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A Faster And Simpler Algorithm For Sorting Signed Permutations By Reversals
, 1997
"... We give a quadratictime algorithm for finding the minimum number of reversals needed to sort a signed permutation. Our algorithm is faster than the previous algorithm of Hannenhalli and Pevzner and its faster implementation of Berman and Hannenhalli. The algorithm is conceptually simple and does no ..."
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Cited by 126 (10 self)
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We give a quadratictime algorithm for finding the minimum number of reversals needed to sort a signed permutation. Our algorithm is faster than the previous algorithm of Hannenhalli and Pevzner and its faster implementation of Berman and Hannenhalli. The algorithm is conceptually simple and does not require special data structures. Our study also considerably simplifies the combinatorial structures used by the analysis.
Transitiveclosure spanners
, 2008
"... We define the notion of a transitiveclosure spanner of a directed graph. Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k. These spanner ..."
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Cited by 38 (11 self)
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We define the notion of a transitiveclosure spanner of a directed graph. Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k. These spanners were studied implicitly in access control, property testing, and data structures, and properties of these spanners have been rediscovered over the span of 20 years. We bring these areas under the unifying framework of TCspanners. We abstract the common task implicitly tackled in these diverse applications as the problem of constructing sparse TCspanners. We study the approximability of the size of the sparsest kTCspanner for a given digraph. Our technical contributions fall into three categories: algorithms for general digraphs,
Two Notes On Genome Rearrangement
 Journal of Bioinformatics and Computational Biology
, 2003
"... A central problem in genome rearrangement is nding a most parsimonious rearrangement scenario using certain rearrangement operations. An important problem of this type is sorting a signed genome by reversals and translocations (SBRT). Hannenhalli and Pevzner presented a duality theorem for SBRT ..."
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Cited by 26 (1 self)
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A central problem in genome rearrangement is nding a most parsimonious rearrangement scenario using certain rearrangement operations. An important problem of this type is sorting a signed genome by reversals and translocations (SBRT). Hannenhalli and Pevzner presented a duality theorem for SBRT which leads to a polynomial time algorithm for sorting a multichromosomal genome using a minimum number of reversals and translocations. However, there is one case for which their theorem and algorithm fail. We describe that case and suggest a correction to the theorem and the polynomial algorithm.
TransitiveClosure Spanners of the Hypercube and the Hypergrid
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY
, 2009
"... Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k. Transitiveclosure spanners were introduced in [7] as a common abstraction for applicati ..."
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Cited by 4 (2 self)
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Given a directed graph G = (V, E) and an integer k ≥ 1, a ktransitiveclosurespanner (kTCspanner) of G is a directed graph H = (V, EH) that has (1) the same transitiveclosure as G and (2) diameter at most k. Transitiveclosure spanners were introduced in [7] as a common abstraction for applications in access control, property testing and data structures. In this work we study the number of edges in the sparsest 2TCspanners for the directed hypercube {0, 1} d and hypergrid {1, 2,..., m} d with the usual partial order, ≼, defined by: x1... xd ≼ y1...yd if and only if xi ≤ yi for all i ∈ {1,..., d}. We show that the number of edges in the sparsest 2TCspanner of the hypercube is 2 cd+Θ(log d) , where c ≈ 1.1620. We also present upper and lower bounds on the size of the sparsest 2TCspanner of the directed hypergrid. Our first pair of upper and lower bounds for the hypergrid is in terms of an expression with binomial coefficients. The bounds differ by a factor of O(d 2m) and, in particular, give tight (up to a poly(d) factor) bounds for constant m. We also give a second set of bounds, which show that the number of edges in the sparsest 2TCspanner of the hypergrid is at most md log d ( { m and at least Ω max md logd m
An InverseAckermann Style Lower Bound for Online Minimum Spanning Tree Verification
 Combinatorica
"... 1 Introduction The minimum spanning tree (MST) problem has seen a flurry of activity lately, driven largely by the success of a new approach to the problem. The recent MST algorithms [20, 8, 29, 28], despite their superficial differences, are all based on the idea of progressively improving an appro ..."
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Cited by 3 (2 self)
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1 Introduction The minimum spanning tree (MST) problem has seen a flurry of activity lately, driven largely by the success of a new approach to the problem. The recent MST algorithms [20, 8, 29, 28], despite their superficial differences, are all based on the idea of progressively improving an approximately minimum solution, until the actual minimum spanning tree is found. It is still likely that this progressive improvement approach will bear fruit. However, the current