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A Fully Dynamic Reachability Algorithm for Directed Graphs with an Almost Linear Update Time

Liam Roditty, Uri Zwick
2016 SIAM journal on computing (Print)  
We obtain a new fully dynamic algorithm for the reachability problem in directed graphs.  ...  It is a new dynamic algorithm for strong connectivity in directed graphs with an interesting persistency property. Each insert operation creates a new version of the graph.  ...  AN ALMOST LINEAR FULLY DYNAMIC REACHABILITY ALGORITHM In this section we describe our fully dynamic reachability algorithm.  ... 
doi:10.1137/13093618x fatcat:vcah45a4kvhmnnpayu3rp3q77e

A fully dynamic reachability algorithm for directed graphs with an almost linear update time

Liam Roditty, Uri Zwick
2004 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04  
We obtain a new fully dynamic algorithm for the reachability problem in directed graphs.  ...  It is a new dynamic algorithm for strong connectivity in directed graphs with an interesting persistency property. Each insert operation creates a new version of the graph.  ...  AN ALMOST LINEAR FULLY DYNAMIC REACHABILITY ALGORITHM In this section we describe our fully dynamic reachability algorithm.  ... 
doi:10.1145/1007352.1007387 dblp:conf/stoc/RodittyZ04 fatcat:wgfp6om7wbabjo72voeyj3w3wq

Fully Dynamic Single-Source Reachability in Practice: An Experimental Study [article]

Kathrin Hanauer, Monika Henzinger, Christian Schulz
2019 arXiv   pre-print
Given a directed graph and a source vertex, the fully dynamic single-source reachability problem is to maintain the set of vertices that are reachable from the given vertex, subject to edge deletions and  ...  In this paper, we bridge this gap by empirically studying an extensive set of algorithms for the single-source reachability problem in the fully dynamic setting.  ...  The paper deals with the fully dynamic single-source reachability problem (SSR): Given a directed graph and a source vertex s, answer reachability queries starting at s, subject to edge insertions and  ... 
arXiv:1905.01216v2 fatcat:z7b7wcziknaulpkoghktqtmuhy

Improved Fully Dynamic Reachability Algorithm for Directed Graph [article]

Venkata Seshu Kumar Kurapati
2007 arXiv   pre-print
We propose a fully dynamic algorithm for maintaining reachability information in directed graphs.  ...  The proposed algorithm improves by a factor of O(n^2/m+n*log(n)) for edge deletion over the best existing fully dynamic algorithm for maintaining reachability information.  ...  Roditty and Zwick [RZ04] obtained an algorithm for maintaining reachability information with an amortized almost linear update time with respect to the number of edges and vertices in the current graph  ... 
arXiv:0711.3250v1 fatcat:ifxxhhxpf5dp3jcpifqrvjiq5m

Average case analysis of fully dynamic reachability for directed graphs

Paola Alimonti, Stefano Leonardi, Alberto Marchetti-Spaccamela
1996 RAIRO - Theoretical Informatics and Applications  
ACKNOWLEDGMENTS We thank an anonymous référée for useful suggestions.  ...  In fact Karp proposed an algorithm for Computing the transitive closure of a sufficiently dense directed graph (with m > A • n • log n, with A constant) in O (n) expected time and linear space [14] .  ...  In the following of this section we will study the expected time complexity of a fully dynamic algorithm for report-path queries, and the expected time complexity of a fully dynamic algorithm for reach  ... 
doi:10.1051/ita/1996300403051 fatcat:spi2b7odifd7neaqhfvf3m47si

Recent Advances in Fully Dynamic Graph Algorithms [article]

Kathrin Hanauer, Monika Henzinger, Christian Schulz
2021 arXiv   pre-print
Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms.  ...  In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms.  ...  The first fully dynamic algorithm for all-pairs shortest paths in graphs with positive integer weights less than a constant was presented by King [152] , with an amortized update time of O( 2.5 log ).  ... 
arXiv:2102.11169v5 fatcat:tcs3lkgcg5f7jax672adyzrstm

Single-Source Shortest Paths and Strong Connectivity in Dynamic Planar Graphs

Panagiotis Charalampopoulos, Adam Karczmarz, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
First, we give a fully dynamic single-source shortest paths data structure for planar weighted digraphs with Õ(n^{4/5}) worst-case update time and O(log² n) query time.  ...  To the best of our knowledge, this is the first fully dynamic strong-connectivity algorithm achieving both sublinear update time and polylogarithmic query time for an important class of digraphs.  ...  The lack of progress on obtaining an exact fully dynamic single-source shortest paths algorithms with O(n 3− ) initialization time, O(m 1− ) amortized update time and O(n 1− ) query time at the same time  ... 
doi:10.4230/lipics.esa.2020.31 dblp:conf/esa/Charalampopoulos20 fatcat:5so72hnvf5emrkngtb6rxxznb4

