I. Ben-Aroya, T. Eilam, and A. Schuster. Greedy hot-potato routing on the two-dimensional mesh. Distributed Computing, 9(1):3-19, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 problems, Ben Aroya et al. 4] give a randomized algorithm for the d dimensional mesh that nishes in O(k=d) steps, with high probability. For the problems we consider here, in which there are n 2 ....

I. Ben-Aroya, T. Eilam, and A. Schuster. Greedy hot-potato routing on the two-dimensional mesh. Distributed Computing, 9(1):3-19, 1995.

....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] 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 ....

I. Ben--Aroya, T. Eilam, and Schuster. Greedy Hot--Potato Routing on the Two-- Dimensional Mesh. Distributed Computing, 9(1):3--19, 1995.

....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 ....

I. Ben-Aroya, T. Eilam, and A. Schuster, Greedy hot-potato routing on the twodimensional mesh. Distributed Computing, 9:3--19, 1995.

.... p from its destination (they also present a simple non greedy algorithm with similar results) For the 2 dimensional mesh and torus this algorithm preserves the O(n 1:5 ) bound given by Bar Noy et al. 2] For the 2 dimensional case a similar result was independently obtained by Ben Aroya et al. [4]. For a single destination or a small set of destinations Ben Aroya et al. 5] present a randomized algorithm on the d dimensional mesh that nishes in O(k=d) steps, with high probability. For non greedy hot potato routing, Feige and Raghavan [9] present an algorithm for the n n torus that ....

I. Ben-Aroya, T. Eilam, and A. Schuster. Greedy hot-potato routing on the two-dimensional mesh. Distributed Computing, 9(1):3-19, 1995.

....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 problems, Ben Aroya et al. 4] give a randomized algorithm for the d dimensional mesh that nishes in O(k=d) steps, with high probability. For the problems we consider here, in which there are n 2 ....

I. Ben-Aroya, T. Eilam, and A. Schuster. Greedy hot-potato routing on the two-dimensional mesh. Distributed Computing, 9(1):3-19, 1995.

....implementation. Deflection routing is a novel packet routing organization where unsatisfied packets 170 To Storage Correctly Forwarded Correctly Forwarded Deflected Deflected Deflected Figure 15.6: Store and Forward vs. Deflection Routing are deflected to any other available link [ Baran, 1964, Ben Ayora and Schuster, 1993, Feige, 1992, Greenberg and Hajek, 1992, Greenberg and Goodman, 1993, Newman and Schuster, 1995 ] With deflection routing, all the packets that are received at a given time step must leave the network processor during the next time step 1 ; no storage is necessary. Although a deflected packet ....

....assignment of packets to links is a deceptively difficult problem, and many assignment algorithms are possible. We first outline some criteria for determining the quality of an assignment. Ben Aroya and Schuster define an assignment algorithm to be greedy if it satisfies the following condition [ Ben Ayora and Schuster, 1993 ] Whenever a packet p is deflected, all of its good links must be assigned to other packets. Moreover, each of the preempting packets must not be deflected into its respective channel (i.e. the link is in its interested set) Ben Aroya and Schuster also define an assignment algorithm to be ....

[Article contains additional citation context not shown here]

I. Ben-Ayora and A. Schuster. Greedy hot-potato routing in the two-dimensional mesh. Technical Report PCL-9320, CS Department, Technion, Haifa, Israel, Nov. 1993.

....the algorithm. We put some emphasis on greedy algorithms, agreeing with Ben Dor, Halevi and Schuster [5] that such algorithms have the practical appeal desired by practitioners. Motivated by the discussion in Ben Dor et al. 5] and similar to the definitions in Ben Aroya, Eilam, and Schuster [4], and Feige [7] we distinguish between two types of greediness. An algorithm is partially greedy if it always assigns a packet an outgoing link on one of the shortest paths to its destination if such a link is available. Note that this property is local in the sense that an algorithm may assign a ....

....in a bounded number of link passes) A modification of this algorithm applied to the two dimensional case achieves the desired dist (p) 2(k Gamma 1) bound and also maintains the O(n 1:5 ) bound given in [2] for permutation routing. For the two dimensional case, Ben Aroya, Eilam and Schuster [4] independently obtained an equivalent algorithm. As Feige [7] observes, the dist (p) 2(k Gamma 1) bound is somewhat arbitrary in that this bound is not a lower bound for all networks (e.g. a star network) For the mesh and, in particular, for the two dimensional mesh, it is not known if the ....

I. Ben-Aroya, T. Eilam, and A. Schuster. Greedy hot-potato routing on the two dimensional mesh, to appear in Distributed computing, 9(1), 1995.

....their routing time was available until recently. The work of Feige and Raghavan[10] which provided analysis for hot potato routing algorithms for the torus and the hypercube renewed the interest in hot potato routing. As a result, several papers appeared with hot potato routing as their main theme [4,7,13,14,17]. Borodin et al. [8] formalised the notion of the deflection sequence, a nice way to charge each deflection of an individual packet 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 ....

