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Deterministic manytomany hot potato routing
 IEEE Transactions on Parallel and Distributed Systems
, 1997
"... We consider algorithms for manytomany hot potato routing. In hot potato (deflection) routing a packet cannot be buffered, and is therefore always moving until it reaches its destination. We give optimal and nearly optimal deterministic algorithms for manytomany packet routing in commonly occurrin ..."
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Cited by 31 (0 self)
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We consider algorithms for manytomany hot potato routing. In hot potato (deflection) routing a packet cannot be buffered, and is therefore always moving until it reaches its destination. We give optimal and nearly optimal deterministic algorithms for manytomany packet routing in commonly occurring networks such as the hypercube, meshes and tori of various dimensions and sizes, trees and hypercubic networks such as the butterfly. All these algorithms are analyzed using a charging scheme that may be applicable to other algorithms as well. Moreover, all bounds hold in a dynamic setting in which packets can be injected at arbitrary times.
Potential Function Analysis of Greedy HotPotato Routing (Extended Abstract)
 Theory of Computing Systems
, 1994
"... Amir BenDor Shai Halevi y Assaf Schuster z January 21, 1994 Abstract In this work we study the problem of packet routing in synchronous networks of processors, in which at most one packet can traverse any communication link in each time step. We consider a class of algorithms known as hotpo ..."
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Cited by 30 (2 self)
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Amir BenDor Shai Halevi y Assaf Schuster z January 21, 1994 Abstract In this work we study the problem of packet routing in synchronous networks of processors, in which at most one packet can traverse any communication link in each time step. We consider a class of algorithms known as hotpotato or deflection routing algorithms. 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. The main advantage in hotpotato routing is that there is no need to store delayed packets in the processors, and therefore, the processors can be much simpler, and contain less hardware. This work is concerned with greedy routing, in which a packet is bound to use an outgoing link in the direction of its destination, whenever such a link is available. In this way, greediness guarantees that, unless some global congestion forbids...
TDM VirtualCircuit Configuration for NetworkonChip
 IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION SYSTEMS
, 2007
"... ... Multiplexing (TDM) Virtual Circuits (VCs) have been proposed to satisfy the QualityofService requirements of applications. TDM VC is a connectionoriented communication service by which two or more connections take turns to share buffers and link bandwidth using dedicated time slots. In the pa ..."
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Cited by 13 (5 self)
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... Multiplexing (TDM) Virtual Circuits (VCs) have been proposed to satisfy the QualityofService requirements of applications. TDM VC is a connectionoriented communication service by which two or more connections take turns to share buffers and link bandwidth using dedicated time slots. In the paper, we first give a formulation of the multinode VC configuration problem for arbitrary NoC topologies. A multinode VC allows multiple source and destination nodes on it. Then we address the two problems of path selection and slot allocation for TDM VC configuration. For the path selection, we use a backtracking algorithm to explore the path diversity, constructively searching the solution space. In the slot allocation phase, overlapped VCs must be configured such that no conflict occurs and their bandwidth requirements are satisfied. We define the concept of a logical network (LN) as an infinite set of associated (time slot, buffer) pairs with respect to a buffer on a given VC. Based on this concept, we develop and prove theorems that constitute sufficient and necessary conditions to establish conflictfree VCs. They are applicable for networks where all nodes operate with the same clock frequency but allowing different phases. Using these theorems, slot allocation for VCs is a procedure of assigning VCs to different LNs. TDM VC configuration can thus be predictable and correctbyconstruction. Our experiments on synthetic and real applications validate the effectiveness and efficiency of our approach.
Õ(Congestion + Dilation) hotpotato routing on leveled networks
 In Proceedings of the Fourteenth ACM Symposium on Parallel Algorithms and Architectures
, 2002
"... We study packet routing problems, in which we are given a set of N packets which will be sent on preselected paths with congestion C and dilation D. For storeandforward routing, in which nodes have buffers for packets in transit, there are routing algorithms with performance that matches the lower ..."
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Cited by 11 (8 self)
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We study packet routing problems, in which we are given a set of N packets which will be sent on preselected paths with congestion C and dilation D. For storeandforward routing, in which nodes have buffers for packets in transit, there are routing algorithms with performance that matches the lower bound Ω(C + D). Motivated from optical networks, we study hotpotato routing in which the nodes are bufferless. Due to the lack of buffers, in hotpotato routing the packets may be delayed more than in storeandforward routing. An interesting question is how much is the performance of routing algorithms affected from the absence of buffers. Here, we answer this question for the class of leveled networks, in which the nodes are partitioned into L + 1 distinct levels. We present a randomized hotpotato routing algorithm for leveled networks, which routes the packets in O((C +L) ln 9 (LN)) time with high probability. For routing problems with dilation Ω(L), and where N is a polynonial in L, this bound is within polylogarithmic factors of the lower bound Ω(C + L). Our algorithm demonstrates that for such routing problems the benefit from using buffers is no more than polylogarithmic; thus, hotpotato routing is an efficient way to route packets in leveled networks. In hotpotato routing, due to the lack of buffers, the packets may not be able to remain on their preselected paths during the course of routing (while in storeandforward routing the packets remain on their preselected paths). However, in our algorithm the actual path that each packet follows contains its original preselected path; thus the lower bound Ω(C + L) is also a lower bound for the new paths. Our algorithm is distributed, that is, routing decisions are taken locally at each node while packets are routed in the network. To our knowledge, this is the first hotpotato algorithm designed and analyzed, in terms of congestion and dilation, for leveled networks.
