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231
Randomized Algorithms
, 1995
"... Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simp ..."
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Cited by 2064 (38 self)
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Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simplest, or both. A randomized algorithm is an algorithm that uses random numbers to influence the choices it makes in the course of its computation. Thus its behavior (typically quantified as running time or quality of output) varies from
Efficient dispersal of information for security, load balancing, and fault tolerance
 Journal of the ACM
, 1989
"... Abstract. An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = ( F ( into n pieces F,, 1 5 i 5 n, each of length ( F, 1 = L/m, so that every m pieces suffice for reconstructing F. Dispersal and reconstruction are computationally efficient. The sum of the lengths ..."
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Cited by 532 (1 self)
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Abstract. An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = ( F ( into n pieces F,, 1 5 i 5 n, each of length ( F, 1 = L/m, so that every m pieces suffice for reconstructing F. Dispersal and reconstruction are computationally efficient. The sum of the lengths ( F, 1 is (n/m). L. Since n/m can be chosen to be close to I, the IDA is space eflicient. IDA has numerous applications to secure and reliable storage of information in computer networks and even on single disks, to faulttolerant and efficient transmission of information in networks, and to communications between processors in parallel computers. For the latter problem provably timeefftcient and highly faulttolerant routing on the ncube is achieved, using just constant size buffers. Categories and Subject Descriptors: E.4 [Coding and Information Theory]: nonsecret encoding schemes
Novel Architectures for P2P Applications: the ContinuousDiscrete Approach
 ACM TRANSACTIONS ON ALGORITHMS
, 2007
"... We propose a new approach for constructing P2P networks based on a dynamic decomposition of a continuous space into cells corresponding to processors. We demonstrate the power of these design rules by suggesting two new architectures, one for DHT (Distributed Hash Table) and the other for dynamic ex ..."
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Cited by 167 (8 self)
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We propose a new approach for constructing P2P networks based on a dynamic decomposition of a continuous space into cells corresponding to processors. We demonstrate the power of these design rules by suggesting two new architectures, one for DHT (Distributed Hash Table) and the other for dynamic expander networks. The DHT network, which we call Distance Halving, allows logarithmic routing and load, while preserving constant degrees. Our second construction builds a network that is guaranteed to be an expander. The resulting topologies are simple to maintain and implement. Their simplicity makes it easy to modify and add protocols. We show it is possible to reduce the dilation and the load of the DHT with a small increase of the degree. We present a provably good protocol for relieving hot spots and a construction with high fault tolerance. Finally we show that, using our approach, it is possible to construct any family of constant degree graphs in a dynamic environment, though with worst parameters. Therefore we expect that more distributed data structures could be designed and implemented in a dynamic environment.
Load Balanced Birkhoffvon Neumann Switches, Part II: Multistage Buffering
, 2001
"... The main objective of this sequel is to solve the outofsequence problem that occurs in the load balanced Birkhoffvon Neumann switch with onestage buffering. We do this by adding a loadbalancing buffer in front of the first stage and a resequencingandoutput buffer after the second stage. Moreo ..."
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Cited by 130 (16 self)
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The main objective of this sequel is to solve the outofsequence problem that occurs in the load balanced Birkhoffvon Neumann switch with onestage buffering. We do this by adding a loadbalancing buffer in front of the first stage and a resequencingandoutput buffer after the second stage. Moreover, packets are distributed at the first stage according to their flows, instead of their arrival times in Part I. In this paper, we consider multicasting ows with two types of scheduling policies: the First Come First Served (FCFS) policy and the Earliest Deadline First (EDF) policy. The FCFS policy requires a jitter control mechanism in front of the second stage to ensure proper ordering of the traffic entering the second stage. For the EDF scheme, there is no need for jitter control. It uses the departure times of the corresponding FCFS outputbuffered switch as deadlines and schedules packets according to their deadlines. For both policies, we show that the endtoend delay through our multistage switch is bounded above by the sum of the delay from the corresponding FCFS outputbuffered switch and a constant that only depends on the size of the switch and the number of multicasting flows supported by the switch.
The Power of Two Random Choices: A Survey of Techniques and Results
 in Handbook of Randomized Computing
, 2000
"... ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately ..."
