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arXiv · 1611.03789

Improved Distance Queries and Cycle Counting by Frobenius Normal Form

Piotr Sankowski·Karol Węgrzycki
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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 $\widetilde{O}(n^\omega)$. 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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Piotr Sankowski, Karol Węgrzycki. 2016-11-11. Improved Distance Queries and Cycle Counting by Frobenius Normal Form. https://doi.org/10.1007/s00224-018-9894-x

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