OPTIMAL LAYOUTS ON A CHAIN ATM NETWORK

We study a routing problem which occurs in high-speed (ATM) networks, termed the ''rooted virtual path layout problem'' on chain networks. T his problem is essentially a tree embedding problem on a chain host gr aph. We present four performance measures for the quality of such an e mbedding 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 I an d number of hops h in a layout, we then present a family of ordered tr ees T(l, h), within which an optimal solution can be found (if one exi sts at all); this holds for either the worst-case or average-case meas ures, and for a chain of length n, with n less than or equal to (l+h/l ). For the worst-case measures these trees are used in characterizing, constructing, and proving the optimality of the solutions. For each a verage-case measure, a recursive formulation of the optimal solution i s presented, from which an optimal polynomial dynamic programming algo rithm is derived. Furthermore, for the unweighted average measures, th ese formulations are explicitly solved, and the optimal solutions are mapped to T(l, h). (C) 1998 Elsevier Science B.V. All rights reserved.