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Optimal Bounds for Matching Routing on Trees
 In Proceedings of the 8th Annual ACMSIAM Symposium on Discrete Algorithms
, 1997
"... The permutation routing problem is studied for trees under the matching model. By introducing a novel and useful (socalled) caterpillar tree partition, we prove that any permutation on an nnode tree (and thus graph) can be routed in 3 2 n + O(log n) steps. This answers an open problem of Alon, ..."
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The permutation routing problem is studied for trees under the matching model. By introducing a novel and useful (socalled) caterpillar tree partition, we prove that any permutation on an nnode tree (and thus graph) can be routed in 3 2 n + O(log n) steps. This answers an open problem of Alon, Chung and Graham. Key words. matching routing, offline algorithms, trees AMS subject classifications. 05C, 68M, 68R 1 Introduction Routing problems on networks arise in different fields such as communications, parallel architectures and VLSI theory, and have been extensively studied in recent years (see [9, 10] for a comprehensive survey). In this paper, we study permutation routing under the matching model, which was proposed by Alon, Chung and Graham[2]. The routing of this type is described as follows. Given a graph G = (V; E) with vertex set V and edge set E. Initially, each vertex v of G is occupied by a "packet" p. To each packet p is associated a destination ß(v) 2 V , so that di...
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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Cited by 12 (5 self)
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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.
ManytoOne Packet Routing via Matchings
 In Proceedings of the Third Annual International Computing and Combinatorics Conference
, 1997
"... In this paper we study the packet routing problem under the matching model proposed by Alon, Chung and Graham [1]. We extend the model to allow more than one packet per origin and destination node. We give tight bounds for the manytoone routing number for complete graphs, complete bipartite graphs ..."
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Cited by 6 (2 self)
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In this paper we study the packet routing problem under the matching model proposed by Alon, Chung and Graham [1]. We extend the model to allow more than one packet per origin and destination node. We give tight bounds for the manytoone routing number for complete graphs, complete bipartite graphs and linear arrays. We also present an efficient algorithm for manytoone routing on an trees (and therefore any graph). Finally, we give bounds for routing arbitrary relations in this model. 1 Introduction Routing packets arises naturally in the design of largescale parallel computers and the study of data flow in parallel computing. Packet routing consists of moving packets of data from each node of a network to the other nodes in the network. The goal is to move all of the packets to their desired locations as quickly as possible. Various routing problems have been extensively studied under different models. We refer the reader to [4] for a survey of the topic. In this paper, we study ...
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...
Sorting by Parallel Insertion on a OneDimensional SubBus Array
 IEEE Trans. on Computers
, 1996
"... We consider the problem of sorting on a onedimensional subbus array of processors. The subbus broadcast operation makes possible a new class of parallel sorting algorithms whose complexity we analyze with the parallel insertion model. A sorting method, or sorting strategy, in the parallel insert ..."
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We consider the problem of sorting on a onedimensional subbus array of processors. The subbus broadcast operation makes possible a new class of parallel sorting algorithms whose complexity we analyze with the parallel insertion model. A sorting method, or sorting strategy, in the parallel insertion model, uses a sequence of left and right insertion steps, of which we give two types: greedy insertion steps and simple insertion steps. For two restricted classes of parallel insertion sorting, the oneway and the alternating sorting strategies, we give lower bounds and optimal sorting strategies that exactly match the lower bounds. Optimal alternating sorting strategies are demonstrated to use a factor of two fewer insertion steps on average than oddeven transposition sort and any optimal oneway sorting strategy. For general sorting strategies, we give a weak lower bound and consider a sorting strategy that uses the fewest greedy insertion steps. Finally, we discuss the issues involve...
Potentialfunctionbased Analysis of an offline Heap Construction Algorithm
, 2000
"... In this paper we examine the problem of heap construction on a rooted tree T from a packet routing perspective. Each node of T initially contains a packet which has a keyvalue associated with it. The aim of the heap construction algorithm is to route the packets along the edges of the tree so that ..."
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Cited by 1 (1 self)
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In this paper we examine the problem of heap construction on a rooted tree T from a packet routing perspective. Each node of T initially contains a packet which has a keyvalue associated with it. The aim of the heap construction algorithm is to route the packets along the edges of the tree so that, at the end of the routing, the tree is heap ordered with respect to the key values associated with the packets. We consider the case where the routing is performed according to the matching model and we present and analyse an offline algorithm that heap orders the tree within 2h(T) routing steps, where h(T) is the height of tree T. The main contribution of the paper is the novel analysis of the algorithm based on potential functions. It is our belief that potential functions will be the main vehicle in analysing fast nonrecursive routing algorithms.
Implementation of Communication Intensive Algorithms On Reconfigurable Mesh Architectures
, 1993
"... The aim of this thesis has been: To demonstrate the superiority of the reconfigurable mesh architecture, especially for communication intensive algorithms, over existing fixed connection architectures. Reconfiguration has been considered by researchers for several years as a means of enhancing perfo ..."
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The aim of this thesis has been: To demonstrate the superiority of the reconfigurable mesh architecture, especially for communication intensive algorithms, over existing fixed connection architectures. Reconfiguration has been considered by researchers for several years as a means of enhancing performance of parallel computers. Recently the most general model of reconfiguration for SIMD architectures was presented by Miller, Prasanna, Reisis and Stout [34]. The work presented in this thesis is based on the reconfigurable mesh model proposed in [34]. The main contribution of this thesis consists of algorithms for three basic applications  sorting, routing, and connected component labelling. These algorithms are significantly faster compared to known algorithms for the same applications on fixed connection mesh architectures. Thus, this thesis has been successful in justifying the hardware cost of adding reconfiguration to fixed connection meshes by demonstrating the superiority of re...
Sorting algorithms based on the oddeven transposition sort and the shearsort with DNA strands
"... Abstract: In recent works for high performance computing, computation with DNA molecules, that is, DNA computing, has considerable attention as one of nonsilicon based computing. In this paper, we propose two procedures for sorting with DNA strands. An input of the algorithms is a set of Ò binary n ..."
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Abstract: In recent works for high performance computing, computation with DNA molecules, that is, DNA computing, has considerable attention as one of nonsilicon based computing. In this paper, we propose two procedures for sorting with DNA strands. An input of the algorithms is a set of Ò binary numbers of Ñ bits, which are denoted by Ç ÑÒ kinds of DNA strands. We first propose a procedure for the compareandexchange operation, which is a basic operation for the sorting algorithms. We next propose two sorting algorithms, which are based on the oddeven transposition sort and the shearsort. The first algorithm runs in Ç Ò steps using Ç ÑÒ DNA strands, and the second algorithm runs in Ç Ô Ò ÐÓ � Ò steps using Ç ÑÒ DNA strands.
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 ...
c ○ 1999 Society for Industrial and Applied Mathematics OPTIMAL BOUNDS FOR MATCHING ROUTING ON TREES ∗
"... Abstract. The permutation routing problem is studied for trees under the matching model. By introducing a novel and useful (socalled) caterpillar tree partition, we prove that any permutation on an nnode tree (and thus graph) can be routed in 3 n + O(log n) steps. This answers an open 2 ..."
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Abstract. The permutation routing problem is studied for trees under the matching model. By introducing a novel and useful (socalled) caterpillar tree partition, we prove that any permutation on an nnode tree (and thus graph) can be routed in 3 n + O(log n) steps. This answers an open 2