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Data Collection for the Sloan Digital Sky Survey  A NetworkFlow Heuristic
 JOURNAL OF ALGORITHMS
, 1996
"... This paper describes an NPhard combinatorial optimization problem arising in the Sloan ..."
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This paper describes an NPhard combinatorial optimization problem arising in the Sloan
The complexity of constructing evolutionary trees using experiments
, 2001
"... We present tight upper and lower bounds for the problem of constructing evolutionary trees in the experiment model. We describe an algorithm which constructs an evolutionary tree of n species in time O(nd log d n) using at most n⌈d/2⌉(log 2⌈d/2⌉−1 n+O(1)) experiments for d> 2, and at most n(log n+ ..."
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Cited by 8 (1 self)
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We present tight upper and lower bounds for the problem of constructing evolutionary trees in the experiment model. We describe an algorithm which constructs an evolutionary tree of n species in time O(nd log d n) using at most n⌈d/2⌉(log 2⌈d/2⌉−1 n+O(1)) experiments for d> 2, and at most n(log n+O(1)) experiments for d = 2, where d is the degree of the tree. This improves the previous best upper bound by a factor Θ(log d). For d = 2 the previously best algorithm with running time O(n log n) had a bound of 4n log n on the number of experiments. By an explicit adversary argument, we show an Ω(nd log d n) lower bound, matching our upper bounds and improving the previous best lower bound by a factor Θ(log d n). Central to our algorithm is the construction and maintenance of separator trees of small height, which may be of independent interest.
Generalized parallel selection in sorted matrices
, 1996
"... This paper presents a parallel algorithm running in time O(log m log m(log log m + log(n=m))) time on an EREW PRAM with O(m=(log m log m)) processors for the problem of selection in an m n matrix with sorted rows and columns, m n. Our algorithm generalizes the result of Sarnath and He [22] for selec ..."
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This paper presents a parallel algorithm running in time O(log m log m(log log m + log(n=m))) time on an EREW PRAM with O(m=(log m log m)) processors for the problem of selection in an m n matrix with sorted rows and columns, m n. Our algorithm generalizes the result of Sarnath and He [22] for selection in a sorted matrix of equal dimensions, and thus answers the open question they posted. The algorithm is workoptimal when n m log m, and near optimal within O(log log m) factor otherwise. We showthat our algorithm can be generalized to solve the selection problem on a set of sorted matrices of arbitrary dimensions.
Fast Parallel Algorithm for Finding the kth Longest Path in A Tree
, 1995
"... We present a fast parallel algorithm running in O(log 2 n) time on a CREW PRAM with O(n) processors for nding the kth longest path in a given tree of n vertices (with (n 2) intervertex distances). Our algorithm is obtained by e cient parallelization of a sequential algorithm which isavariant of both ..."
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We present a fast parallel algorithm running in O(log 2 n) time on a CREW PRAM with O(n) processors for nding the kth longest path in a given tree of n vertices (with (n 2) intervertex distances). Our algorithm is obtained by e cient parallelization of a sequential algorithm which isavariant of both Megiddo et al's algorithm [12] andFredrickson et al's algorithm [3] based on centroid decomposition of tree and succinct representation of the set of intervertex distances. With the same time and space bound as the best known result, our sequential algorithm maintains a shorter length of the decomposition tree. Keywords: Centroid of a tree, decomposition, kth longest path, parallel algorithm, PRAM, selection in ordered matrices.
Partial and Perfect Path Covers of Cographs
"... A set P of disjoint paths in a graph G is called a (complete) path cover of G if every vertex of G belongs to one of the paths in P. A path cover of any subgraph of G is called a partial path cover of G. ..."
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A set P of disjoint paths in a graph G is called a (complete) path cover of G if every vertex of G belongs to one of the paths in P. A path cover of any subgraph of G is called a partial path cover of G.
Chapter 34 Data Collection for the Sloan Digital Sky Survey A NetworkFlow Heuristic
"... This note describes a combinatorial optimization problem arising in the Sloan Digital Sky Survey and an effective heuristic for the problem that has been implemented and will be used in the Survey. The heuristic is based on network flow theory. ..."
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This note describes a combinatorial optimization problem arising in the Sloan Digital Sky Survey and an effective heuristic for the problem that has been implemented and will be used in the Survey. The heuristic is based on network flow theory.