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Cited by 117 (4 self)
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ITo motivate this survey, we begin with a simple problem that demonstrates a powerful fundamental idea. Suppose that n balls are thrown into n bins, with each ball choosing a bin independently and uniformly at random. Then the maximum load, or the largest number of balls in any bin, is approximately log n= log log n with high probability. Now suppose instead that the balls are placed sequentially, and each ball is placed in the least loaded of d 2 bins chosen independently and uniformly at random. Azar, Broder, Karlin, and Upfal showed that in this case, the maximum load is log log n= log d + (1) with high probability [ABKU99]. The important implication of this result is that even a small amount of choice can lead to drastically different results in load balancing. Indeed, having just two random choices (i.e.,...
ChernoffHoeffding bounds for applications with limited independence
 SIAM Journal on Discrete Mathematics
, 1995
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Flattened butterfly: A costefficient topology for highradix networks
 in Proc. of the Intl. Symp. on Computer Architecture
, 2007
"... Increasing integratedcircuit pin bandwidth has motivated a corresponding increase in the degree or radix of interconnection networks and their routers. This paper introduces the flattened butterfly, a costefficient topology for highradix networks. On benign (loadbalanced) traffic, the flattened b ..."
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Cited by 92 (12 self)
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Increasing integratedcircuit pin bandwidth has motivated a corresponding increase in the degree or radix of interconnection networks and their routers. This paper introduces the flattened butterfly, a costefficient topology for highradix networks. On benign (loadbalanced) traffic, the flattened butterfly approaches the cost/performance of a butterfly network and has roughly half the cost of a comparable performance Clos network. The advantage over the Clos is achieved by eliminating redundant hops when they are not needed for load balance. On adversarial traffic, the flattened butterfly matches the cost/performance of a foldedClos network and provides an order of magnitude better performance than a conventional butterfly. In this case, global adaptive routing is used to switch the flattened butterfly from minimal to nonminimal routing — using redundant hops only when they are needed. Minimal and nonminimal, oblivious and adaptive routing algorithms are evaluated on the flattened butterfly. We show that loadbalancing adversarial traffic requires nonminimal globallyadaptive routing and show that sequential allocators are required to avoid transient load imbalance when using adaptive routing algorithms. We also compare the cost of the flattened butterfly to foldedClos, hypercube, and butterfly networks with identical capacity and show that the flattened butterfly is more costefficient than foldedClos and hypercube topologies.
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 89 (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).
Models of Machines and Computation for Mapping in Multicomputers
, 1993
"... It is now more than a quarter of a century since researchers started publishing papers on mapping strategies for distributing computation across the computation resource of multiprocessor systems. There exists a large body of literature on the subject, but there is no commonlyaccepted framework ..."
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Cited by 80 (1 self)
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It is now more than a quarter of a century since researchers started publishing papers on mapping strategies for distributing computation across the computation resource of multiprocessor systems. There exists a large body of literature on the subject, but there is no commonlyaccepted framework whereby results in the field can be compared. Nor is it always easy to assess the relevance of a new result to a particular problem. Furthermore, changes in parallel computing technology have made some of the earlier work of less relevance to current multiprocessor systems. Versions of the mapping problem are classified, and research in the field is considered in terms of its relevance to the problem of programming currently available hardware in the form of a distributed memory multiple instruction stream multiple data stream computer: a multicomputer.
Faulttolerant Routing in Peertopeer Systems
, 2003
"... We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peertopeer system. We argue that many existing approaches to this problem can be modeled as the construction of a random graph embedded in a metric space whose points repre ..."
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Cited by 70 (1 self)
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We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peertopeer system. We argue that many existing approaches to this problem can be modeled as the construction of a random graph embedded in a metric space whose points represent resource identifiers, where the probability of a connection between two nodes depends only on the distance between them in the metric space. We study the performance of a peertopeer system where nodes are embedded at grid points in a simple metric space: a onedimensional real line. We prove upper and lower bounds on the message complexity of locating particular resources in such a system, under a variety of assumptions about failures of either nodes or the connections between them. Our lower bounds in particular show that the use of inverse powerlaw distributions in routing, as suggested by Kleinberg [5], is close to optimal. We also give efficient heuristics to dynamically maintain such a system as new nodes arrive and old nodes depart. Finally, we give experimental results that suggest promising directions for future work.