The optimal routing of augmented cubes. - Archive ouverte HAL
Article Dans Une Revue Information Processing Letters Année : 2018

The optimal routing of augmented cubes.

Résumé

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, AQ n , is the Cayley graph (Z n 2 , {e 1 , e 2 ,. .. , e n , J 2 ,. .. , J n }) where e i 's are the vectors of the standard basis and J i = n j=n−i+1 e j. S.A. Choudum and V. Sunitha showed that the greedy algorithm provides a shortest path between each pair of vertices of AQ n. Min Xu and Jun-Ming Xu claimed that this routing also proves that the edge-forwarding index of AQ n is 2 n−1. Here we disprove this claim, by showing that in this specific routing some edges are repeated nearly 4 3 2 n−1 times (to be precise, 2 n+1 3 for even values of n and 2 n+1 3 for odd values of n). However, by providing other routings, we prove that 2 n−1 is indeed the edge-forwarding index of AQ n .
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Dates et versions

hal-01934333 , version 1 (25-11-2018)

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  • HAL Id : hal-01934333 , version 1

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Meirun Chen, Reza Naserasr. The optimal routing of augmented cubes.. Information Processing Letters, 2018. ⟨hal-01934333⟩
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