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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 102 (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.
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 100 (2 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.,...
Extractors and Pseudorandom Generators
 Journal of the ACM
, 1999
"... We introduce a new approach to constructing extractors. Extractors are algorithms that transform a "weakly random" distribution into an almost uniform distribution. Explicit constructions of extractors have a variety of important applications, and tend to be very difficult to obtain. ..."
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Cited by 93 (5 self)
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We introduce a new approach to constructing extractors. Extractors are algorithms that transform a "weakly random" distribution into an almost uniform distribution. Explicit constructions of extractors have a variety of important applications, and tend to be very difficult to obtain.
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).
Robust PCPs of Proximity, Shorter PCPs and Applications to Coding
 in Proc. 36th ACM Symp. on Theory of Computing
, 2004
"... We continue the study of the tradeo between the length of PCPs and their query complexity, establishing the following main results (which refer to proofs of satis ability of circuits of size n): 1. We present PCPs of length exp( ~ O(log log n) ) n that can be veri ed by making o(log log n) ..."
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Cited by 84 (28 self)
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We continue the study of the tradeo between the length of PCPs and their query complexity, establishing the following main results (which refer to proofs of satis ability of circuits of size n): 1. We present PCPs of length exp( ~ O(log log n) ) n that can be veri ed by making o(log log n) Boolean queries.
Symmetry Breaking
, 2001
"... Symmetries in constraint satisfaction or combinatorial optimization problems can cause considerable difficulties for exact solvers. One way to overcome ..."
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Cited by 84 (5 self)
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Symmetries in constraint satisfaction or combinatorial optimization problems can cause considerable difficulties for exact solvers. One way to overcome
Parallel Algorithms for Hierarchical Clustering
 Parallel Computing
, 1995
"... Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces. O(n 2 ) algorithms are known for this problem [3, 4, 10, 18]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms f ..."
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Cited by 81 (1 self)
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Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces. O(n 2 ) algorithms are known for this problem [3, 4, 10, 18]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms for hierarchical clustering. Parallel algorithms to perform hierarchical clustering using several distance metrics are then described. Optimal PRAM algorithms using n log n processors are given for the average link, complete link, centroid, median, and minimum variance metrics. Optimal butterfly and tree algorithms using n log n processors are given for the centroid, median, and minimum variance metrics. Optimal asymptotic speedups are achieved for the best practical algorithm to perform clustering using the single link metric on a n log n processor PRAM, butterfly, or tree. Keywords. Hierarchical clustering, pattern analysis, parallel algorithm, butterfly network, PRAM algorithm. 1 In...
Efficient Routing and Scheduling Algorithms for Optical Networks
"... This paper studies the problems of dedicating routes and scheduling transmissions in optical networks. In optical networks, the vast bandwidth available in an optical fiber is utilized by partitioning it into several channels, each at a different optical wavelength. A connection between two nodes is ..."
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Cited by 80 (4 self)
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This paper studies the problems of dedicating routes and scheduling transmissions in optical networks. In optical networks, the vast bandwidth available in an optical fiber is utilized by partitioning it into several channels, each at a different optical wavelength. A connection between two nodes is assigned a specific wavelength, with the constraint that no two connections sharing a link in the network can be assigned the same wavelength. This paper classifies several models related to optical networks and presents optimal or nearoptimal algorithms for permutation routing and/or scheduling problems in many of these models. some scheduling problems in one specific model.