B. Hajek, Bounds on evacuation time for deflection routing, Distributed Computing, 5 (1991) 1--6.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....its source to its destination and proceeds along this path; if it arrives at a node and finds its prefered outgoing edge occupied, it is stored in a queue of packets wishing to use that edge. The first hot potato algorithm was proposed by Baran [2] Borodin and Hopcroft [7] Prager [17] and Hajek [12] presented algorithms for hypercubes. Hot potato routing algorithms for 2 dimensional meshes and tori were proposed by Bar Noy et al. 3] Ben Aroya et al. 4] Newman and Schuster [16] Kaufman et al. 14] Feige and Raghavan [11] Kaklamanis et al. 13] Borodin et al. 6] and Feige [10] ....

....and Borodin et al. 6] are in this direction. Their results are comparable to earlier ones but their algorithms are more appropriate for practical implementations. In particular, a desired characteristic that indicates simplicity of these algorithms is the one pass property introduced by Hajek [12] and by Feige and Raghavan [11] Packets that enter a node are considered one by one in a predefined order and each of them is assigned to an outgoing link not previously assigned to another packet. An extension of this property is the k pass, according to which, each input packet is considered k ....

B. Hajek. Bounds on Evacuation Time for Deflection Routing. Distributed Computing, 5:1--6, 1991.

....their algorithms may be too specifically tailored to static permutations and synchronous networks to be practical. The desire to have simple routing algorithms with constant sized queues per node has led to the growing body of literature on hot potato (or deflection) routing [BNRST93, BC91, FR92, Haj91, KKR93, NS92] where at each step every node in the network must send all packets it received during the previous step. In these algorithms, no extra queues are needed, and packets again typically take nonminimal paths. Newman and Schuster [NS92] give an algorithm that routes any permutation in ....

....4.6. This difference is small because the algorithm is using more randomness than in Experiments 1 and 2, so the initial random state has less impact on delivery time than in the previous experiments. 64 4. 3 A Greedy Hot Potato Algorithm Hot potato or deflection routing [BNRST93, BDHS93, FR92, Haj91, KKR93] where a node must send on the next step any packets it receives in the current step, offers the possibility of simple logic and simple algorithms. Greedy hot potato routing [BDHS93] where packets use profitable outlinks whenever they are available, might be a nonminimal adaptive ....

B. Hajek. Bounds for evacuation time for deflection routing. Distributed Computing, 5:1--6, 1991.

....like the sorting based algorithms, their algorithms may be too specifically tailored to static permutations and synchronous networks to be practical. The desire to have simple routing algorithms with constant sized queues per node has led to the growing body of literature on hot potato routing [1, 5, 8, 9, 12, 22], where at each step every node in the network must send all packets it received during the previous step. In these algorithms, packets again typically take nonminimal paths. Newman and Schuster [22] 3 give an algorithm that routes any permutation in 7n o(n) steps, but the algorithm uses ....

B. Hajek. Bounds for evacuation time for deflection routing. Distributed Computing, 5:1--6, 1991.

....because in such situations there is no reason to deroute. Given that assumption, then only when congestion is heavy can a nonminimal algorithm behave differently from a minimal algorithm. But by then, it perhaps is too late to try to relieve the congestion. Hot potato or deflection routing [1, 2, 9, 10, 12], where a node must send on the next step any packets it receives in the current step, offers the possibility of simple logic and simple algorithms. Because nodes in hot potato routing do not use extra buffer space, congestion does not have a chance to build as it does in networks where nodes do ....

B. Hajek. Bounds for evacuation time for deflection routing. Distributed Computing, 5:1--6, 1991.

....A packet may be deflected to unexpected regions of the network, interfering with other packets in these regions. Nevertheless, deflection routing seems to perform very well in practice, parallel machines that use this method include the Tera computer, the HEP multiprocessor, and others. Hajek [17] gave a 2k log N deterministic hot potato algorithm for routing k packets (with arbitrary destinations) on the N node hypercube. His algorithm is the first proven livelock free algorithm. Feige and Raghavan [15] developed and analyzed hot potato algorithms that use random oblivious delays. Their ....

B. Hajek. Bounds on evacuation time for deflection routing. Distributed Computing, 5:1--6, 1991.

....algorithms which differ with regard to their methods for resolving conflicts. We say a greedy hot potato routing algorithm is oblivious if, for each conflict, the packet to traverse the link is chosen arbitrarily from those packets which wish to do so. The minimum distance heuristic, proposed in [21, 34], chooses a packet with minimum distance to its destination to advance, and in the maximum distance heuristic, a packet with maximum distance to its destination is chosen to advance. Only recently has there been any precise analysis of the performance of greedy hot potato 2 algorithms [6 8, 12, ....

