On-line Matching Routing on Trees

In this paper we examine on-line heap construction and on-line permutation routing on trees under the matching model. Let T be and n-node tree of maximum degree d. By providing on-line algorithms we prove that: (i) For a rooted tree of height h, on-line heap construction can be completed within (2d \Gamma 1)h routing steps. (ii) For an arbitrary tree, on-line permutation routing can be completed within 4dn routing steps. (iii) For a complete d-ary tree, on-line permutation routing can be completed within 2(d \Gamma 1)n+ 2d log 2 n routing steps. Technical Report 514 Basser Department of Computer Science University of Sydney Original: 27 May 1997 1 The work of Dr Symvonis was supported by an ARC Institutional Grant. 27 May 1997 1 Introduction In packet routing problems we are given a network (usually represented by a connected, undirected graph) and a set of packets distributed over the nodes of the network. Each packet has an origin node and a destination node and our aim ..

On-line Matching Routing on Trees

Abstract. We examine on-line heap construction and on-line permutation routing on trees under the matching model. Let T be and n-node tree of maximum degree d. By providing on-line algorithms we prove that: 1. For a rooted tree of height h, on-line heap construction can be completed within (2d − 1)h routing steps. 2. For an arbitrary tree, on-line permutation routing can be completed within 4dn routing steps. 3. For a complete d-ary tree, on-line permutation routing can be completed within 2(d − 1)n +2dlog 2 n routing steps.