Detecting directed 4-cycles still faster

Authors:
Friedrich Eisenbrand;Fabrizio Grandoni
Affiliations:
Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany;Dipartimento di Informatica, Sistemi e Produzione, Universita di Roma "Tor Vergata", Via del Politecnico 1, 00133 Roma, Italy
Venue:
Information Processing Letters
Year:
2003

Citing 5
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Abstract

We present a method to detect simple cycles of length 4 of a directed graph in O(n1/ωe2-2/ω) steps, where n denotes the number of nodes, e denotes the number of edges and ω is the exponent of matrix multiplication. This improves upon the currently fastest methods for α ∈ (2/(4 - ω), (ω + 1)/2), where e = nα.