B. Hajek, Bounds on evacuation time for deflection routing. Distributed Computing, 5(1):1-- 6, 1991.

....and Computer Science, Haifa University, Haifa, Israel 31905. E mail: ilan mathcs.haifa.ac.il Department of Computer Science, Technion, Haifa, Israel 32000. E mail: assaf cs.technion.ac. il 1 Introduction In this work we consider a routing mode known as hot potato or deflection routing [AS91, GG86, GH92, Haj91, Max89, Szy90, ZA91, NS89]. The important characteristic of algorithms which assume this mode is that they use no buffer space for storing delayed packets. Each packet, unless it has already reached its destination, must leave the processor at the step following its arrival. Packets may reach a processor from all its ....

....on meshes was given by [NS92] The algorithm is based on sorting. An improvement in the leading constant was later obtained by [KLS94] Very recently, a lower bound on routing permutations by a certain class of algorithms was given [BS94] Work on general type of routing problems was done by [Haj91, BC91, BHS94, Fei94, BRS94, BTS95]. The goal in earlier works [Haj91, BC91] which was pursued in [BTS95, Fei94, BRS94] was to present a simple algorithm for hypercubes and meshes which routes k packets with any combination of origins and destinations, in d max 2(k Gamma 1) steps, where d max is the maximal sourceto ....

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B. Hajek. Bounds on evacuation time for deflection routing. Distributed Computing, 5:1--6, 1991.

....1 packets in dn O(log 2 n) time steps on the d dimensional n d node torus and in 2dn O(log 2 n) time steps on the d dimensional n d node mesh, with high probability. This research was partially supported by the NEC Research Institute. 1 Introduction A number of researchers [1, 4, 3, 2, 5, 6, 7, 8, 10, 11, 14, 12] have suggested algorithms for routing packets in a network with the property that on each step, each node in the network sends all of the packets it received on the previous step along one of its outgoing edges (with at most one packet leaving per edge) Such schemes are generally referred to as ....

....[16] and in high speed communications networks [12] While the apparent advantages of hot potato algorithms have been borne out by numerous simulation studies [1, 6, 7, 11, 12, 15] exact analysis of their behavior (i.e. without any independence assumptions) has proven to be difficult. Hajek [8] showed that for a natural algorithm on the N node hypercube, k packets with worst case destinations are delivered in 2k log N time steps. An algorithm for the hypercube suggested by Borodin and Hopcroft [4] was shown by Prager [15] to terminate in O(log N) steps on a special class of ....

Hajek, B., "Bounds on evacuation time for deflection routing", Distributed Computing, 5, 1991, 1--6.

....: 75 Chapter 1 Introduction 1.1 Background This work studies packet routing in synchronous network of processors, in which any communication link can carry at most one packet at each time step. We consider a form of packet routing known as hot potato routing or deflection routing [1, 12, 13, 15, 21, 27, 28]. The important characteristic of this form is that it requires no buffer space for storing delayed packets. Each packet must leave the processor at the step following its arrival, unless it has arrived to its destination. Packets arriving to a processor from its neighbors have to be redirected to ....

....to some of the packets such that all those packets strictly gain from the change (get an edge that leads them closer to their destination) ffl Maximum Advance: The maximum possible number of packets advance. These restrictions by themselves do not guarantee good performance. Hajek (Fig. 1 in [15]) demonstrated a livelock situation on the 4 cycle (and hence also on the mesh) for a stable algorithm. Feige [11] exhibited a livelock situation for a maximum advance algorithm, on a permutation problem on certain networks (including the torus) Hence, the maximum advance principle is not ....

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B. Hajek. "Bounds on evacuation time for deflection routing". Distributed Computing, 5:1-6, 1991.

....z IBM T.J. Watson Research Center, Yorktown, NY. E mail: sbar watson.ibm.com 1 Introduction This paper studies routing in a synchronous network, in which at most one packet can traverse any link in each time step. We consider a form of routing known as hot potato routing or deflection routing [1, 5, 8, 9, 10, 11, 12, 13, 15, 20, 21]. The striking feature of this form of routing is that unlike traditional store and forward packet routing, it involves no queues at intermediate nodes. Thus packets are always moving, giving rise to the term hot potato. A packet attempts to travel towards its destination. However, due to ....

....the analysis quite difficult. Feige and Raghavan [8] resurrected interest in this topic within the theoretical computer science community by analyzing average case and randomized hot potato algorithms for the torus and hypercube networks. They also called attention to an important paper by Hajek [11] concerning worst case hot potato routing for arbitrary (i.e. many to many) routing problems. Mansour and Patt Shamir [14] considered the general problem of many to many routing of k packets in a store and forward manner. They were able to show that any greedy store and forward algorithm that ....

