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72
Packet routing and jobshop scheduling in O(congestion+dilation) steps
 Combinatorica
, 1994
"... In this paper, we prove that there exists a schedule for routing any set of packets with edgesimple paths, on any network, in O(c+d) steps, where c is the congestion of the paths in the network, and d is the length of the longest path. The result has applications to packet routing in parallel machi ..."
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Cited by 104 (8 self)
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In this paper, we prove that there exists a schedule for routing any set of packets with edgesimple paths, on any network, in O(c+d) steps, where c is the congestion of the paths in the network, and d is the length of the longest path. The result has applications to packet routing in parallel machines, network emulations, and jobshop scheduling.
Provably efficient scheduling for languages with finegrained parallelism
 IN PROC. SYMPOSIUM ON PARALLEL ALGORITHMS AND ARCHITECTURES
, 1995
"... Many highlevel parallel programming languages allow for finegrained parallelism. As in the popular worktime framework for parallel algorithm design, programs written in such languages can express the full parallelism in the program without specifying the mapping of program tasks to processors. A ..."
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Cited by 82 (25 self)
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Many highlevel parallel programming languages allow for finegrained parallelism. As in the popular worktime framework for parallel algorithm design, programs written in such languages can express the full parallelism in the program without specifying the mapping of program tasks to processors. A common concern in executing such programs is to schedule tasks to processors dynamically so as to minimize not only the execution time, but also the amount of space (memory) needed. Without careful scheduling, the parallel execution on p processors can use a factor of p or larger more space than a sequential implementation of the same program. This paper first identifies a class of parallel schedules that are provably efficient in both time and space. For any
Workpreserving emulations of fixedconnection networks
 21st ACM Symp. on Theory of Computing
, 1989
"... Abstract. In this paper, we study the problem of emulating T G steps of an N Gnode guest network, G, on an N Hnode host network, H. We call an emulation workpreserving if the time required by the host, T H,isO(T GN G/N H), because then both the guest and host networks perform the same total work ..."
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Cited by 46 (18 self)
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Abstract. In this paper, we study the problem of emulating T G steps of an N Gnode guest network, G, on an N Hnode host network, H. We call an emulation workpreserving if the time required by the host, T H,isO(T GN G/N H), because then both the guest and host networks perform the same total work (i.e., processortime product), �(T GN G), to within a constant factor. We say that an emulation occurs in realtime if T H � O(T G), because then the host emulates the guest with constant slowdown. In addition to describing several workpreserving and realtime emulations, we also provide a general model in which lower bounds can be proved. Some of the more interesting and diverse consequences of this work include: (1) a proof that a linear array can emulate a (much larger) butterfly in a workpreserving fashion, but that a butterfly cannot emulate an expander (of any size) in a workpreserving fashion, (2) a proof that a butterfly can emulate a shuffleexchange network in a realtime workpreserving fashion, and vice versa, (3) a proof that a butterfly can emulate a mesh (or an array of higher, but fixed, dimension) in a realtime workpreserving fashion, even though any O(1)to1 embedding of an Nnode mesh in an Nnode butterfly has dilation �(log N), and
On the Fault Tolerance of Some Popular BoundedDegree Networks
 SIAM Journal on Computing
, 1992
"... In this paper, we analyze the ability of several boundeddegree networks that are commonly used for parallel computation to tolerate faults. Among other things, we show that an Nnode butterfly containing N 1\Gammaffl worstcase faults (for any constant ffl ? 0) can emulate a faultfree butterfly ..."
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Cited by 44 (7 self)
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In this paper, we analyze the ability of several boundeddegree networks that are commonly used for parallel computation to tolerate faults. Among other things, we show that an Nnode butterfly containing N 1\Gammaffl worstcase faults (for any constant ffl ? 0) can emulate a faultfree butterfly of the same size with only constant slowdown. Similar results are proved for the shuffleexchange graph. Hence, these networks become the first connected boundeddegree networks known to be able to sustain more than a constant number of worstcase faults without suffering more than a constantfactor slowdown in performance. We also show that an Nnode butterfly whose nodes fail with some constant probability p can emulate a faultfree version of itself with a slowdown of 2 O(log N) , which is a very slowly increasing function of N . The proofs of these results combine the technique of redundant computation with new algorithms for (packet) routing around faults in hypercubic networks. Tech...
Fast Algorithms for BitSerial Routing on a Hypercube
, 1991
"... In this paper, we describe an O(log N)bitstep randomized algorithm for bitserial message routing on a hypercube. The result is asymptotically optimal, and improves upon the best previously known algorithms by a logarithmic factor. The result also solves the problem of online circuit switching in ..."
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Cited by 36 (9 self)
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In this paper, we describe an O(log N)bitstep randomized algorithm for bitserial message routing on a hypercube. The result is asymptotically optimal, and improves upon the best previously known algorithms by a logarithmic factor. The result also solves the problem of online circuit switching in an O(1)dilated hypercube (i.e., the problem of establishing edgedisjoint paths between the nodes of the dilated hypercube for any onetoone mapping). Our algorithm is adaptive and we show that this is necessary to achieve the logarithmic speedup. We generalize the BorodinHopcroft lower bound on oblivious routing by proving that any randomized oblivious algorithm on a polylogarithmic degree network requires at least \Omega\Gammaast 2 N= log log N) bit steps with high probability for almost all permutations. 1 Introduction Substantial effort has been devoted to the study of storeandforward packet routing algorithms for hypercubic networks. The fastest algorithms are randomized, and c...
