighted graph $G=(V,E)$ is called stable if the value of a maximum-weight matching equals the value of a maximum-weight fractional matching. Stable graphs play an important role in some interesting game theory problems, such as…

Data Structures and Algorithms · Computer Science 2017-11-28 Zhuan Khye Koh , Laura Sanità

A well-known problem in data science and machine learning is {\em linear regression}, which is recently extended to dynamic graphs. Existing exact algorithms for updating the solution of dynamic graph regression require at least a linear…

Machine Learning · Computer Science 2022-10-10 Mostafa Haghir Chehreghani

A finite dynamical system is a system of multivariate functions over a finite alphabet used to model a network of interacting entities. The main feature of a finite dynamical system is its interaction graph, which indicates which local…

Combinatorics · Mathematics 2017-01-12 Maximilien Gadouleau

Graphlet counting is an important problem as it has numerous applications in several fields, including social network analysis, biological network analysis, transaction network analysis, etc. Most of the practical networks are dynamic. A…

Data Structures and Algorithms · Computer Science 2023-08-29 Hriday G , Pranav Saikiran Sista , Apurba Das

In the dynamic approximate maximum bipartite matching problem we are given bipartite graph $G$ undergoing updates and our goal is to maintain a matching of $G$ which is large compared the maximum matching size $\mu(G)$. We define a dynamic…

Data Structures and Algorithms · Computer Science 2023-07-13 Joakim Blikstad , Peter Kiss

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