Citations: Bounds on maximum delay in networks with deflection routing

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J. T. Brassil and R. L. Cruz. Bounds on maximum delay in networks with deflection routing. IEEE Transactions on Parallel and Distributed Systems, 6(7):724--732, July 1995.

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Õ(Congestion + Dilation) Hot-Potato Routing on Leveled.. - Busch (2003) (Correct)

....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 problems than the ones we ....

J. T. Brassil and R. L. Cruz. Bounds on maximum delay in networks with deflection routing. IEEE Transactions on Parallel and Distributed Systems, 6(7):724--732, July 1995.

Packet Routing in Multiprocessor Networks - Chinn (1995) (Correct)

....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 (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 ....

J. T. Brassil and R. L. Cruz. Bounds on maximum delay in networks with deflection routing. In 29th Annual Allerton Conference on Communication, Control, and Computing, pages 571--580, 1991.

Minimal Adaptive Routing on the Mesh with Bounded Queue Size - Chinn, Leighton, Tompa (1994) (4 citations) (Correct)

....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 ....

J. T. Brassil and R. L. Cruz. Bounds on maximum delay in networks with deflection routing. In 29th Annual Allerton Conference on Communication, Control, and Computing, pages 571--580, 1991.

Hot-Potato Routing on Unbuffered 2-D Tori - Grammatikakis, Kraetzl, Fleury (Correct)

....each packet assigned a random destination. All generated packets are routed in parallel. Continuous circuit switching has been considered extensively, especially for multistage networks [6] Good empirical results and approximate models exist for dynamic hot potato implementations on the hypercube [4, 5, 6, 2]. We consider dynamic routing on vertex symmetric graphs, focusing on unbuffered 2 dimensional tori. We assume d port multiaccepting, full duplex communication, with unit delay for node to neighbor transmission (constant delay model) Hence, at each step, any processor node may simultaneously ....

Brassil J. T. and Cruz R. L. Bounds on Maximum Delay in networks with Deflection Routing. IEEE Trans. Parallel and Distr. Systems 6 (7), 1995, pp. 724--732.

Shortest-Path and Hot-Potato Routing on Unbuffered.. - Grammatikakis.. (1998) (Correct)

....nodes increases. 3.2 Hot Potato Packet Routing We consider hot potato routing on an unbuffered n Theta n torus. Analysis of dynamic hot potato routing is extremely hard because current packet moves 7 depend on previous packet history (e.g. whether the packet has been deflected before) [3]. To simplify the analysis we introduce link symmetry by assuming that any network node generates packets whenever an outgoing link is idle, i.e. there is no shortage of packets to be sent. As we shall prove, although this limits the generating rate m g to a single point, it provides a ....

J.T. Brassil and R.L. Cruz, Bounds on maximum delay in networks with deflection routing, IEEE Trans. Parallel Distr. Systems 6 (7) (1995) 724--732.

Lower Bounds for One-to-one Packet Routing on Trees using .. - Roberts, Symvonis, Wood (2000) (Correct)

....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 a greedy hot potato algorithm to route a packet p on a wide class of ....

J. Brassil and R. Cruz, Bounds on maximum delay in networks with deflection routing. IEEE Trans. Parallel Distrib. Systems, 6(7):724--732, 1995.

Randomized Single-Target Hot-Potato Routing - Aroya, Newman, Schuster (1995) (4 citations) (Correct)

....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 ....

.... 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 destination distance. But what do we mean by a ....

[Article contains additional citation context not shown here]

J.T. Brassil and R.L. Cruz. Bounds on Maximum Delay in Networks with Deflection Routing. In Proc. 29th Allerton conf. on Communication, Control and Computing, pages 571--580, 1991.

Simple Algorithms for Hot-Potato Routing - Krauthgamer (1996) (Correct)

....are closer to their destination. Part of our work concerns worst case bounds for general networks. Using the closest first priority rule devised by Hajek, it is clear that any minimum advance algorithm on any network terminates in O(k Delta D) The work of Hajek was continued by Brassil and Cruz [9]. In the context of general networks, Brassil and Cruz considered a minimum advance algorithms with fixed priorities and obtained the following result. Let W p be the length of the shortest path that connects, in order of decreasing priority, the destinations of packets with priority up to the ....

J.T. Brassil, R.L. Cruz. "Bounds on Maximum Delay in Networks with Deflection Routing". 29th Annual Allerton Conference on Communication, Control, and computing, 571-580, 1991.

Deterministic Many-to-Many Hot Potato Routing - Borodin, Rabani, Schieber (1994) (26 citations) (Correct)

....of store and forward routing, an edge conflict results in the buffering and thereby delaying of a packet by one step. In the case of hot potato routing on an undirected network an edge conflict may result in a deflection that may delay a packet by two steps. Hajek [11] and later Brassil and Cruz [6]) considered two cases: i) many to one routing in arbitrary networks (i.e. the special case when all packets have the same destination) and (ii) many to many routing in the hypercube network. For both cases Hajek was able to devise a routing algorithm that guarantees delivery in at most ffi N ....

