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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 ..."
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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.
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.
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.
Partial and Perfect Path Covers of Cographs
, 1998
"... 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. For fixed ..."
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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. For fixed
Optimal Algorithms for Generalized Matrix Search Problem
, 1995
"... We present a set of optimal and asymptotically optimal sequential and parallel algorithms for the problem of searching on an m n sorted matrix, m n. Our two sequential algorithms have a time complexityofO(m log(2n=m)) whichisshown to be optimal. Our parallel algorithm runs in O(log(log m = log log m ..."
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We present a set of optimal and asymptotically optimal sequential and parallel algorithms for the problem of searching on an m n sorted matrix, m n. Our two sequential algorithms have a time complexityofO(m log(2n=m)) whichisshown to be optimal. Our parallel algorithm runs in O(log(log m = log log m) log(2n=m 1;z)) time using m = log(log m = log log m) processors on a COMMON CRCW PRAM, where 0 z<1 is a monotonically decreasing function on m, which is asymptotically workoptimal. The two sequential algorithms di er mainly in the ways of matrix partitioning: one uses rowsearching and the other applies diagonalsearching. The parallel algorithm is based on some nontrivial matrix partitioning and processor allocation schemes. All the proposed algorithms can be easily generalized for searching on a set of sorted matrices.