Title

Sorting Networks on Restricted Topologies

Abstract

The sorting number of a graph with n vertices is the minimum depth of a sorting network with n inputs and n outputs that uses only the edges of the graph to perform comparisons. Many known results on sorting networks can be stated in terms of sorting numbers of different classes of graphs. In this paper we show the following general results about the sorting number of graphs.

1. Any n-vertex graph that contains a simple path of length d has a sorting network of depth (O(n log(n/d)).
2. Any n-vertex graph with maximal degree Δ has a sorting network of depth (formula Presented).

We also provide several results relating the sorting number of a graph with its routing number, size of its maximum matching, and other well known graph properties. Additionally, we give some new bounds on the sorting number for some typical graphs.

Meeting Name

45th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2018 (2018: Jan. 27-30, Nový Smokovec, Slovakia)

Department(s)

Computer Science

Comments

Published as Indranil Banerjee.

Keywords and Phrases

Matchings In Graphs; Routing via Matchings; Sorting Networks

International Standard Book Number (ISBN)

978-303010800-7

International Standard Serial Number (ISSN)

0302-9743

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Springer Verlag, All rights reserved.

Publication Date

01 Jan 2019

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