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B. Hajek. Bounds on evacuation time for deflection routing. Distributed Computing, 5:1--6, 1991.

.... with regular geometries such as buildings or factory floors in which the movable entities are identical (say, carts of the same size moving in corridors that can accommodate one cart at a time, or vehicles moving on a network of tracks) Packet routing using the deflection or hot potato model [3] provides a related example (see Section 4) In some of these cases, a better cost metric may account for the physical lengths of edges. In others, intersections in the building railroad may be able to hold more than one obstacle robot at a time. In Section 4 we outline extensions of some of our ....

....size. 2) Study the case of several robots, each with its own destination; this is the GMPkR problem discussed in Section 1. 3) In situations such as railway networks, several objects can move simultaneously under their own power. This version is closely related to deflection routing for packets [3]. Thus, we would study plans with parallel moves allowed, and study the number of steps to deliver every robot to its destination. ....

B. Hajek. Bounds on evacuation time for deflection routing. Distributed Computing, 5:1--6, 1991.

....must defer to messages that are already in the network. These characteristics have led to this technique also being referred to as hot potato routing. Because deflection routing eliminates the need for switch buffering, investigation of its performance is currently receiving widespread attention [4, 6, 7, 8, 11, 12, 19, 21, 26, 30]. The typical strategy of these analyses is to make uniformity assumptions about the network that allow it to be decomposed, reducing the problem from studying the entire network to studying only a single switch. Another assumption that is commonly made is that messages unable to enter the network ....

Hajek, B. Bounds on evacuation time for deflection routing. Distributed Computing 5 (1991), 1--6.

....proved for nonoblivious or offline algorithms. However, they are of no great practical interest because they use complex models, like offline scheduling computation or link multiplexing. Deflection routing A lot of research has be done on deflection routing, both theoretical and experimental. HJK 91] gave a simple greedy algorithm for the hypercube, with running time of 2k n steps, where k is the number of the packets in the system. His work was simplified and generalized by [BC 91] who showed a bound of diam P 2(k 1) for any network, where diam is the diameter of the network and P the ....

B. Hajek. Bounds on evacuation time for deflection routing. In Distributed Computing, Springer-Verlag, 5:pages 1-6, 1991

....to distinct packets participating in the routing. Among other results, they show that routing k packets in a hot potato manner can be completed within 2(k Gamma 1) dist steps for trees where dist is the initial maximum distance a packet has to travel. A similar result was proven earlier by Hajek [12] and Brassil and Cruz [9] for hypercubes. 1.1 Our Results In this paper, we present an extensive study of many to many packet routing on n node trees under the matching routing model. We limit the investigation of the matching model to trees, however, the same results apply to undirected graphs ....

B. Hajek. Bounds on evacuation time for deflection routing. Distributed Computing, 5(1):1-- 6, 1991.

....indegree(v) outdegree(v) for all nodes v, so that deflection routing makes sense. Consider an arbitrary static routing problem of k packets (not necessarily a partial permutation) where the number of packets with source v is at most outdegree(v) The results in this section are due to Hajek [8]. Define one pass deflection routing as follows. At each node and each step, there is some ordering of the packets, and a packet P is deflected if and only if the outgoing links on all the shortest paths to P s destination are assigned to packets earlier in the ordering. LECTURE 12. DEFLECTION ....

....ffi is n. For the remainder of this section, we consider any nearest first deflection routing of k packets on the n dimensional hypercube H n . Our goal is to improve Theorem 12.4 to show that deflection routing on H n can be performed in O(ffi k) O(n k) steps. This result is due to Hajek [8]. See Theorem 14.4 for a closely related result. Definition 13.2: Suppose packet P has destination w and is about to traverse the link from u to v. P s conditional distance is 1 dist(v; w) where dist(v; w) is the length of a shortest path from v to w. On the hypercube, the conditional ....

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B. Hajek. Bounds for evacuation time for deflection routing. Distributed Computing, 5:1--6, 1991.

....They are focused on oblivious, online, delayed greedy algorithms which are simple and easy to implement on real machines. Better bounds were proved for non oblivious or offline algorithms. Deflection routing A lot of research has be done on deflection routing, both theoretical and experimental. HJK 91] gave a simple greedy algorithm for the hypercube, with running time of 2k n steps, where k is the number of the packets in the system. A potential function analysis of greedy routing algorithms on d dimensional arrays was given by [BHS 94] For two dimensional meshes their results yield a 8 p ....