....to go have priority. Once again, we observe that achieving a bound of ffi N Delta 2(k Gamma 1) is quite easy for such schemes but Hajek s proof is relatively subtle. In fact, it is not at all clear that Hajek s analysis can be applied in the dynamic setting. The analysis by Brassil and Cruz [6] can be used to obtain a dist (p) 2(k Gamma 1) bound for hypercube, improving upon the ffi N 2(k Gamma 1) bound in Hajek [11] Recognizing that Hajek s analysis does not extend to the mesh, Ben Dor, Halevi and Schuster [5] were the first to give many to many algorithms for the n Theta n ....

J.T. Brassil and R.L. Cruz. Bounds on maximum delay in networks with deflection routing. In Proc. 29th Allerton Conf. on Communication, Control and Computing, pages 571--580, 1991.

Wormhole versus deflection routing: A case study on the .. - Karaivazoglou.. (Correct)

....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 length of a walk connecting all destinations in a certain order. A potential function analysis of greedy routing algorithms on d dimensional arrays was given by [BHS 94] For two ....

J.T. Brassil and R.L. Cruz. Bounds on maximum delay in networks with deflection routing. In 29th annual Allerton conf. on Communication, Control and Computing, pages 571-580, 1991

Many-to-Many Routing on Trees via Matchings - Pantziou, Roberts, Symvonis (1996) (9 citations) (Correct)

....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 since the routing can be ....

J.T. Brassil and R.L. Cruz. Bounds on maximum delay in networks with deflection routing. In Proceedings of the 29th Allerton Conference on Communication, Control and Computing, pages 571--580, 1991.

Dynamic Tree Routing under the "Matching with Consumption" .. - Pantziou, Roberts.. (1996) (1 citation) (Correct)

....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 be ordered according to ....

J.T. Brassil and R.L. Cruz. Bounds on maximum delay in networks with deflection routing. In Proceedings of the 29th Allerton Conference on Communication, Control and Computing, pages 571--580, 1991.

Potential Function Analysis of Greedy Hot-Potato Routing .. - Ben-Dor, Halevi.. (1994) (6 citations) (Correct)

....packets in the system and diam is the network diameter. This implies, for example, O(n 3 ) upper bound for such an algorithm on the two dimensional n Theta n mesh, where each node is the origin of a single packet. The work of Hajek was simplified and generalized in a work by Brassil and Cruz [BC91]. For any regular network with undirected edges (such as the mesh and the hypercube) the algorithm of Brassil and Cruz assumes some pre specified order on the destinations, and packets are given priority according to the rank of their destination in that order. They show a bound of diam P 2(k ....

....problem is that the method that is used is inherently sequential : Suppose some important parameter improves, for example, the maximal distance to destination becomes smaller, or the network degree becomes higher. Clearly, this accelerates the routing time. Using the method in [Haj91] and [BC91], however, such information fails to improve the bound. Some recent results concern structured (non greedy) hot potato permutation routing: Feige and Raghavan [FR92] presented an algorithm for the 2 dimensional torus, that routes most of the routing problems in no more then 2n O(log n) steps. ....

[Article contains additional citation context not shown here]

J.T. Brassil and R.L. Cruz. Bounds on maximum delay in networks with deflection routing. In 29th annual Allerton conf. on Communication, Control and Computing, pages 571--580, 1991.

Dynamic Tree Routing under the "Matching with Consumption" .. - Pantziou, Roberts.. (1996) (1 citation) (Correct)

....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 hot potato routing models and ....

J.T. Brassil and R.L. Cruz. Bounds on maximum delay in networks with deflection routing. In Proceedings of the 29th Allerton Conference on Communication, Control and Computing, pages 571--580, 1991.

A Lower Bound for Nearly Minimal Adaptive and Hot Potato.. - Ben-Aroya, Chinn.. (Correct)

....type, in which there is no restriction on the distribution of the destinations. The goal in this research was to obtain a bound of d max 2(k Gamma 1) steps for meshes and hypercubes, where k is the number of packets in the system and d max is the maximal initial distance to destination [4, 6, 8, 9, 11, 15]. A recent result [5] gives hope in achieving the bound of O(d max W ) for general type requests, where W is the network bandwidth lower bound (defined as the maximum, over all node subsets S, of the number of packets destined to S divided by the number of links leading to S from nodes not in ....

J.T. Brassil and R.L. Cruz. Bounds on maximum delay in networks with deflection routing. In Proceedings of the 29th Allerton Conference on Communication, Control and Computing, pages 571--580, 1991.

Near-Optimal Hot-Potato Routing on Trees - Busch, Magdon-Ismail.. (2004) (Correct)