Improved Distance Queries and Cycle Counting by Frobenius Normal Form
Data Structures and Algorithms
2023-03-14 v4
Abstract
Consider an unweighted, directed graph with the diameter . 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.
Keywords
Cite
@article{arxiv.1611.03789,
title = {Improved Distance Queries and Cycle Counting by Frobenius Normal Form},
author = {Piotr Sankowski and Karol Węgrzycki},
journal= {arXiv preprint arXiv:1611.03789},
year = {2023}
}
Comments
Lemma 2 in the previous version of this paper is incorrect. We thank Adam Karczmarz for pointing out the mistake