Optimal layouts on a chain ATM network

Abstract

We study a routing problem which occurs in high-speed (ATM) networks, termed the “one-to-many 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 to 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 $\mathcal{T}$(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 ≤ $\left( {\begin{array}{*{20}c}{l + h} \\l \\\end{array} } \right)$. For the worstcase measures these trees are used in characterizing, constructing, and proving the optimality of the solutions. For the average-case measures polynomial dynamic programming algorithms are presented which find optimal solutions for all cases.