DFS is Unsparsable and Lookahead Can Help in Maximal Matching

Kitti Gelle, Szabolcs Iván
2018 Acta Cybernetica  
graph, preferably with a better time bound than that when running a classical algorithm from scratch each time a query arrives.  ...  In the second part, we show that a maximal matching can be maintained in an (undirected) graph with a deterministic amortized update cost of O(log m) (where m is the all-time maximum number of the edges  ...  In order to give the reader a better insight, we give an example before analyzing the time complexity.  ... 
doi:10.14232/actacyb.23.3.2018.10 fatcat:hnbtabpsh5f67hvveyizpas4ze

Popular Conjectures Imply Strong Lower Bounds for Dynamic Problems

Amir Abboud, Virginia Vassilevska Williams
2014 2014 IEEE 55th Annual Symposium on Foundations of Computer Science  
3) Is the All Pairs Shortest Paths problem for graphs on n vertices in O(n 3−ε ) time for some ε > 0? 4) Is there a linear time algorithm that detects whether a given graph contains a triangle?  ...  5) Is there an O(n 3−ε ) time combinatorial algorithm for n×n Boolean matrix multiplication?  ...  This research was supported by a Stanford School of Engineering Hoover Fellowship, NSF Grant CCF-1417238 and BSF Grant BSF:2012338.  ... 
doi:10.1109/focs.2014.53 dblp:conf/focs/AbboudW14 fatcat:ayagllj5svejblnqsmsenj64ge

Decremental Single-Source Reachability in Planar Digraphs [article]

Giuseppe F. Italiano, Adam Karczmarz, Jakub Łącki, Piotr Sankowski
2017 arXiv   pre-print
We also show an algorithm for decremental maintenance of strongly connected components in directed planar graphs with the same total update time.  ...  To the best of our knowledge, these are the first dynamic algorithms with polylogarithmic update times on general directed planar graphs for non-trivial reachability-type problems, for which only polynomial  ...  ., in polylog amortized time per update, even in the fully dynamic setting [47] .  ... 
arXiv:1705.11163v1 fatcat:emfjtuogsjcppgjlpwa4yh4ikm

Fully Dynamic Transitive Closure in plane dags with one source and one sink [chapter]

Thore Husfeldt
1995 Lecture Notes in Computer Science  
We give an algorithm for the Dynamic Transitive Closure Problem for planar directed acyclic graphs with one source and one sink.  ...  This is the first dynamic directed graph problem with almost matching lower and upper bounds.  ...  fully dynamic reachability algorithms within polylogarithmic time bounds.  ... 
doi:10.1007/3-540-60313-1_144 fatcat:c4comackdbgorgdspqbcamejry

Fully Dynamic Transitive Closure in Plane Dags with one Source and one Sink

Thore Husfeldt
1994 BRICS Report Series  
We give an algorithm for the Dynamic Transitive Closure Problem for planar directed acyclic graphs with one source and one sink.  ...  This is the first dynamic directed graph problem with almost matching lower and upper bounds.  ...  fully dynamic reachability algorithms within polylogarithmic time bounds.  ... 
doi:10.7146/brics.v1i30.21613 fatcat:ljwdxqn2azcivh2wsisrqvtypi

Popular conjectures imply strong lower bounds for dynamic problems [article]

Amir Abboud, Virginia Vassilevska Williams
2014 arXiv   pre-print
Is the All Pairs Shortest Paths problem for graphs on n vertices in O(n^3-ϵ) time for some ϵ>0? 4. Is there a linear time algorithm that detects whether a given graph contains a triangle? 5.  ...  Is there an O(n^3-ϵ) time combinatorial algorithm for n× n Boolean matrix multiplication?  ...  This research was supported by a Stanford School of Engineering Hoover Fellowship, NSF Grant CCF-1417238 and BSF Grant BSF:2012338.  ... 
arXiv:1402.0054v1 fatcat:bgdvvk4e2naetd5taffv2ilovy

DAGGER: A Scalable Index for Reachability Queries in Large Dynamic Graphs [article]

Hilmi Yildirim, Vineet Chaoji, Mohammed J. Zaki
2013 arXiv   pre-print
In this paper, we present a fully dynamic reachability index over dynamic graphs.  ...  Whereas many methods have been proposed for static graph reachability, many real-world graphs are constantly evolving, which calls for dynamic indexing.  ...  In this paper, we propose a scalable, light-weight reachability index for dynamic graphs called DAGGER (an anagram of the bold letters in Dynamic Graph REAchability, with an extra 'G'), which has linear  ... 
arXiv:1301.0977v1 fatcat:s4jhbxae7vex3ijplmyh7jubhu

On Dynamic DFS Tree in Directed Graphs [chapter]

Surender Baswana, Keerti Choudhary
2015 Lecture Notes in Computer Science  
We present an efficient randomized decremental algorithm for maintaining a DFS tree for a directed acyclic graph.  ...  (b) Any decremental (or incremental) algorithm for maintaining the ordered DFS tree is at least as hard as computing all-pairs reachability in a directed graph.  ...  -Does there exist an incremental/decremental algorithm with O(mn) update time for DFS tree in general directed graphs ?  ... 
doi:10.1007/978-3-662-48054-0_9 fatcat:j6x2gvddefdfllja3ands7ut2e
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