Recent Advances in Fully Dynamic Graph Algorithms – A Quick Reference Guide

Hanauer, Kathrin; Henzinger, Monika; Schulz, Christian

doi:10.1145/3555806

Cited by 15 publications

(5 citation statements)

References 251 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There has been a large body of work on dynamic matching and many variants of the problem have been studied, e.g, the maximum, maximal, as well as α-approximate setting for a variety of values of α, both in the weighted as well as in the unweighted setting. See [10] for a survey of the current state of the art for the fully dynamic setting. We just mention here a few of the most relevant prior works.…”

Section: Dynamic Matching Algorithmsmentioning

confidence: 99%

Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching

Zheng¹,

Henzinger²

2023

Preprint

View full text Add to dashboard Cite

We present an auction algorithm using multiplicative instead of constant weight updates to compute a (1 − ε)-approximate maximum weight matching (MWM) in a bipartite graph with n vertices and m edges in time O(mε −1 log(ε −1 )), matching the running time of the linear-time approximation algorithm of Duan and Pettie [JACM '14]. Our algorithm is very simple and it can be extended to give a dynamic data structure that maintains a (1 − ε)-approximate maximum weight matching under (1) edge deletions in amortized O(ε −1 log(ε −1 )) time and (2) one-sided vertex insertions. If all edges incident to an inserted vertex are given in sorted weight the amortized time is O(ε −1 log(ε −1 )) per inserted edge. If the inserted incident edges are not sorted, the amortized time per inserted edge increases by an additive term of O(log n). The fastest prior dynamic (1 − ε)-approximate algorithm in weighted graphs took time O( √ mε −1 log(w max )) per updated edge, where the edge weights lie in the range [1, w max ].

show abstract

Section: Dynamic Matching Algorithmsmentioning

confidence: 99%

Multiplicative Auction Algorithm for Approximate Maximum Weight Bipartite Matching

Zheng¹,

Henzinger²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Note that, a thorough survey on recent advances in the field of dynamic graph algorithms has been drawn up by Hanauer et al in [31].…”

Section: A Related Workmentioning

confidence: 99%

Top-k Distance Queries on Large Time-Evolving Graphs

D’ascenzo,

D’emidio

2023

IEEE Access

View full text Add to dashboard Cite

Fast extraction of top-k distances from graph data is a primitive of paramount importance in the fields of data mining, network analytics and machine learning, where ranked distances are exploited for several purposes (e.g. link prediction or network classification). While investigation on computational methods to address this retrieval task for regularly sized, static inputs has been extensive, much less is known when managed graphs are massive, i.e. having millions of vertices/edges, and time-evolving, i.e. when their structure can grow over time, a scenario that introduces a number of scalability and effectiveness issues otherwise not arising. Since, nowadays, most real-world applications exploiting top-k distances have to handle inherently dynamic and rapidly growing graphs, in this paper we present the first dynamic indexing scheme that supports very fast queries on top-k distances when graphs are massive and incrementally timeevolving. We assess the scalability and effectiveness of our method through extensive experimentation on both real-world and artificial graph datasets.

show abstract

“…One of the major advancements in algorithms recently has been in the area of fully dynamic graph algorithms for many central graph problems such as spanning forest [4], minimum spanning forest [5], [8], transitive closure [68], [69], strongly connected component [26], shortest path [12], [31], maximum matching [1], [2], maximal independent set [13], maximal matching [70], [71], set cover [72], [73], vertex cover [74] and various others. See the survey [33] on recent advances in fully dynamic graph algorithms.…”

Section: A Related Workmentioning

confidence: 99%

“…Examples include maximum matchings in graphs [1]- [3], connectivity [4], [5], maximum flow [6], [7], minimum spanning trees [5], [8], clustering [9]- [11], diameter estimation [12], independent set [13], pattern matching [14]- [17], lossless compression [18], string similarity [19], longest increasing subsequence [20]- [22], suffix arrays [23], and many others. Several related models with varying difficulties have been studied, including incremental (insertion-only, where elements can only be added) [7], [24]- [26], decremental (deletion-only, where elements can only be deleted) [27]- [30], and fully-dynamic (supporting both insertions and deletions) [2], [31]- [33].…”

Section: Introductionmentioning

confidence: 99%