Incremental topological sort and cycle detection in Õ (m √n) expected total time

Aaron Bernstein, Shiri Chechik

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

In the incremental cycle detection problem edges are inserted to a directed graph (initially empty) and the algorithm has to report once a directed cycle is formed in the graph. A closely related problem to the incremental cycle detection is that of the incremental topological sort problem, in which edges are inserted to an acyclic graph and the algorithm has to maintain a valid topological sort on the vertices at all times. Both incremental cycle detection and incremental topological sort have a long history. The state of the art is a recent breakthrough of Bender, Fineman, Gilbert and Tarjan [TALG 2016], with two different algorithms with respective total update times of Õ (n2) and O(m minfm1=2; n2=3g). The two algorithms work for both incremental cycle detection and incremental topological sort. In this paper we introduce a novel technique that allows us to improve upon the state of the art for a wide range of graph sparsity. Our algorithms has a total expected update time of Õ(m p n) for both the incremental cycle detection and the topological sort problems.

Original languageEnglish (US)
Title of host publication29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
EditorsArtur Czumaj
PublisherAssociation for Computing Machinery
Pages21-34
Number of pages14
ISBN (Electronic)9781611975031
DOIs
StatePublished - Jan 1 2018
Externally publishedYes
Event29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States
Duration: Jan 7 2018Jan 10 2018

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
CountryUnited States
CityNew Orleans
Period1/7/181/10/18

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Fingerprint Dive into the research topics of 'Incremental topological sort and cycle detection in Õ (m √n) expected total time'. Together they form a unique fingerprint.

Cite this