Optimal layouts on a chain ATM network

Ornan Gerstel*, Avishai Wool, Shmuel Zaks

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We study a routing problem which occurs in high-speed (ATM) networks, termed the "rooted virtual path layout problem" on chain networks. This problem is essentially a tree embedding problem on a chain host graph. We present four performance measures for the quality of such an embedding which have practical implications, and find optimal solutions for each of them. We first show that the search can be restricted to the class of layouts with no crossovers. Given bounds on the load l and number of hops h in a layout, we then present a family of ordered trees T (ℓ, h), within which an optimal solution can be found (if one exists at all); this holds for either the worst-case or average-case measures, and for a chain of length n, with n ≤ (ℓ+h). For the worst-case measures these trees are used in characterizing, constructing, and proving the optimality of the solutions. For each average-case measure, a recursive formulation of the optimal solution is presented, from which an optimal polynomial dynamic programming algorithm is derived. Furthermore, for the unweighted average measures, these formulations are explicitly solved, and the optimal solutions are mapped to T (ℓ, h).

Original languageEnglish
Pages (from-to)157-178
Number of pages22
JournalDiscrete Applied Mathematics
Issue number1-3
StatePublished - 25 Mar 1998
Externally publishedYes


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