Three-in-a-tree in near linear time
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- Three-in-a-Tree in Near Linear Time∗
Final published version, 2.63 MB, PDF document
The three-in-a-tree problem is to determine if a simple undirected graph contains an induced subgraph which is a tree connecting three given vertices. Based on a beautiful characterization that is proved in more than twenty pages, Chudnovsky and Seymour [Combinatorica 2010] gave the previously only known polynomial-time algorithm, running in O(mn2) time, to solve the three-in-a-tree problem on an n-vertex m-edge graph. Their three-in-a-tree algorithm has become a critical subroutine in several state-of-the-art graph recognition and detection algorithms. In this paper we solve the three-in-a-tree problem in O(mlog2 n) time, leading to improved algorithms for recognizing perfect graphs and detecting thetas, pyramids, beetles, and odd and even holes. Our result is based on a new and more constructive characterization than that of Chudnovsky and Seymour. Our new characterization is stronger than the original, and our proof implies a new simpler proof for the original characterization. The improved characterization gains the first factor n in speed. The remaining improvement is based on dynamic graph algorithms.
Original language | English |
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Title of host publication | STOC 2020 - Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing |
Editors | Konstantin Makarychev, Yury Makarychev, Madhur Tulsiani, Gautam Kamath, Julia Chuzhoy |
Publisher | Association for Computing Machinery |
Publication date | 2020 |
Pages | 1279-1292 |
ISBN (Electronic) | 9781450369794 |
DOIs | |
Publication status | Published - 2020 |
Event | 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020 - Chicago, United States Duration: 22 Jun 2020 → 26 Jun 2020 |
Conference
Conference | 52nd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2020 |
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Land | United States |
By | Chicago |
Periode | 22/06/2020 → 26/06/2020 |
Sponsor | ACM Special Interest Group on Algorithms and Computation Theory (SIGACT) |
Series | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN | 0737-8017 |
- Dynamic graph algorithm, Even hole, Graph recognition, Induced subgraph detection, Odd hole, Perfect graph, SPQR-tree, Top tree
Research areas
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