Show how given a graph G in adjacency matrix representation, it is possible to use Strassen's matrix multiplication algorithm to determine if the graph has a triangle in time o(n3).
Show how given a graph G in adjacency matrix representation, it is possible to use Strassen's matrix multiplication algorithm to determine if the graph has a triangle in time o(n3).
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question
In the last homework, we gave an
undirected graph in O(n2 +nm) time, which is Θ(n3) when the graph is dense. Show how given a graph
G in adjacency matrix representation, it is possible to use Strassen's matrix multiplication algorithm
to determine if the graph has a triangle in time o(n3). (You can use the algorithm
without description or proof, but you must explain connection to the existence of a triangle in the graph).
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