On the totalk-diameter of connection networks

Yefim Dinitz, Tamar Eilam, Shlomo Moran, Shmuel Zaks

Research output: Contribution to journalArticlepeer-review

Abstract

We study connection networks in which certain pairs of nodes have to be connected by k edge-disjoint paths, and study bounds for the minimal sum of lengths of such k paths. We define the related notions of totalk-distance for a pair of nodes and totalk-diameter of a connection network, and study the value TDk(d) which is the maximal such totalk-diameter of a network with diameter d. These notions have applications in fault-tolerant routing problems, in ATM networks, and in compact routing in networks. We prove an upper bound on TDk(d) and a lower bound on the growth of TDk(d) as functions of k and d; those bounds are tight, θ(dk), when k is fixed. Specifically, we prove that TDk(d)≤2k-1dk, with the exceptions TD2(1) = 3, TD3(1) = 5, and that for every k,d0>0, there exists (a) an integer d≥d0 such that TDk(d)≥dk/kk, and (b) a k-connected simple graph G with diameter d such that d≥d0, and whose totalk-diameter is at least (d - 2)k/kk.

Original languageEnglish
Pages (from-to)213-228
Number of pages16
JournalTheoretical Computer Science
Volume247
Issue number1-2
DOIs
StatePublished - 28 Sep 2000
Externally publishedYes

Keywords

  • Communication network
  • Connection network
  • Edge-disjoint paths
  • Flow in networks
  • Total-diameter
  • Total-distance

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