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59
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.
ChernoffHoeffding Bounds for Applications with Limited Independence
 SIAM J. Discrete Math
, 1993
"... ChernoffHoeffding bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables. We present a simple technique which gives slightly better bounds than these, and which more importantly requires only limited independence among the rando ..."
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Cited by 104 (10 self)
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ChernoffHoeffding bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables. We present a simple technique which gives slightly better bounds than these, and which more importantly requires only limited independence among the random variables, thereby importing a variety of standard results to the case of limited independence for free. Additional methods are also presented, and the aggregate results are sharp and provide a better understanding of the proof techniques behind these bounds. They also yield improved bounds for various tail probability distributions and enable improved approximation algorithms for jobshop scheduling. The "limited independence" result implies that a reduced amount of randomness and weaker sources of randomness are sufficient for randomized algorithms whose analyses use the ChernoffHoeffding bounds, e.g., the analysis of randomized algorithms for random sampling and oblivious packet routi...
Randomized routing and sorting on fixedconnection networks
 Journal of Algorithms
, 1994
"... This paper presents a general paradigm for the design of packet routing algorithms for fixedconnection networks. Its basis is a randomized online algorithm for scheduling any set of N packets whose paths have congestion c on any boundeddegree leveled network with depth L in O(c + L + log N) steps ..."
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Cited by 88 (13 self)
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This paper presents a general paradigm for the design of packet routing algorithms for fixedconnection networks. Its basis is a randomized online algorithm for scheduling any set of N packets whose paths have congestion c on any boundeddegree leveled network with depth L in O(c + L + log N) steps, using constantsize queues. In this paradigm, the design of a routing algorithm is broken into three parts: (1) showing that the underlying network can emulate a leveled network, (2) designing a path selection strategy for the leveled network, and (3) applying the scheduling algorithm. This strategy yields randomized algorithms for routing and sorting in time proportional to the diameter for meshes, butterflies, shuffleexchange graphs, multidimensional arrays, and hypercubes. It also leads to the construction of an areauniversal network: an Nnode network with area Θ(N) that can simulate any other network of area O(N) with slowdown O(log N).
Improved Approximation Algorithms for Shop Scheduling Problems
, 1994
"... In the job shop scheduling problem we are given m machines and n jobs; a job consists of a sequence of operations, each of which must be processed on a specified machine; the objective is to complete all jobs as quickly as possible. This problem is strongly NPhard even for very restrictive special ..."
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Cited by 84 (7 self)
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In the job shop scheduling problem we are given m machines and n jobs; a job consists of a sequence of operations, each of which must be processed on a specified machine; the objective is to complete all jobs as quickly as possible. This problem is strongly NPhard even for very restrictive special cases. We give the first randomized and deterministic polynomialtime algorithms that yield polylogarithmic approximations to the optimal length schedule. Our algorithms also extend to the more general case where a job is given not by a linear ordering of the machines on which it must be processed but by an arbitrary partial order. Comparable bounds can also be obtained when there are m 0 types of machines, a specified number of machines of each type, and each operation must be processed on one of the machines of a specified type, as well as for the problem of scheduling unrelated parallel machines subject to chain precedence constraints. Key Words: scheduling, approximation algorithms AM...
The Network Architecture of the Connection Machine CM5
 Journal of Parallel and Distributed Computing
, 1992
"... The Connection Machine Model CM5 Supercomputer is a massively parallel computer system designed to offer performance in the range of 1 teraflops (10 12 floatingpoint operations per second). The CM5 obtains its high performance while offering ease of programming, flexibility, and reliability. Th ..."
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Cited by 77 (2 self)
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The Connection Machine Model CM5 Supercomputer is a massively parallel computer system designed to offer performance in the range of 1 teraflops (10 12 floatingpoint operations per second). The CM5 obtains its high performance while offering ease of programming, flexibility, and reliability. The machine contains three communication networks: a data network, a control network, and a diagnostic network. This paper describes the organization of these three networks and how they contribute to the design goals of the CM5. 1 Introduction In the design of a parallel computer, the engineering principle of economy of mechanism suggests that the machine should employ only a single communication network to convey information among the processors in the system. Indeed, many parallel computers contain only a single network: typically, a hypercube or a mesh. The Connection Machine Model CM5 Supercomputer has three networks, however, and none is a hypercube or a mesh. This paper describes the...
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...
Efficient Communication Strategies for AdHoc Wireless Networks
, 2000
"... An adhoc wireless network is a collection of wireless mobile hosts forming a temporary network without the aid of any established infrastructure or centralized administration. This type of network is of great importance in situations where it is very difficult to provide the necessary infrastructur ..."
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Cited by 34 (3 self)
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An adhoc wireless network is a collection of wireless mobile hosts forming a temporary network without the aid of any established infrastructure or centralized administration. This type of network is of great importance in situations where it is very difficult to provide the necessary infrastructure, but it is a challenging task to enable fast and reliable communication within such a network. In this paper, we model and analyze the performance of socalled powercontrolled adhoc wireless networks: networks where the mobile hosts are able to change their transmission power. We concentrate on finding schemes for routing arbitrary permutations in these networks. In general, it is NPhard even to find a n 1 approximation for any constant to the fastest possible strategy for routing a given permutation problem on n mobile hosts. However, we here demonstrate that if we allow ourselves to consider slightly less general problems, efficient solutions can be found. We first demonstrate that there is a natural class of distributed schemes for handling nodetonode communication on top of which online route selection and scheduling strategies can be constructed such that the performance of this class of schemes can be exploited in a nearly optimal way for routing permutations in any static powercontrolled adhoc network. We then demonstrate