The random-adversary technique is a general method for proving lower bounds on randomized parallel algorithms. The bounds apply Do the number of communication steps, and they apply regardless of the processors' in...
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The random-adversary technique is a general method for proving lower bounds on randomized parallel algorithms. The bounds apply Do the number of communication steps, and they apply regardless of the processors' instruction sets, the lengths of messages, etc. This paper introduces the random-adversary technique and shows how it can be used to obtain lower bounds on randomized parallel algorithms for load balancing, compaction, padded sorting, and finding Hamiltonian cycles in random graphs. Using the random-adversary technique, we obtain the first lower bounds for randomized parallel algorithms which are provably faster than their deterministic counterparts (specifically, for load balancing and related problems).
The maximal linear forest problem is to find, given a graph G = (V, E), a maximal subset of V that induces a linear forest. Three parallelalgorithms for this problem are presented. The first one is randomized and run...
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The maximal linear forest problem is to find, given a graph G = (V, E), a maximal subset of V that induces a linear forest. Three parallelalgorithms for this problem are presented. The first one is randomized and runs in O(log n) expected time using n(2) processors on a CRCW PRAM. The second one is deterministic and runs in O(log(2) n) time using n(4) processors on an EREW PRAM. The last one is deterministic and runs in O(log(5) n) time using n(3) processors on an EREW PRAM. The results put the problem in the class NC.
We present two parallelalgorithms for finding a maximal set of paths in a given undirected graph. One is randomized and runs in O(log n) expected time with O(n + m) processors on a CRCW PRAM. The other is determinist...
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We present two parallelalgorithms for finding a maximal set of paths in a given undirected graph. One is randomized and runs in O(log n) expected time with O(n + m) processors on a CRCW PRAM. The other is deterministic and runs in O(log(2) n) time with O(Delta(2)(n + m)/ log n) processors on an EREW PRAM. The results improve on the previous bests and can also be extended to digraphs. We then use the results to improve the time complexity of the best previous NC approximation algorithm for the shortest superstring problem. (C) 1999-Elsevier Science B.V. All rights reserved
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