A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Tran. on Parallel and Dist. Sys., 8(6):587--596, June 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for more practical algorithms that come to the same or even better performance guarantee. 1. 3 Related Work Hot potato routing algorithms have been studied for specific network multiprocessor architectures such as the 2 dimensional mesh and torus [5, 9, 10, 12, 14] the d dimensional mesh [5, 7], the hypercube [8, 12] and trees [2] Meyer auf der Heide and Scheideler [20] study the more general class of vertex symmetric networks. For more about multiprocessor architectures you can look at [15] Bhatt et al. 6] study hot potato routing on leveled networks, but for di#erent routing ....

A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587--596, June 1997.

....at random. Since the distance to a randomly chosen destination is n) this complexity is also asymptotically optimal. Our algorithm exploits techniques for randomized hot potato routing ( home runs ) rst described by Busch et al. 10] That algorithm, like most prior hot potato algorithms [12, 5, 17, 2, 7, 10, 9], is static: all packets are injected at time zero, and the analysis examines the time needed to deliver them. Static algorithms, by de nition, need not be concerned with ow control. Our new algorithm, like only a few others [8, 11] is dynamic: nodes may inject packets into the network ....

....packet on each outgoing link. The links are bidirectional. The distance between two nodes corresponds to the minimum time needed to send a packet from one node to the other. 1. 3 Packet Generation and Delivery As noted, most earlier hot potato algorithms consider only one shot (static) problems [12, 5, 17, 2, 7, 10, 9]. By contrast, our algorithm and analysis is dynamic, nodes may inject packets repeatedly over a long duration. We are aware of only two other dynamic hot potato algorithms [8, 11] All the packets have random destination, distributed uniformly over the n nodes in the network. As the ....

A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587-596, June 1997.

....at random. Since the distance to a randomly chosen destination is #) this complexity is also asymptotically optimal. Our algorithm exploits techniques for randomized hot potato routing ( home runs ) rst described by Buschetal. 10] That algorithm, like most prior hot potato algorithms [12, 5, 17, 2, 7, 10, 9], is ######: all packets are injected at time zero, and the analysis examines the time needed to deliver them. Static algorithms, by de nition, need not be concerned with ow control. Our new algorithm, like only a few others [8, 11] is dynamic: nodes may inject packets into the network ....

....packet on each outgoing link. The links are bidirectional. The distance between two nodes corresponds to the minimum time needed to send a packet from one node to the other. 1. 3 Packet Generation and Delivery As noted, most earlier hot potato algorithms consider only one shot (static) problems [12, 5, 17, 2, 7, 10, 9]. By contrast, our algorithm and analysis is #######, nodes may inject packets repeatedly over a long duration. We are aware of only two other dynamic hot potato algorithms [8, 11] All the packets have random destination, distributed uniformly over the # # nodes in the network. As the ....

A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. #### ############ ## ######## ### ########### #######, 8(6):587-596, June 1997.

....function analysis, Ben Dor et al. 5] provide a simple algorithm for the 2 dimensional n n mesh with O(n p k) steps, where k is the total number of packets to be routed. They generalized their techniques for the d dimensional mesh to obtain O(e d n d 1 k 1=d ) steps. Borodin et al. [6] present a hot potato routing algorithm for the d dimensional mesh with DI 2(k 1) steps, where DI is the distance lower bound for any routing problem instance I. Similarly, Ben Aroya et al. 3] give an algorithm that nishes in DI 2(k 1) steps in the two dimensional mesh. For single target ....

A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587{ 596, June 1997.

....[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] Some of the above results (e.g. 13] extend to meshes and tori of higher dimensions. All of them deal with batch routing problems. The only study of the dynamic case we are aware of is that of Broder and Upfal [8] In spite of the important theoretical work done so far, there ....

....decisions. Especially in cases of continuous generation of packets and heavy traffic, routing decisions should be simple and fast. There have been several attempts to give a formal definition of the term simple for hot potato routing algorithms. The papers of 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 ....

