Abstract
We present new algorithms for counting and detecting small tournaments in a given tournament. In particular, we prove that every tournament on four vertices (there are four) can be detected in O(n2) time and counted in O(nω) time where ω<2.372 is the matrix multiplication exponent. We further prove that any tournament on five vertices (there are 12) can be counted in O(nω+1) time. As for lower-bounds, we prove that for almost all k-vertex tournaments, the complexity of the detection problem is not easier than the complexity of the corresponding well-studied counting problem for undirected cliques of order k−O(logk).
Original language | English |
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Article number | 114911 |
Journal | Theoretical Computer Science |
Volume | 1024 |
DOIs | |
State | Published - 12 Jan 2025 |
Bibliographical note
Publisher Copyright:© 2024 Elsevier B.V.
Keywords
- Counting
- Detection
- Tournament
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science