A Simpler 1.5-Approximation Algorithm for Sorting by Transpositions

Hartman, Tzvika

doi:10.1007/3-540-44888-8_12

Cited by 53 publications

(52 citation statements)

References 14 publications

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“…The problem of Ulam distance with block moves is equivalent to a well-known problem in computational biology called Sorting-by-Transpositions (SBT) [7,21,16]. This problem is neither known to be NPhard nor known to lie in P. Therefore, we decided to start by considering a related problem, Sorting-byReversal (SBR), which is known to lie in P. For this problem, Hannenhalli and Pevzner [20,25] proved a combinatorial characterization of the distance.…”

Section: Ideas Behind This Work and Suggestions For Further Workmentioning

confidence: 99%

The Streaming Complexity of Cycle Counting, Sorting By Reversals, and Other Problems

Verbin¹,

Yu²

2011

Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms

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In this paper we introduce a new technique for proving streaming lower bounds (and one-way communication lower bounds), by reductions from a problem called the Boolean Hidden Hypermatching problem (BHH). BHH is a generalization of the well-known Boolean Hidden Matching problem, which was used by Gavinsky et al. to prove an exponential separation between quantum communication complexity and one-way randomized communication complexity. We are the first to introduce BHH, and to prove a lower bound for it.The hardness of the BHH problem is inherently oneway: it is easy to solve BHH using logarithmic two-way communication, but it requires √ n communication if Alice is only allowed to send messages to Bob, and not vice-versa. This one-wayness allows us to prove lower bounds, via reductions, for streaming problems and related communication problems whose hardness is also inherently one-way.By designing reductions from BHH, we prove lower bounds for the streaming complexity of approximating the sorting by reversal distance, of approximately counting the number of cycles in a 2-regular graph, and of other problems.For example, here is one lower bound that we prove, for a cycle-counting problem: Alice gets a perfect matching EA on a set of n nodes, and Bob gets a perfect matching EB on the same set of nodes. The union EA ∪ EB is a collection of cycles, and the goal is to approximate the number of cycles in this collection. We prove that if Alice is allowed to send o( √ n) bits to Bob (and Bob is not allowed to send anything to Alice), then the number of cycles cannot be approximated to within a factor of 1.999, even using a randomized protocol. We prove that it is not even possible to distinguish the case where all cycles are of length 4, from the case where all cycles are of length 8. This lower bound is "natively" one-way: With 4 rounds of communication, it is easy to distinguish these two cases.

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Section: Ideas Behind This Work and Suggestions For Further Workmentioning

confidence: 99%

The Streaming Complexity of Cycle Counting, Sorting By Reversals, and Other Problems

Verbin¹,

Yu²

2011

Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms

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“…In order to explain the existence of essentially the same set of genes but differences in their order in different species, several rearrangement operations have been suggested, including reversals [6][7][8], block interchange [9], transpositions [10][11][12], transreversals [13], fission and fusion [14], prefix transposition [15], etc.…”

Section: Introductionmentioning

confidence: 99%

Pancake Flipping with Two Spatulas

Sharmin

Yeasmin

Hasan

et al. 2010

Electronic Notes in Discrete Mathematics

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Abstract. In this paper we study several variations of the pancake flipping problem, which is also well known as the problem of sorting by prefix reversals. We consider the variations in the sorting process by adding with prefix reversals other similar operations such as prefix transpositions and prefix transreversals. These type of sorting problems have applications in interconnection networks and computational biology. We first study the problem of sorting unsigned permutations by prefix reversals and prefix transpositions and present a 3-approximation algorithm for this problem. Then we give a 2-approximation algorithm for sorting by prefix reversals and prefix transreversals. We also provide a 3-approximation algorithm for sorting by prefix reversals and prefix transpositions where the operations are always applied at the unsorted suffix of the permutation. We further analyze the problem in more practical way and show quantitatively how approximation ratios of our algorithms improve with the increase of number of prefix reversals applied by optimal algorithms. Finally, we present experimental results to support our analysis.

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“…However, while some of the same theoretical framework can be used (Bafna and Pevzner, 1995), results here are disappointing: no efficient algorithm has yet been developed to compute the transposition distance. The best result to date remains an approximation algorithm that could suffer from up to a 50% error (Bafna and Pevzner, 1995;Hartman, 2003); this result was recently extended, with the same error bound, to the computation of edit distances under a combination of inversions and inverted transpositions, with equal weights assigned to each (Hartman and Sharan, 2004).…”

Section: Distances Between Two Chromosomes With Equal Gene Content Anmentioning

confidence: 94%

Advances in Phylogeny Reconstruction from Gene Order and Content Data

Moret¹,

Warnow²

2004

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Genomes can be viewed in terms of their gene content and the order in which the genes appear along each chromosome. Evolutionary events that affect the gene order or content are "rare genomic events" (rarer than events that affect the composition of the nucleotide sequences) and have been advocated by systematists for inferring deep evolutionary histories. This chapter surveys recent developments in the reconstruction of phylogenies from gene order and content, focusing on their performance under various stochastic models of evolution. Because such methods are currently quite restricted in the type of data they can analyze, we also present current research aimed at handling the full range of whole-genome data.

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A Simpler 1.5-Approximation Algorithm for Sorting by Transpositions

Cited by 53 publications

References 14 publications

The Streaming Complexity of Cycle Counting, Sorting By Reversals, and Other Problems

The Streaming Complexity of Cycle Counting, Sorting By Reversals, and Other Problems

Pancake Flipping with Two Spatulas

Advances in Phylogeny Reconstruction from Gene Order and Content Data

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