A. Borodin, Y. Rabani, and B. Schieber. Deterministic Many--to--Many Hot--Potato Routing. IEEE Transactions on Parallel and Distributed Systems, 8(6): 587--596, 1997.

....algorithm requires at least 2n Gamma o(n) time steps. This lower bound is also shown to be valid for the minimum distance heuristic. We also establish a lower bound of 2( d Gamma3 d Gamma2 )n Gamma o(n) for trees of maximum d. As an upper bound, we apply the charging argument of Borodin et al. [12] to show that any greedy hot potato algorithm routes a one to one routing pattern on an n node tree within 2(n Gamma 1) steps. 1 Introduction In a packet routing problem we are given a synchronous network represented by a connected undirected graph and a set of packets distributed over the nodes ....

....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, 14, 15, 18]. Non greedy hot potato algorithms have appeared in [13, 18, 23, 26 28] and lower bounds for hot potato routing on meshes have been presented by Ben Aroya et al. 5] An important result of Borodin et al. 12] establishes an upper bound of dist(p) 2(k Gamma 1) on the number of steps used by ....

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A. Borodin, Y. Rabani, and B. Schieber, Deterministic many-to-many hot potato routing. IEEE Trans. Parallel Distrib. Systems, 8(6):587--596, 1997.

....give a potential function analysis and they provide a simple algorithm for the 2 dimensional n n mesh with O(n p k) steps, where k is the total number of packets to be routed. They generalized their techniques for the d dimensional mesh to obtain O(e d n d 1 k 1=d ) steps. Borodin et al. [7] present a complicated deterministic greedy hot potato routing algorithm for the d dimensional mesh and the 2 dimensional torus where any packet p nishes in at most dist(p) 2(k 1) steps, where dist(p) is the initial distance of p from its destination (they also present a simple non greedy ....

A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587-596, June 1997.

....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 ....

.... 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 destination distance. But what do we mean by a simple algorithm The permutation routing ....

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. Manuscript, 1994.

....function analysis, Ben Dor et al. 5] provide a simple algorithm for the 2 dimensional n n mesh with O(n p k) steps, where k is the total number of packets to be routed. They generalized their techniques for the d dimensional mesh to obtain O(e d n d 1 k 1=d ) steps. Borodin et al. [6] present a hot potato routing algorithm for the d dimensional mesh with DI 2(k 1) steps, where DI is the distance lower bound for any routing problem instance I. Similarly, Ben Aroya et al. 3] give an algorithm that nishes in DI 2(k 1) steps in the two dimensional mesh. For single target ....

A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587{ 596, June 1997.

....n torus in 4n o(n) steps. Using the same method, Kaufmann, Lauer and Schroder [18] improved the result for the mesh. Other works [4, 6] present simpler algorithms for the n Theta n two dimensional mesh and torus networks, but their bounds are not as good as O(n) Borodin, Rabani and Schieber [8] show an algorithm that achieves t p d p 2(k Gamma1) on mesh networks of arbitrary dimension, if each node is the source of at most one packet. Feige [11] shows an algorithm for mesh and torus networks of arbitrary dimension that achieves t p d p 2k in any problem. Other works involving ....

....to ensure evacuation of any routing problem on any tree networks. However, we also show an example where this principle is not enough to guarantee t p d p 2(k Gamma 1) Note that the high end class of maximum advance algorithms is known to achieve t p d p 2(k Gamma 1) on trees (see [11, 8]) The question whether the mid range classes, namely weakly stable and stable algorithms, achieve this bound remains open. Definition 12 A configuration of packets in a network is any placement (mapping) of the packets to the nodes of the network. We denote by Gamma the set of all possible ....

