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A Randomized LinearTime Algorithm to Find Minimum Spanning Trees
, 1994
"... We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost ra ..."
Abstract

Cited by 115 (7 self)
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We present a randomized lineartime algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered lineartime algorithm for verifying a minimum spanning tree. Our computational model is a unitcost randomaccess machine with the restriction that the only operations allowed on edge weights are binary comparisons.
A linearwork parallel algorithm for finding . . .
, 1994
"... We give the first linearwork parallel algorithm for finding a minimum spanning tree. It is a randomized algorithm, and requires O(2log \Lambda n log n) expected time. It is a modification of the sequential lineartime algorithm of Klein and Tarjan. ..."
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Cited by 14 (1 self)
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We give the first linearwork parallel algorithm for finding a minimum spanning tree. It is a randomized algorithm, and requires O(2log \Lambda n log n) expected time. It is a modification of the sequential lineartime algorithm of Klein and Tarjan.
The SetMaxima Problem: an Overview
, 1998
"... Sorting problems have long been one of the foundations of theoretical computer science. Sorting problems attempt to learn properties of an unknown total order of a known set. We test the order by comparing pairs of elements, and through repeated tests deduce some order structure on the set. The set ..."
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Cited by 1 (0 self)
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Sorting problems have long been one of the foundations of theoretical computer science. Sorting problems attempt to learn properties of an unknown total order of a known set. We test the order by comparing pairs of elements, and through repeated tests deduce some order structure on the set. The setmaxima problem is: given a family S of subsets of a set X, produce the maximal element of each element of S. Local sorting is a subproblem of setmaxima, when S ` i X 2 j , i.e. there exists a graph G with vertex set X and edge set S: We compare algorithms by estimating the number of comparisons needed, as a function of n = jXj; and m = jSj. In this paper, we review the informationtheory lower bounds for the setmaxima and localsorting problems. We review deterministic algorithms which have optimally solved the setmaxima problem, as a function of m;n, in settings where extra assumptions about S have been made. Also, we review randomized algorithms for local sorting and setmaxima ...