Approaches to unweighted and undirected graph cut sparsification
Date
2023
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Producer
Director
Performer
Choreographer
Costume Designer
Music
Videographer
Lighting Designer
Set Designer
Crew Member
Funder
Rehearsal Director
Concert Coordinator
Advisor
Moderator
Panelist
Alternative Title
Department
Haverford College. Department of Computer Science
Type
Thesis
Original Format
Running Time
File Format
Place of Publication
Date Span
Copyright Date
Award
Language
eng
Note
Table of Contents
Terms of Use
Rights Holder
Access Restrictions
Tri-College users only
Terms of Use
Tripod URL
Identifier
Abstract
Graph sparsification is a type of graph algorithm that approximates a dense graph G by a sparse graph G’, where G’ has fewer edges. The motivation for graph sparsification is that we can perform computation on G’ to derive results with regard to G with much fewer computational resources. In other words, G’ is similar enough to G that computation results of one can be used to approximate those of the other. In this paper, we examine different approaches to cut sparsification. Cut sparsification is one type of sparsification where the sparsified graph G’ should have cuts within certain bounds of the corresponding cuts in the original graph G. There are two cut sparsification algorithms that we examine in this paper: namely uniform sampling and non-uniform sampling. As their names suggest, uniform sampling means that each edge is sampled with the same probability, whereas non-uniform sampling means that each edge is sampled with a different probability. In general, uniform sampling has better asymptotic than non-uniform sampling because each edge is treated indiscriminately. However, non-uniform sampling can reduce a bigger number of edges than uniform sampling in certain cases of dense graph.