Minimal Adaptive Routing on the Mesh with Bounded Queue Size
, 1994
"... An adaptive routing algorithm is one in which the path a packet takes from its source to its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around "hot spots." Minimal adaptive routing algorithms have the additional ..."
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Cited by 10 (4 self)
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An adaptive routing algorithm is one in which the path a packet takes from its source to its destination may depend on other packets it encounters. Such algorithms potentially avoid network bottlenecks by routing packets around "hot spots." Minimal adaptive routing algorithms have the additional advantage that the path each packet takes is a shortest one. For a large class of minimal adaptive routing algorithms, we present an \Omega# n 2 =k 2 ) bound on the worst case time to route a static permutation of packets on an n 2 n mesh or torus with nodes that can hold up to k 1 packets each. This is the first nontrivial lower bound on adaptive routing algorithms. The argument extends to more general routing problems, such as the hh routing problem. It also extends to a large class of dimension order routing algorithms, yielding an \Omega# n 2 =k) time bound. To complement these lower bounds, we present two upper bounds. One is an O(n 2 =k) time dimension order routing...
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.
Unslotted Deflection Routing: A Practical and Efficient Protocol for MultiHop Optical Networks
, 2001
"... Slotted Optical Time Division Multiplexing Deflection networks make use of the synchronous arrival of the packets to the routers in order to optimize locally the number of deflections. In this paper, it is shown that the difference of performances between slotted and unslotted networks is mainly due ..."
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Cited by 10 (0 self)
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Slotted Optical Time Division Multiplexing Deflection networks make use of the synchronous arrival of the packets to the routers in order to optimize locally the number of deflections. In this paper, it is shown that the difference of performances between slotted and unslotted networks is mainly due to the fact that unslotted networks cannot directly make benefit of such local optimization. It is also shown that, unfortunately, optimizing locally the routing in unslotted networks gives rise to an NPcomplete problem. Therefore a heuristic for routing in unslotted networks is proposed. In the experimental context considered, our heuristic enhances unslotted routing almost at the same level as slotted routing. It makes unslotted deflection routing a competitive alternative to slotted deflection routing for OTDM networks.
A Lower Bound for Nearly Minimal Adaptive and Hot Potato Algorithms
"... Recently, Chinn, Leighton, and Tompa [10] presented lower bounds for storeandforward permutation routing algorithms on the n × n mesh with bounded buffer size and where a packet must take a shortest (or minimal) path to its destination. We extend their analysis to algorithms that are nearly ..."
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Cited by 7 (1 self)
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Recently, Chinn, Leighton, and Tompa [10] presented lower bounds for storeandforward permutation routing algorithms on the n × n mesh with bounded buffer size and where a packet must take a shortest (or minimal) path to its destination. We extend their analysis to algorithms that are nearly minimal. We also apply this technique to the domain of hot potato algorithms, where there is no storage of packets and the shortest path to a destination is not assumed (and is in general impossible). We show that "natural" variants and "improvements" of several algorithms in the literature perform poorly in the worst case. As a result, we identify algorithmic features that are undesirable for worst case hot potato permutation routing. Recent works in hot potato routing have tried to define simple and greedy classes of algorithms. We show that when an algorithm is too simple and too greedy, its performance in routing permutations is poor in the worst case. Specifically, the technique of [10] ...
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...
Universal Bufferless Routing
, 2004
"... In a routing problem, a set of packets must be routed from their sources to their destinations along specified paths in a connected network. The celebrated result of Leighton, Maggs and Rao (1988) established, nonconstructively, the existence of a routing schedule which uses constant size bffers an ..."
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Cited by 5 (2 self)
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In a routing problem, a set of packets must be routed from their sources to their destinations along specified paths in a connected network. The celebrated result of Leighton, Maggs and Rao (1988) established, nonconstructively, the existence of a routing schedule which uses constant size bffers and routes the packets in optimal time. Since then, constructive algorithms, as well as generalizations to distributed, buffered routing schedules have been developed. A long standing open problem...