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Improved Distance Queries and Cycle Counting by Frobenius Normal Form
Piotr Sankowski1, Karol Węgrzycki1
1Institute of Informatics, University of Warsaw, Warsaw, Poland.
Abstract:
Consider an unweighted, directed graph G with the diameter D. In this paper, we introduce the framework for counting cycles and walks of given length in matrix multiplication time . The framework is based on the fast decomposition into Frobenius normal form and the Hankel matrix-vector multiplication. It allows us to solve the All-Nodes Shortest Cycles, All-Pairs All Walks problems efficiently and also give some improvement upon distance queries in unweighted graphs.
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