Distributed Packet Switching in Arbitrary Networks
 In Proceedings of the 28th Annual ACM Symposium on Theory of Computing
, 1996
"... In a seminal paper Leighton, Maggs, and Rao consider the packet scheduling problem when a single packet has to traverse each path. They show that there exists a schedule where each packet reaches its destination in O(C + D) steps, where C is the congestion and D is the dilation. The proof relies o ..."
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Cited by 34 (2 self)
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In a seminal paper Leighton, Maggs, and Rao consider the packet scheduling problem when a single packet has to traverse each path. They show that there exists a schedule where each packet reaches its destination in O(C + D) steps, where C is the congestion and D is the dilation. The proof relies on the Lov'asz Local Lemma, and hence is not algorithmic. In a followup paper Leighton and Maggs use an algorithmic version of the Local Lemma due to Beck to give centralized algorithms for the problem. Leighton, Maggs, and Rao also give a distributed randomized algorithm where all packets reach their destinations with high probability in O(C +D log n) steps. In this paper we develop techniques to guarantee the high probability of delivering packets without resorting to the Lov'asz Local Lemma. We improve the distributed algorithm for problems with relatively high dilation to O(C) + (log n) O(log n) D + poly(log n). We extend the techniques to handle the case of infinite streams of ...
Universal Algorithms for StoreandForward and Wormhole Routing
 IN PROC. OF THE 28TH ACM SYMP. ON THEORY OF COMPUTING (STOC
, 1996
"... In this paper we present routing algorithms that are universal in the sense that they route messages along arbitrary (simple) paths in arbitrary networks. The algorithms are analyzed in terms of the number of messages being routed, the maximum number of messages that must cross any edge in the netwo ..."
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Cited by 34 (18 self)
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In this paper we present routing algorithms that are universal in the sense that they route messages along arbitrary (simple) paths in arbitrary networks. The algorithms are analyzed in terms of the number of messages being routed, the maximum number of messages that must cross any edge in the network (edge congestion), the maximum number of edges that a message must cross (dilation), the buffer size, and the bandwidth of the links. We present two main results, both of which have applications to universal storeand forward routing and universal wormhole routing. Our results yield significant performance improvements over all previously known universal routing algorithms for a wide range of parameters, and they even improve many time bounds for standard networks. In addition, we present adaptations of our main results for routing along shortest paths in arbitrary networks, and for routing in leveled networks, nodesymmetric networks, edgesymmetric networks, expanders, butterflies, and ...
A Packet Routing Protocol for Arbitrary Networks
 In Proceedings of the 12th Symposium on Theoretical Aspects of Computer Science
, 1995
"... . In this paper, we introduce an online protocol which routes any set of packets along shortest paths through an arbitrary Nnode network in O(congestion + diameter + log N) rounds, with high probability. This time bound is optimal up to the additive log N , and it was previously only reached for ..."
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Cited by 31 (16 self)
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. In this paper, we introduce an online protocol which routes any set of packets along shortest paths through an arbitrary Nnode network in O(congestion + diameter + log N) rounds, with high probability. This time bound is optimal up to the additive log N , and it was previously only reached for boundeddegree levelled networks. Further, we prove bounds on the congestion of random routing problems for Cayley networks and general node symmetric networks based on the construction of shortest paths systems. In particular, we give construction schemes for shortest paths systems and show that if every processor sends p packets to random destinations along the paths described in the paths system, then the congestion is bounded by O(p \Delta diameter + log N ), with high probability. Finally, we prove an (apparently suboptimal) congestion bound for random routing problems on randomly chosen regular networks. 1 Introduction Communication among the processors of a parallel computer usually ...
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.
Universal Continuous Routing Strategies
 IN PROC. OF THE 8TH ACM SYMP. ON PARALLEL ALGORITHMS AND ARCHITECTURES (SPAA
, 1996
"... In this paper we present routing protocols that are universal in the sense that they route messages along arbitrary (simple or shortest) paths in arbitrary networks. We study these protocols under a stochastic model of continuous message generation. The performance of such protocols is characterized ..."
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Cited by 25 (7 self)
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In this paper we present routing protocols that are universal in the sense that they route messages along arbitrary (simple or shortest) paths in arbitrary networks. We study these protocols under a stochastic model of continuous message generation. The performance of such protocols is characterized by three parameters: the maximum message generation rate for which the protocol is stable, the expected delay of a message from generation to service, and the time the protocol needs to recover from worst case scenarios. Our main results are a universal continuous storeandforward routing protocol and a universal continuous wormhole routing protocol. Both protocols yield significant performance improvements over all previously known continuous routing protocols. In addition, we present adaptations of our main results to continuous routing in nodesymmetric networks, butterflies, and meshes.