Abstract
Consider the following problem: Given an n × n multiplication table, decide whether it is a Cayley multiplication table of a group. Among deterministic algorithms for this problem, the best known algorithm is implied by F. W. Light's associativity test (1949) and has running time of O(n2log n). Allowing randomization. the best known algorithm has running time of O(n2log(1/Δ)), where Δ > 0 is the error probability of the algorithm (Rajagopalan and Schulman, FOCS 1996, SICOMP 2000). In this work, we improve upon both of the above known algorithms. Specifically, we present a deterministic algorithm for the above problem whose running time is O(n2). This performance is optimal up to constants. A central tool we develop is an efficient algorithm for finding a subset A of a group G satisfying A2=G while |A|=O(√{|G|}).
Original language | English |
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Title of host publication | Proceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024 |
Publisher | IEEE Computer Society |
Pages | 2131-2147 |
Number of pages | 17 |
ISBN (Electronic) | 9798331516741 |
State | Published - 2024 |
Event | 65th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2024 - Chicago, United States Duration: 27 Oct 2024 → 30 Oct 2024 |
Publication series
Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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ISSN (Print) | 0272-5428 |
Conference
Conference | 65th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2024 |
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Country/Territory | United States |
City | Chicago |
Period | 27/10/24 → 30/10/24 |
Bibliographical note
Publisher Copyright:© 2024 IEEE.
Keywords
- Computational group theory