Order Adjustment Approach Using Cayley Graphs for the Order/Degree Problem

Teruaki KITASUKA  Takayuki MATSUZAKI  Masahiro IIDA  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E101-D   No.12   pp.2908-2915
Publication Date: 2018/12/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.2018PAP0008
Type of Manuscript: Special Section PAPER (Special Section on Parallel and Distributed Computing and Networking)
Category: Graph Algorithms
Keyword: 
order/degree problem,  Cayley graph,  diameter,  average shortest path length (ASPL),  vertex bisection,  vertex injection,  vertex removal,  

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Summary: 
The order/degree problem consists of finding the smallest diameter graph for a given order and degree. Such a graph is beneficial for designing low-latency networks with high performance for massively parallel computers. The average shortest path length (ASPL) of a graph has an influence on latency. In this paper, we propose a novel order adjustment approach. In the proposed approach, we search for Cayley graphs of the given degree that are close to the given order. We then adjust the order of the best Cayley graph to meet the given order. For some order and degree pairs, we explain how to derive the smallest known graphs from the Graph Golf 2016 and 2017 competitions.