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ManytoMany Routing on Trees via Matchings
, 1996
"... In this paper we present an extensive study of manytomany routing on trees under the matching routing model. Our study includes online and offline algorithms. We present an asymptotically optimal online algorithm which routes k packets to their destination within d(k \Gamma 1) + d \Delta dist r ..."
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In this paper we present an extensive study of manytomany routing on trees under the matching routing model. Our study includes online and offline algorithms. We present an asymptotically optimal online algorithm which routes k packets to their destination within d(k \Gamma 1) + d \Delta dist routing steps, where d is the degree of tree T on which the routing takes place and dist is the maximum distance any packet has to travel. We also present an offline algorithm that solves the same problem within 2(k \Gamma 1)+dist steps. The analysis of our algorithms is based on the establishment of a close relationship between the matching and the hotpotato routing models that allows us to apply tools which were previously used exclusively in the analysis of hotpotato routing.
Dynamic Tree Routing under the "Matching with Consumption" Model
, 1996
"... . In this paper we consider dynamic routing on trees under the "matching with consumption" routing model, a natural extension of the matching routing model introduced by Alon, Chung and Graham [1, 2], which allows for the consumption of packets when they reach their destination. We present ..."
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Cited by 5 (2 self)
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. In this paper we consider dynamic routing on trees under the "matching with consumption" routing model, a natural extension of the matching routing model introduced by Alon, Chung and Graham [1, 2], which allows for the consumption of packets when they reach their destination. We present an asymptotically optimal online algorithm that routes k packets to their destination within d(k \Gamma 1) + d \Delta dist routing steps where d is the degree of tree T on which the routing takes place and dist is the maximum distance some packet has to travel. We present an offline algorithm that solves the same problem within 2(k \Gamma 1) + dist steps. Versions of both the online and the offline algorithms which avoid livelock situations are also provided. We establish a close relation between the "matching with consumption" and the hotpotato routing models, and we exploit it in the analysis of our routing algorithms. 1 Introduction In a packet routing problem on a connected undirected gra...
Permutation Routing via Matchings
, 1996
"... The following routing problem on an undirected graph is considered: Initially, each node of the graph contains exactly one packet. Each node is the destination node of exactly one packet, so the initial state can be considered a permutation of the packets. The packets are routed to their destination ..."
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Cited by 4 (1 self)
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The following routing problem on an undirected graph is considered: Initially, each node of the graph contains exactly one packet. Each node is the destination node of exactly one packet, so the initial state can be considered a permutation of the packets. The packets are routed to their destination nodes by a sequence of steps. In one step, each packet can either remain at its current location, or it can be swapped with a neighbor, i.e., a step is determined by a matching of the participating nodes. The time complexity of the previously best algorithm for routing all packets to their destination nodes given any initial permutation in a graph with n nodes was bounded by 13 5 n. We present an algorithm running in at most 2n \Gamma 3 steps, where n 2, at the same time simplifying the analysis of the time complexity.
Parametric Permutation Routing via Matchings
, 1996
"... The problem of routing permutations on graphs via matchings is considered, and we present a general algorithm which can be parameterized by dierent heuristics. This leads to a framework which makes the analysis simple and local. 1 Introduction The routing problem we consider is the following: W ..."
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The problem of routing permutations on graphs via matchings is considered, and we present a general algorithm which can be parameterized by dierent heuristics. This leads to a framework which makes the analysis simple and local. 1 Introduction The routing problem we consider is the following: We are given an undirected connected graph with n nodes and a permutation of the nodes. Each node u contains one packet which must be routed to (u). The routing is carried out in a sequence of steps. In one step, each packet can either remain at its current location, or it can be swapped with a neighbor. Thus, at all times each node has exactly one packet. We are interested in designing an algorithm for this problem with a low complexity measured in the number of steps necessary in the worst case to ensure that all packets are routed to their correct locations independent of the initial conguration. This problem was rst dened and investigated in [ACG93, ACG94], and an upper bound of 3...
Online Matching Routing on Trees
, 1997
"... In this paper we examine online heap construction and online permutation routing on trees under the matching model. Let T be and nnode tree of maximum degree d. By providing online algorithms we prove that: (i) For a rooted tree of height h, online heap construction can be completed within (2d ..."
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In this paper we examine online heap construction and online permutation routing on trees under the matching model. Let T be and nnode tree of maximum degree d. By providing online algorithms we prove that: (i) For a rooted tree of height h, online heap construction can be completed within (2d \Gamma 1)h routing steps. (ii) For an arbitrary tree, online permutation routing can be completed within 4dn routing steps. (iii) For a complete dary tree, online 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 ...