Path layout on tree networks: Bounds in different label switching models

Path Layout is a fundamental graph problem in label switching protocols. This problem is raised in various protocols such as the traditional ATM protocol and MPLS which is a new label switching protocol standardized recently by the IETF. Path layout is essentially the problem of reducing the size of the label-table in a router. The size is equivalent to the number of different paths that pass through the router, or start from it. A reduction in the size can be achieved by choosing a relatively small number of paths, from which a larger set is composed using concatenation. In this paper we deal with three variations of the Path Layout Problem according to the special characteristics of paths in three label switching protocols, MPLS, ATM and TRAINET. We focus on tree networks and show an algorithm which finds label-tables of small size while permitting concatenation of at most k paths. We prove that this algorithm gives worst case tight bounds (up to constant factor) for all three models. The bounds are given as a function of the size of the tree, and the maximum degree.