Super-Logarithmic Lower Bounds for Dynamic Graph Problems
In this work, we prove a \tilde{\Omega}(\lg^{3/2} n) unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in n-node directed acyclic graphs under edge insertions. This is the first super-logarithmic lower bound for any...
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| Veröffentlicht in: | Proceedings / annual Symposium on Foundations of Computer Science S. 1589 - 1604 |
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06.11.2023
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| ISSN: | 2575-8454 |
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| Abstract | In this work, we prove a \tilde{\Omega}(\lg^{3/2} n) unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in n-node directed acyclic graphs under edge insertions. This is the first super-logarithmic lower bound for any natural graph problem. In proving the lower bound, we also make novel contributions to the state-of-the-art data structure lower bound techniques that we hope may lead to further progress in proving lower bounds. |
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| AbstractList | In this work, we prove a \tilde{\Omega}(\lg^{3/2} n) unconditional lower bound on the maximum of the query time and update time for dynamic data structures supporting reachability queries in n-node directed acyclic graphs under edge insertions. This is the first super-logarithmic lower bound for any natural graph problem. In proving the lower bound, we also make novel contributions to the state-of-the-art data structure lower bound techniques that we hope may lead to further progress in proving lower bounds. |
| Author | Yu, Huacheng Larsen, Kasper Green |
| Author_xml | – sequence: 1 givenname: Kasper Green surname: Larsen fullname: Larsen, Kasper Green email: larsen@cs.au.dk organization: Aarhus University,Aarhus,Denmark – sequence: 2 givenname: Huacheng surname: Yu fullname: Yu, Huacheng email: yuhch123@gmail.com organization: Princeton University Princeton,NJ,United States |
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| Snippet | In this work, we prove a \tilde{\Omega}(\lg^{3/2} n) unconditional lower bound on the maximum of the query time and update time for dynamic data structures... |
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| SubjectTerms | cell-probe model Computational modeling Computer science data structure lower bounds Data structures Directed acyclic graph dynamic graph algorithms dynamic reachability Heuristic algorithms |
| Title | Super-Logarithmic Lower Bounds for Dynamic Graph Problems |
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