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- W3100962231 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 O-tilde(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 following problems efficiently.* All Nodes Shortest Cycles - for every node return the length of the shortest cycle containing it. We give an O-tilde(n^omega) algorithm that improves the previous O-tilde(n^((omega + 3)/2)) algorithm for unweighted digraphs.* We show how to compute all D sets of vertices lying on cycles of length c in {1, ..., D} in randomized time O-tilde(n^omega). It improves upon an algorithm by Cygan where algorithm that computes a single set is presented.* We present a functional improvement of distance queries for directed, unweighted graphs.* All Pairs All Walks - we show almost optimal O-tilde(n^3) time algorithm for all walks counting problem. We improve upon the naive O(D n^omega) time algorithm." @default.
- W3100962231 created "2020-11-23" @default.
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- W3100962231 date "2017-01-01" @default.
- W3100962231 modified "2023-09-23" @default.
- W3100962231 title "Improved Distance Queries and Cycle Counting by Frobenius Normal Form" @default.
- W3100962231 doi "https://doi.org/10.4230/lipics.stacs.2017.56" @default.
- W3100962231 hasPublicationYear "2017" @default.
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