I. Ben-Aroya and A. Schuster. Greedy hot-potato routing on the two-dimensional mesh. In Jan van Leeuwen, editor, Proceedings of the 2nd European Symposium on Algorithms ESA '94 (Utrecht, September 1994), LNCS 855, pages 365--376. Springer-Verlag, 1994.

....optimal algorithms for routing permutations on the mesh and the torus networks and a near optimal algorithm for the hypercube. Kaufmann et al. [6] fine tuned their results for the case of meshes and managed to reduce the constant hidden in the asymptotic analysis. Ben Aroya and Schuster [2] considered the general situation where a mesh is loaded with 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 ....

....[3] which appears to belong in the class of simple and greedy like algorithms, actually needs Omega Gamma n p n) steps for the routing of some permutations. Currently we are trying to establish nontrivial upper and lower bounds for the permutation routing algorithm of Ben Aroya and Schuster [2]. ....

I. Ben-Aroya and A. Schuster. Greedy hotpotato routing on the two-dimensional mesh. In Jan van Leeuwen, editor, Proceedings of the 2nd European Symposium on Algorithms ESA '94 (Utrecht, September 1994), LNCS 855, pages 365--376. Springer-Verlag, 1994.

.... also investigated to examine the possibility of constructing on line solutions [15] Hot potato routing schemes, as studied in this paper, have been considered for more than thirty years [5] and the running times of hot potato routing schemes have more recently been studied in various networks [4, 6, 10, 13, 29]. Trees have always been a subject of special interest in the routing literature (see e.g. 1, 33, 27, 28, 29, 16, 20, 22, 23] As pointed out by Leighton [17] many networks are simply trees, and, moreover, routing in general graphs may be done using only the edges of a spanning tree of the ....

I. Ben-Aroya and A. Schuster. Greedy hot-potato routing on the two-dimensional mesh. In Proceedings of the 2nd european symposium on algorithms (ESA'94), pages 365--376, 1994.

....optimal algorithms for routing permutations on the mesh and the torus networks and a near optimal algorithm for the hypercube. Kaufmann et al. [7] fine tuned their results for the case of meshes and managed to reduce the constant hidden in the asymptotic analysis. Ben Aroya and Schuster [2] considered the general situation where a mesh is loaded with 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 ....

....in a hot potato manner can be completed within dist 2(k Gamma 1) steps for trees, butterflies and multidimensional meshes, where dist is the initial maximum distance 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 ....

[Article contains additional citation context not shown here]

I. Ben-Aroya and A. Schuster. Greedy hot-potato routing on the two-dimensional mesh. In Jan van Leeuwen, editor, Proceedings of the 2nd European Symposium on Algorithms ESA '94 (Utrecht, September 1994), LNCS 855, pages 365--376. Springer-Verlag, 1994.

....analysis of their routing time was available. The work of Feige and Raghavan[8] which provided analysis for hot potato routing algorithms for the torus and the hypercube, renewed the interest in hot potato routing. As a result, several papers appeared with hotpotato routing as their main theme [3, 5, 10, 11, 12]. Borodin et al. [6] formalized the notion of the deflection sequence, a nice way to charge each deflection of an individual packets 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 dist 2(k ....

I. Ben-Aroya and A. Schuster. Greedy hot-potato routing on the two-dimensional mesh. In Jan van Leeuwen, editor, Proceedings of the 2nd European Symposium on Algorithms ESA '94 (Utrecht, September 1994), LNCS 855, pages 365--376. Springer-Verlag, 1994.

....optimal algorithms for routing permutations on the mesh and the torus networks and a near optimal algorithm for the hypercube. Kaufmann et al. [6] fine tuned their results for the case of meshes and managed to reduce the constant hidden in the asymptotic analysis. Ben Aroya and Schuster [2] considered the general situation where a mesh is loaded with 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 ....

....[3] which appears to belong in the class of simple and greedy like algorithms, actually needs Omega Gamma n p n) steps for the routing of some permutations. Currently we are trying to establish nontrivial upper and lower bounds for the permutation routing algorithm of Ben Aroya and Schuster [2]. ....

I. Ben-Aroya and A. Schuster. Greedy hotpotato routing on the two-dimensional mesh. In Jan van Leeuwen (editor), Proceedings of the 2nd European Symposium on Algorithms ESA '94 (Utrecht, September 1994), LNCS 855, pages 365--376. Springer-Verlag, 1994.

....bufferless routing algorithms, which allow simpler, faster switches. Optical networks provide strong incentives to avoid buffering, due to the cost of optical electronic conversions [22] The important class of hot potato (a k a deflection) bufferless routing algorithms has been widely studied [1, 4, 10, 20, 8, 44]. More general approaches to bufferless routing can be found in [5, 37, 39, 9, 12] These sources focus on optimizing a global parameter such as overall completion time or average message latency: individual messages do not have deadlines. Some recent papers focus on the session model, wherein ....

I. Ben-Aroya, T. Eilam, A. Schuster (1995): Greedy hot-potato routing on the two-dimensional mesh. Distr. Computing 9, 3-19.

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