Solving SCS for bounded length strings in fewer than steps

Golovnev, Alexander; Mihajlin, Ivan

doi:10.1016/j.ipl.2014.03.004

Cited by 11 publications

(8 citation statements)

References 12 publications

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“…It works faster than existing classical algorithms. At the same time, there are faster classical algorithms in the case of restricted length of strings [11,12]. It is interesting to explore quantum algorithms for such a restriction.…”

Section: Discussionmentioning

confidence: 99%

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Quantum Algorithm for the Shortest Superstring Problem

Khadiev¹,

Machado²

2021

Preprint

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In this paper, we consider the "Shortest Superstring Problem"(SSP) or the "Shortest Common Superstring Problem"(SCS). The problem is as follows. For a positive integer n, a sequence of n strings S = (s 1 , . . . , s n ) is given. We should construct the shortest string t (we call it superstring) that contains each string from the given sequence as a substring. The problem is connected with the sequence assembly method for reconstructing a long DNA sequence from small fragments. We present a quantum algorithm with running time O * (1.728 n ). Here O * notation does not consider polynomials of n and the length of t.

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Section: Discussionmentioning

confidence: 99%

“…If a length of strings s i is at most 3, then the there is an algorithm [11] with running time O * (1.443 n ). For a constant c, if a length of strings s i is at most c, then there is a randomized algorithm [12] with running time O * (2…”

Section: Introductionmentioning

confidence: 99%

Quantum Algorithm for the Shortest Superstring Problem

Khadiev¹,

Machado²

2021

Preprint

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“…The HOG is reminiscent of the "Hierarchical Graph" of [6], where the arcs also encodes inclusion between substrings of the input words. However, in the Hierarchical Graph, each arc extends or shortens the string by a single symbol, making it larger than the HOG.…”

Section: Related Workmentioning

confidence: 99%

Hierarchical Overlap Graph

Cazaux

Rivals

2020

Information Processing Letters

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Given a set of finite words, the Overlap Graph (OG) is a complete weighted digraph where each word is a node and where the weight of an arc equals the length of the longest overlap of one word onto the other (Overlap is an asymmetric notion). The OG serves to assemble DNA fragments or to compute shortest superstrings which are a compressed representation of the input. The OG requires a space is quadratic in the number of words, which limits its scalability. The Hierarchical Overlap Graph (HOG) is an alternative graph that also encodes all maximal overlaps, but uses a space that is linear in the sum of the lengths of the input words. We propose the first algorithm to build the HOG in linear space for words of equal length.

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“…Such algorithms can only be used in practice to solve instances of very moderate size. Stronger upper bounds are known for a special case when input strings have bounded length [12,13]. There are heuristic methods for solving Traveling Salesman, and hence also Shortest Superstring, they are efficient in practice, however have no efficient provable guarantee on the running time (see, e.g., [1]).…”

Section: Shortest Superstringmentioning

confidence: 99%

Parameterized Complexity of Superstring Problems

et al. 2016

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In the Shortest Superstring problem we are given a set of strings S = {s 1 , . . . , s n } and integer ℓ and the question is to decide whether there is a superstring s of length at most ℓ containing all strings of S as substrings. We obtain several parameterized algorithms and complexity results for this problem.In particular, we give an algorithm which in time 2 O(k) poly(n) finds a superstring of length at most ℓ containing at least k strings of S. We complement this by the lower bound showing that such a parameterization does not admit a polynomial kernel up to some complexity assumption. We also obtain several results about "below guaranteed values" parameterization of the problem. We show that parameterization by compression admits a polynomial kernel while parameterization "below matching" is hard. * The research leading to these results has received funding from the Government of the Russian Federation (grant 14.Z50.31.0030).

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Solving SCS for bounded length strings in fewer than steps

Cited by 11 publications

References 12 publications

Quantum Algorithm for the Shortest Superstring Problem

Quantum Algorithm for the Shortest Superstring Problem

Hierarchical Overlap Graph

Parameterized Complexity of Superstring Problems

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