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Parallel Algorithmic Techniques for Combinatorial Computation
 Ann. Rev. Comput. Sci
, 1988
"... this paper and supplied many helpful comments. This research was supported in part by NSF grants DCR8511713, CCR8605353, and CCR8814977, and by DARPA contract N0003984C0165. ..."
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Cited by 30 (3 self)
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this paper and supplied many helpful comments. This research was supported in part by NSF grants DCR8511713, CCR8605353, and CCR8814977, and by DARPA contract N0003984C0165.
The parallel complexity of element distinctness is \Omega\Gamma p log n
 SIAM J. Disc. Math
, 1988
"... Abstract. We consider the problem of element distinctness. Here n synchronized processors, each given an integer input, must decide whether these integers are pairwise distinct, while communicating via an infinitely large shared memory. If simultaneous write access to a memory cell is forbidden, the ..."
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Abstract. We consider the problem of element distinctness. Here n synchronized processors, each given an integer input, must decide whether these integers are pairwise distinct, while communicating via an infinitely large shared memory. If simultaneous write access to a memory cell is forbidden, then a lower bound of f(log n) on the number of steps easily follows (from S. Cook, C. Dwork, and R. Reischuk, SIAM J. Comput., 15 (1986), pp. 8797.) When several (different) values can be written simultaneously to any cell, then there is an simple algorithm requiring O(1) steps. We consider the intermediate model, in which simultaneous writes to a single cell are allowed only if all values written are equal. We prove a lower bound of f((logn) 1/2) steps, improving the previous lower bound of f(log log log n) steps (F.E. Fich, F. Meyer auf der Heide, and A. Wigderson, Adv. in Comput., 4 (1987), pp. 115). The proof uses Ramseytheoretic and combinatorial arguments. The result implies a separation between the powers of some variants of the PRAM model of parallel computation.
Prefix Graphs and Their Applications
 IN &QUOT;PROCEEDINGS, 20TH INTERNATIONAL WORKSHOP ON GRAPHTHEORETIC CONCEPTS IN COMPUTER SCIENCE,&QUOT; LECTURE NOTES IN COMPUTER SCIENCE
, 1994
"... The range product problem is, for a given set S equipped with an associative operator ffi, to preprocess a sequence a1 ; : : : ; an of elements from S so as to enable efficient subsequent processing of queries of the form: Given a pair (s; t) of integers with 1 s t n, return as ffi as+1 ffi \Delt ..."
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Cited by 3 (2 self)
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The range product problem is, for a given set S equipped with an associative operator ffi, to preprocess a sequence a1 ; : : : ; an of elements from S so as to enable efficient subsequent processing of queries of the form: Given a pair (s; t) of integers with 1 s t n, return as ffi as+1 ffi \Delta \Delta \Delta ffi a t . The generic range product problem and special cases thereof, usually with ffi computing the maximum of its arguments according to some linear order on S, have been extensively studied. We show that a large number of previous sequential and parallel algorithms for these problems can be unified and simplified by means of prefix graphs.
SIMPLE AND WORKEFFICIENT PARALLEL ALGORITHMS FOR THE MINIMUM SPANNING TREE PROBLEM
 PARALLEL PROCESSING LETTERS
"... Two simple and workefficient parallel algorithms for the minimum spanning tree problem are presented. Both algorithms perform O(m log n) work. The first algorithm runs in O(logĀ² n) time on an EREW PRAM, while the second algorithm runs in O(log n) time on a Common CRCW PRAM. ..."
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Two simple and workefficient parallel algorithms for the minimum spanning tree problem are presented. Both algorithms perform O(m log n) work. The first algorithm runs in O(logĀ² n) time on an EREW PRAM, while the second algorithm runs in O(log n) time on a Common CRCW PRAM.
Ramsey Theory Applications
"... There are many interesting applications of Ramsey theory, these include results in number theory, algebra, geometry, topology, set theory, logic, ergodic theory, information theory and theoretical computer science. Relations of Ramseytype theorems to various fields in mathematics are well documente ..."
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There are many interesting applications of Ramsey theory, these include results in number theory, algebra, geometry, topology, set theory, logic, ergodic theory, information theory and theoretical computer science. Relations of Ramseytype theorems to various fields in mathematics are well documented in published books and monographs. The main objective of this survey is to list applications mostly in theoretical computer science of the last two decades not contained in these. 1