Adjacent Swaps on Strings

Chitturi, Bhadrachalam; Sudborough, Hal; Voit, Walter; Feng, Xuerong

doi:10.1007/978-3-540-69733-6_30

Cited by 10 publications

(13 citation statements)

References 2 publications

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“…Recently, cube-connected circulants topology is shown to be better than some well-known network topologies [19]. In addition to permutations, such distance measures and their upper bounds have been extensively studied on strings [9,24,23,25].…”

Section: Introductionmentioning

confidence: 99%

Sorting permutations with a transposition tree

Chitturi¹,

Indulekha

2019

2019 8th International Conference on Modeling Simulation and Applied Optimization (ICMSAO)

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The set of all permutations with n symbols is a symmetric group denoted by Sn. A transposition tree, T , is a spanning tree over its n vertices VT =1, 2, 3, . . . n where the vertices are the positions of a permutation π and π is in Sn. T is the operation and the edge set ET denotes the corresponding generator set. The goal is to sort a given permutation π with T . The number of generators of ET that suffices to sort any π ∈ Sn constitutes an upper bound. It is an upper bound, on the diameter of the corresponding Cayley graph Γ i.e. diam(Γ ). A precise upper bound equals diam(Γ ). Such bounds are known only for a few tress. Jerrum showed that computing diam(Γ ) is intractable in general if the number of generators is two or more whereas T has n − 1 generators. For several operations computing a tight upper bound is of theoretical interest. Such bounds have applications in evolutionary biology to compute the evolutionary relatedness of species and parallel/distributed computing for latency estimation. The earliest algorithm computed an upper bound f (Γ ) in a Ω(n!) time by examining all π in Sn. Subsequently, polynomial time algorithms were designed to compute upper bounds or their estimates. We design an upper bound δ * whose cumulative value for all trees of a given size n is shown to be the tightest for n ≤ 15. We show that δ * is tightest known upper bound for full binary trees. 4

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Section: Introductionmentioning

confidence: 99%

Sorting permutations with a transposition tree

Chitturi¹,

Indulekha

2019

2019 8th International Conference on Modeling Simulation and Applied Optimization (ICMSAO)

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“…A string is a sequence of symbols from an alphabet Σ, in which a symbol can be repeated. An adjacent swap exchanges two consecutive elements in a sequence [1,2]. In a signed string (π, ∀ i π[i]) the following signs are assigned: + for normal orientation and − for reverse orientation.…”

Section: Introductionmentioning

confidence: 99%

“…Adjacent swap over positions i, i + 1 are denoted by (i i + 1). For unsigned strings (π), where π = π [1], π [2], π [3], . .…”

Section: Introductionmentioning

confidence: 99%

“…. , π[n], π transforms into π , where π = π [1], π [2], π [3] [n]. Two strings are compatible under some operation if they can be transformed into each other with the operation.…”

Section: Introductionmentioning

confidence: 99%

“…That is, the unsigned string (2, 1, 3, 2) is compatible with (2, 1, 2, 3), whereas it is not compatible with (3, 2, 1, 1). The computation of the minimum number of adjacent swaps required to transform one given string into another compatible string, i.e., the adjacent swap distance, has applications in genetics and music theory [1]. A 1-flip toggles the orientation of a particular π [i]; it is denoted by f 1 (i).…”

Section: Introductionmentioning

confidence: 99%

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Layered Graphs: Applications and Algorithms

et al. 2018

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The computation of distances between strings has applications in molecular biology, music theory and pattern recognition. One such measure, called short reversal distance, has applications in evolutionary distance computation. It has been shown that this problem can be reduced to the computation of a maximum independent set on the corresponding graph that is constructed from the given input strings. The constructed graphs primarily fall into a class that we call layered graphs. In a layered graph, each layer refers to a subgraph containing, at most, some k vertices. The inter-layer edges are restricted to the vertices in adjacent layers. We study the MIS, MVC, MDS, MCV and MCD problems on layered graphs where MIS computes the maximum independent set; MVC computes the minimum vertex cover; MDS computes the minimum dominating set; MCV computes the minimum connected vertex cover; and MCD computes the minimum connected dominating set. MIS, MVC and MDS run in polynomial time if k = Θ(log | V |). MCV and MCD run in polynomial time if k = O((log | V |) α), where α < 1. If k = Θ((log | V |) 1+), for > 0, then MIS, MVC and MDS run in quasi-polynomial time. If k = Θ(log | V |), then MCV and MCD run in quasi-polynomial time.

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Sorting Circular Permutations by Bounded Transpositions

Feng

Chitturi

Sudborough³

2010

Advances in Experimental Medicine and Biology

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A k-bounded (k ≥ 2) transposition is an operation that switches two elements that have at most k - 2 elements in between. We study the problem of sorting a circular permutation π of length n for k = 2, i.e., adjacent swaps and k = 3, i.e., short swaps. These transpositions mimic microrearrangements of gene order in viruses and bacteria. We prove a (1/4)n (2) lower bound for sorting by adjacent swaps. We show upper bounds of (5/32)n (2) + O(n log n) and (7/8)n + O(log n) for sequential and parallel sorting, respectively, by short swaps.

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Adjacent Swaps on Strings

Cited by 10 publications

References 2 publications

Sorting permutations with a transposition tree

Sorting permutations with a transposition tree

Layered Graphs: Applications and Algorithms

Sorting Circular Permutations by Bounded Transpositions

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