Computing the diameter of 17-pancake graph using a PC cluster

Authors:
Shogo Asai;Yuusuke Kounoike;Yuji Shinano;Keiichi Kaneko
Affiliations:
Tokyo University of Agriculture and Technology, Tokyo, Japan;Tokyo University of Agriculture and Technology, Tokyo, Japan;Tokyo University of Agriculture and Technology, Tokyo, Japan;Tokyo University of Agriculture and Technology, Tokyo, Japan
Venue:
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
Year:
2006

Citing 6
Cited 3

Introduction to parallel computing: design and analysis of algorithms

Introduction to parallel computing: design and analysis of algorithms
Parallel computing (2nd ed.): theory and practice

Parallel computing (2nd ed.): theory and practice
Optimal Information Dissemination in Star and Pancake Networks

IEEE Transactions on Parallel and Distributed Systems
On the diameter of the pancake network

Journal of Algorithms
Pancake problems with restricted prefix reversals and some corresponding Cayley networks

Journal of Parallel and Distributed Computing
Computing the Diameters of 14- and 15-Pancake Graphs

ISPAN '05 Proceedings of the 8th International Symposium on Parallel Architectures,Algorithms and Networks

Cluster fault-tolerant routing in pancake graphs

PDCS '07 Proceedings of the 19th IASTED International Conference on Parallel and Distributed Computing and Systems
On average and highest number of flips in pancake sorting

Theoretical Computer Science
On some structural properties of star and pancake graphs

Information Theory, Combinatorics, and Search Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

An n-pancake graph is a graph whose vertices are the permutations of n symbols and each pair of vertices are connected with an edge if and only if the corresponding permutations can be transitive by a prefix reversal. Since the n-pancake graph has n! vertices, it is known to be a hard problem to compute its diameter by using an algorithm with the polynomial order of the number of vertices. Fundamental approaches of the diameter computation have been proposed. However, the computation of the diameter of 15-pancake graph has been the limit in practice. In order to compute the diameters of the larger pancake graphs, it is indispensable to establish a sustainable parallel system with enough scalability. Therefore, in this study, we have proposed an improved algorithm to compute the diameter and have developed a sustainable parallel system with the Condor/MW framework, and computed the diameters of 16- and 17-pancake graphs by using PC clusters.