B. Hajek. Bounds on evacuation time for deflection routing. In Distributed Computing, Springer-Verlag, 5:pages 1-6, 1991

.... It appears that the idea of replicating data (messages) was first proposed in computer networks research by Baran in 1964 [Bar64] After a long hiatus, the idea was revived and widely studied recently, and practically used in a number of models and implementations of computer networks protocols [Szy90, Haj91]. More recently, in the related distributed computer architecture research on wormhole routing, it was suggested and demonstrated that replicating messages can be effectively used for avoiding or reducing probability of deadlocks [Dal87, Lin91] The intuitive and detailed exposure of wormhole ....

B. Hajek: "Bounds on Evacuation Time for Deflection Routing", Distributed Computing, Vol. 5, No. 1, pp. 1-5, 1991.

....links, without encountering intra nodal queuing nor switching delays. Nonetheless, such a strategy demands careful planning, both of the predetermined schedule and of its actual use once it has been set. Hot potato (also called Deflection) routing has been given attention in recent years, e.g. [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], mainly in the area of multiprocessing. Typically, however, hot potato routing does consider the identity (label) of the packet for making its routing decision. Scheduled routing also started to gain attention, e.g. 14, 15, 16] However, these works considered the use of store and forward ....

B. Hajek, "Bounds on evacuation time for deflection routing," Distributed Computing, vol. 5, pp. 1--6, 1991.

....distinct packets participating in the routing. Among other results, they show that routing k packets in a hot potato manner can be completed within 2(k Gamma 1) dist steps for trees where dist is the initial maximum distance a packet has to travel. A similar result was proven earlier by Hajek [7] and Brassil and Cruz [4] for hypercubes. Due to space limitations, it is not possible to provide complete proofs for most of our results. Details can be found in [12] 2 Preliminaries A tree T = V; E) is an undirected acyclic graph with node set V and edge set E. The nodes of V are supposed to ....

B. Hajek. Bounds on evacuation time for deflection routing. Distributed Computing, 5(1):1--6, 1991.

....the same with that of Ben Aroya and Schuster [2] their algorithm is considered to be superior since it is has better performance for the significant case of permutation routing 1 . In their paper, Borodin et al. [3] mention several open problems. Among them, i) the problem (attributed to Hajek [6]) of deriving a deflection routing algorithm for an arbitrary undirected graph which routes any routing pattern consisting of k packets within dist 2(k Gamma 1) steps where dist is the initial maximum distance a packet has to travel, and ii) whether the one pass of links property (as defined ....

B. Hajek. Bounds on evacuation time for deflection routing. Distributed Computing, 5(1):1--6, 1991.

....1 Introduction In this work we study the problem of batch packet routing in synchronous networks of processors in which at most one packet can traverse any directed link in each time step. We consider a class of algorithms known as hot potato or deflection routing algorithms [AS91, GG86, GH92, Haj91, LP80, Max89, Szy90, ZA91, NS89]. The important characteristic of these algorithms is that they use no buffer space for storing delayed packets. Each packet, unless already arrived to its destination, must leave the processor at the step following its arrival. Packets may arrive to a processor from all its neighbors and have to ....

....resist formal analysis attacks. Numerous experimental results on hot potato routing have been published [AS91, GG86, GH92, LP80, Max89, Pra86] Prager [Pra86] showed that the Borodin Hopcroft algorithm terminates in n steps on the 2 n nodes hypercube for a special class of permutations. Hajek [Haj91] presented a simple greedy algorithm for the same network that runs in 2k n steps, where k is the number of packets in the system. The algorithm by Hajek gives priority to packets that are closer to their destinations [Haj91] It is straightforward to see that using this basic rule, any greedy ....

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B. Hajek. Bounds on evacuation time for deflection routing. Distributed Computing, 5:1--6, 1991.

....distinct packets participating in the routing. Among other results, they show that routing k packets in a hot potato manner can be completed within dist 2(k Gamma 1) steps for trees where dist is the initial maximum distance a packet has to travel. A similar result was proven earlier by Hajek [9] and Brassil and Cruz [7] for hypercubes. In this paper we study dynamic on line and off line routing on trees under the matching with consumption model (referred to as matching model in the rest of the paper) We establish a closed relationship between the matching with consumption and the ....

B. Hajek. Bounds on evacuation time for deflection routing. Distributed Computing, 5(1):1--6, 1991.

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B. Hajek, Bounds on evacuation time for deflection routing, Distributed Computing, 5 (1991) 1--6.

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B. Hajek, "Bounds on evacuation time for deflection routing," Distributed Computing, vol. 5, pp. 1--6, 1991.

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B. Hajek. "Bounds on evacuation time for deflection routing", Distributed Computing, vol. 5, pp. 1-6, 1991.

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