Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6874163 | Information Processing Letters | 2018 | 5 Pages |
Abstract
A routing in a graph G is a set of paths connecting each ordered pair of vertices. Load of an edge e is the number of times it appears on these paths. The edge-forwarding index of G is the smallest of maximum loads over all routings. Augmented cube of dimension n, AQn, is the Cayley graph (Z2n,{e1,e2,â¦,en,J2,â¦,Jn}) where ei's are the vectors of the standard basis and Ji=âj=nâi+1nej. S.A. Choudum and V. Sunitha showed that the greedy algorithm provides a shortest path between each pair of vertices of AQn. Min Xu and Jun-Ming Xu claimed that this routing also proves that the edge-forwarding index of AQn is 2nâ1. Here we disprove this claim, by showing that in this specific routing some edges are repeated nearly 432nâ1 times (to be precise, â2n+13â for even values of n and â2n+13â for odd values of n). However, by providing other routings, we prove that 2nâ1 is indeed the edge-forwarding index of AQn.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Meirun Chen, Reza Naserasr,