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 tdk(G)≥(d-2)k/kk.
|Number of pages||11|
|State||Published - 1 Jan 1997|
|Event||Proceedings of the 1997 5th Israel Symposium on Theory of Computing and Systems, ISTCS - Ramat-Gan, Isr|
Duration: 17 Jun 1997 → 19 Jun 1997
|Conference||Proceedings of the 1997 5th Israel Symposium on Theory of Computing and Systems, ISTCS|
|Period||17/06/97 → 19/06/97|