A. Borodin, Y. Rabani, B. Schieber. "Deterministic many-to-many hotpotato routing". manuscript, 1994.

....for a discussion of the drawbacks of routing algorithms based on sorting. Lecture 14 Deflection Routing on Multidimensional Meshes May 31, 1994 Notes: Donald Chinn In this lecture, we conclude our discussion of deflection packet routing with a recent result of Borodin, Rabani, and Schieber [5]. The goal of their work is to prove a bound of the following form: any packet P with distance d P from its source to its destination is delivered in time d P 2(k 0 1) where k is the number of packets in the network. Recall that Hajek s result [8] on deflection packet routing on the ....

....one pass over the incoming links in decreasing order of dimension. This scheduling involves very simple decisions, possibly more practical than Hajek s nearest first scheme [8] which involves sorting the incoming packets according to their distance to destination. Borodin, Rabani, and Schieber [5] also give a d P 2(k01) algorithm in the fully loaded case, where each node begins with a number of packets that can be as great as the outdegree of the node. Open Problem 14.5: Devise an O(d P k) deflection algorithm for arbitrary networks. LECTURE 14. DEFLECTION ROUTING ON ....

A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. Preprint, 1994.

....As a consequence, rt(G) 3n for any graph G of n vertices. To the best of our knowledge, this is the only known work on routing on trees under the matching model. Algorithms for routing permutations on trees under different routing models have been presented by Borodin, Rabani and Schieber [4] (hot potato routing model) and Symvonis [9] simplified routing model) In our attempt to obtain an upper bound on the routing number of complete d ary trees, we run into a problem of independent interest. This is the problem of heap construction. Consider a rooted tree T and let each of its ....

A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing, 1994. Unpublished manuscript.

....k packets that have to be routed to their destinations in a hot potato manner. Through clever analysis of their greedy algorithm they showed that routing will terminate within dist 2(k Gamma 1) steps where dist is the initial maximum distance a packet has to travel. Indepedently, Borodin et al. [3] formalized the notion of the deflection sequence, a nice way to charge each deflection of an individual packets to distinct packets traveling on the network. By using their method, they show that routing k packets in a hot potato manner can be completed within dist 2(k Gamma 1) steps for ....

....a packet has to travel. For two dimensional meshes, even though their result is 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 ....

[Article contains additional citation context not shown here]

A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing, 1994. Unpublished manuscript.

....they did not give a complete analysis of its behavior they observed that experimentally the algorithm appears promising . During the years, this phenomenon was observed over 1 This is by no means the only possible way to define what a simple algorithm is. Other notions were suggested e.g. in [BRS94]. and over again: although fairly simple greedy hot potato algorithms perform very well in simulations, they 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 ....

.... Eilam and Schuster showed a greedy algorithm on the 2dimensional mesh for routing a batch of k packets with maximal source todestination distance d max in 2(k Gamma 1) d max steps [BTS95] Independently, this bound was also obtained by Feige [Fei95] and by Borodin, Rabani and Schieber [BRS94]. Furthermore, the bound in [BRS94] holds also for higher dimensional meshes (The bound in [Fei95] also holds for higher dimensional meshes, however the algorithm does not remain greedy) Fei95] and [BTS95] define a stronger notion of greed. Fei95] contains several upper and lower bounds for ....

[Article contains additional citation context not shown here]

A. Borodin, Y. Rabani, and B. Schieber. Deterministic manyto -many hot potato routing. Manuscript, 1994.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Tran. on Parallel and Dist. Sys., 8(6):587--596, June 1997.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587--596, June 1997.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587--596, June 1997.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587--596, June 1997.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587--596, June 1997.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587--596, 1997.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587{ 596, June 1997.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587--596, June 1997.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587--596, June 1997.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587--596, June 1997.

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A. Borodin, Y. Rabani, and B. Schieber. Deterministic many-to-many hot potato routing. IEEE Transactions on Parallel and Distributed Systems, 8(6):587--596, June 1997.

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Borodin, A. Rabani, Y. and Schieber, B. (1997) Deterministic many-to-many hot potato routing. IEEE Trans. Parallel Distrib. Systems, 8(6), 587-596.

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