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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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Cited by 10 (4 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.
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 an asympt ..."
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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...
A Note on Deflection Routing on Undirected Graphs
, 1994
"... We provide an algorithm that routes a load of k packets on an undirected graph G within 2diamG+ 2(k \Gamma 1) routing steps where diamG is the diameter of graph G. For a ddimensional mesh M the required number of routing steps is at most diamM + (d \Gamma 1) + 2(k \Gamma 1) where diamM is the diame ..."
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Cited by 2 (0 self)
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We provide an algorithm that routes a load of k packets on an undirected graph G within 2diamG+ 2(k \Gamma 1) routing steps where diamG is the diameter of graph G. For a ddimensional mesh M the required number of routing steps is at most diamM + (d \Gamma 1) + 2(k \Gamma 1) where diamM is the diameter of mesh M . The algotithm satisfies the "onepass of links" property. 1 Introduction In this note, we study the routing of messages in undirected graphs. Message routing has been abstracted in several ways. In packet routing it is assumed that a message can be transmitted between two adjacent processors (vertices of the undirected graph) in a single step as a packet. We examine the routing model known as deflection (or hotpotato) routing in which packets continously move between processors from the time they are injected into the network until the time they are consumed at their destination. The advantage of deflection routing is obvious. No queueing area is required at the processors...
A General Method for Deflection Worm Routing on Meshes Based on Packet Routing Algorithms
, 1994
"... In this paper, we consider the deflection worm routing problem on n \Theta n meshes. In deflection routing a message cannot be queued and it is always moving until it reaches its destination. In worm routing, the message is considered to be a worm; a sequence of k flits which, during the routing, fo ..."
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In this paper, we consider the deflection worm routing problem on n \Theta n meshes. In deflection routing a message cannot be queued and it is always moving until it reaches its destination. In worm routing, the message is considered to be a worm; a sequence of k flits which, during the routing, follow the head of the worm which knows the destination address. We show how to derive a deflection worm routing algorithm from a packet routing algorithm which uses queues of size O(f(N)) (N is the sidelength of the mesh in which the packet routing algorithm is applied). Our result generalises the method of Newman and Schuster in which only packet routing algorithms with a maximum queue of 4 packets can be used. KeywordsDeflection routing, Mesh connected computer, Online routing algorithm, Packet routing, Permutation routing, Worm routing, I. Introduction Routing messages between the processors of a parallel machine is a crucial task which directly affects the performance of the machin...
Networks on Which HotPotato Routing Does Not Livelock
 Distributed Computing
, 1999
"... Hotpotato routing is a form of synchronous routing which makes no use of buffers at intermediate nodes. Packets must move at every time step, until they reach their destination. If contention prevents a packet from taking its preferred outgoing edge, it is deflected on a different edge. Two simp ..."
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Hotpotato routing is a form of synchronous routing which makes no use of buffers at intermediate nodes. Packets must move at every time step, until they reach their destination. If contention prevents a packet from taking its preferred outgoing edge, it is deflected on a different edge. Two simple design principles for hot potato routing algorithms are minimum advance, that advances at least one packet towards its destination from every nonempty node (and possibly deflects all other packets), and maximum advance, that advances the maximum possible number of packets. Livelock is a situation in which packets keep moving indefinitely in the network without any packet ever reaching its destination. It is known that even maximum advance algorithms might livelock on some networks. We show that minimum advance algorithms never livelock on tree networks, and that maximum advance algorithms never livelock on triangulated networks. 1 Introduction A network of processors is modeled ...
Simple Algorithms for HotPotato Routing
, 1996
"... Hotpotato routing is a particular form of routing in a synchronous network of processors, which makes no use of buffers at intermediate nodes. Packets must keep moving in the network (possibly deflected to "bad" directions), giving rise to the term "hotpotato". Simple hotpotato algorithms are int ..."
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Hotpotato routing is a particular form of routing in a synchronous network of processors, which makes no use of buffers at intermediate nodes. Packets must keep moving in the network (possibly deflected to "bad" directions), giving rise to the term "hotpotato". Simple hotpotato algorithms are interesting for both practical and theoretical reasons. We analyze the worst case performance of some simple hotpotato routing algorithms. For example, we show that any "minimumadvance" algorithm cannot livelock on a tree network, and present a deterministic algorithm for general graphs, inspired by random walks. One of our main topics studies an algorithm for the mesh based on selecting a small number of Hamiltonian paths, such that vertices that are close together on the mesh are also close together on at least one of these paths. Based on these families of Hamiltonian paths, routing between vertices is achieved in time that depends only on the distance between these vertices, regardless of ...
On the HotPotato Permutation Routing Algorithm of Borodin, Rabani and Schieber
, 1995
"... Borodin, Rabani and Schieber [3] presented an O(n p n)step algorithm for hotpotato routing of permutations on n \Theta n meshes. They conjectured that their algorithm completes the routing of a permutation in O(n) steps. In this paper, we present worstcase partial permutations which force thei ..."
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Borodin, Rabani and Schieber [3] presented an O(n p n)step algorithm for hotpotato routing of permutations on n \Theta n meshes. They conjectured that their algorithm completes the routing of a permutation in O(n) steps. In this paper, we present worstcase partial permutations which force their algorithm to use\Omega\Gamma n p n) routing steps.
Pure Greedy HotPotato Routing in the 2D Mesh . . .
 PARALLEL PROCESSING LETTERS
"... We analyze here a pure greedy hotpotato routing strategy on a twodimensional mesh of n² nodes. We specifically study the case of n² packets, originating one per node, to be delivered at random uniform destinations. Each packet attempts to follow the shortest path leading first to the destinatio ..."
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We analyze here a pure greedy hotpotato routing strategy on a twodimensional mesh of n² nodes. We specifically study the case of n² packets, originating one per node, to be delivered at random uniform destinations. Each packet attempts to follow the shortest path leading first to the destination row/column (whichever is closest) and then to the actual destination node. A deflection policy is adopted to solve conflicts. We prove that all packets are delivered to the destinations in average time O(n log n). The average is taken over all possible destination functions. No average case analysis of pure greedy hotpotato routing was known up to now.