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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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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...
Packet Routing In FixedConnection Networks: A Survey
, 1998
"... We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing ..."
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Cited by 29 (3 self)
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We survey routing problems on fixedconnection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, krelation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results. We also provide a list of unsolved problems and numerous references.
Desnakification of Mesh Sorting Algorithms
 Proc. 2nd European Symp. on Algorithms, LNCS 855
, 1994
"... In all recent nearoptimal sorting algorithms for meshes, the packets are sorted with respect to some snakelike indexing. In this paper we present deterministic algorithms for sorting with respect to the more natural rowmajor indexing. For 11 sorting on an n \Theta n mesh, we give an algorithm t ..."
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Cited by 15 (11 self)
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In all recent nearoptimal sorting algorithms for meshes, the packets are sorted with respect to some snakelike indexing. In this paper we present deterministic algorithms for sorting with respect to the more natural rowmajor indexing. For 11 sorting on an n \Theta n mesh, we give an algorithm that runs in 2\Deltan+o(n) steps, matching the distance bound, with maximal queue size five. It is considerably simpler than earlier algorithms. Another algorithm performs kk sorting in k \Delta n=2 + o(k \Delta n) steps, matching the bisection bound. Furthermore, we present uniaxial algorithms for rowmajor sorting. Uniaxial algorithms have clear practical and theoretical advantages over biaxial algorithms. We show that 11 sorting can be performed in 2 1 = 2 \Delta n + o(n) steps. Alternatively, this problem is solved with maximal queue size five in 4 1 = 3 \Delta n steps, without any additional terms. For practically important values of n, this algorithm is much faster than any alg...
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.
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.
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 a ..."
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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...
Overview of Mesh Results
 MAXPLANCK INSTITUT FUR INFORMATIK, SAARBRUCKEN
, 1995
"... This paper provides an overview of lower and upper bounds for algorithms for meshconnected processor networks. Most of our attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and ..."
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Cited by 8 (0 self)
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This paper provides an overview of lower and upper bounds for algorithms for meshconnected processor networks. Most of our attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and open problems. The text is completed with an index. This is a workedout version of the author's contribution to a joint paper with Miltos D. Grammatikakis, D. Frank Hsu and Miro Kraetzl on multicomputer routing, submitted to the Journal of Parallel and Distributed Computing.
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 nea ..."
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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 &times; 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] ...
Experimental evaluation of hotpotato routing algorithms on 2dimensional processor arrays
 In EUROPAR: Parallel Processing, 6th International EUROPAR Conference
, 2000
"... Abstract. In this paper we consider the problem of routing packets in twodimensional torusconnected processor arrays. We describe the implementation of four hotpotato routing algorithms and study their performance by experimentation. The algorithms are either greedy in the sense that packets try ..."
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Abstract. In this paper we consider the problem of routing packets in twodimensional torusconnected processor arrays. We describe the implementation of four hotpotato routing algorithms and study their performance by experimentation. The algorithms are either greedy in the sense that packets try to move towards their destination by adaptively using a shortest path, or have the property that the path traversed by any packet approximates the path traversed by the greedy routing algorithm in the storeandforward model. Moreover, they are simple and were implemented according to the one or twopass scheme. In our experiments, we consider the static case of the routing problem where we study permutation and random destination input instances as well as the dynamic case of the problem under the stochastic model for the continuous generation of packets. Our experimental results demonstrate that, although the running time of all the algorithms is close to the optimal for static routing problems, heavy traffic may influence differently the performance of each algorithm in the dynamic case.
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...