Decremental strongly-connected components and single-source reachability in near-linear time
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Computing the Strongly-Connected Components (SCCs) in a graph G = (V, E) is known to take only O(m + n) time using an algorithm by Tarjan from 1972[SICOMP 72] where m = |E|, n = |V |. For fully-dynamic graphs, conditional lower bounds provide evidence that the update time cannot be improved by polynomial factors over recomputing the SCCs from scratch after every update. Nevertheless, substantial progress has been made to find algorithms with fast update time for decremental graphs, i.e. graphs that undergo edge deletions. In this paper, we present the first algorithm for general decremental graphs that maintains the SCCs in total update time Õ(m)1, thus only a polylogarithmic factor from the optimal running time. Previously such a result was only known for the special case of planar graphs [Italiano et al, STOC 17]. Our result should be compared to the formerly best algorithm for general graphs achieving Õ(mn) total update time by Chechik et.al. [FOCS 16] which improved upon a breakthrough result leading to O(mn0.9+o(1)) total update time by Henzinger, Krinninger and Nanongkai [STOC 14, ICALP 15]; these results in turn improved upon the longstanding bound of O(mn) by Roditty and Zwick [STOC 04]. All of the above results also apply to the decremental Single-Source Reachability (SSR) problem, which can be reduced to decrementally maintaining SCCs. A bound of O(mn) total update time for decremental SSR was established already in 1981 by Even and Shiloach [JACM 81].
Original language | English |
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Title of host publication | STOC 2019 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing |
Editors | Moses Charikar, Edith Cohen |
Number of pages | 12 |
Publisher | Association for Computing Machinery |
Publication date | 2019 |
Pages | 365-376 |
ISBN (Electronic) | 9781450367059 |
DOIs | |
Publication status | Published - 2019 |
Event | 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 - Phoenix, United States Duration: 23 Jun 2019 → 26 Jun 2019 |
Conference
Conference | 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019 |
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Land | United States |
By | Phoenix |
Periode | 23/06/2019 → 26/06/2019 |
Sponsor | ACM SIGACT |
Series | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN | 0737-8017 |
- Dynamic algorithm, Single source reachability, Strongly connected components
Research areas
Links
- http://arxiv.org/pdf/1901.03615
Submitted manuscript
ID: 239207274