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Linear approximation of shortest superstrings
1991
Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91
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Let n denote the length of the optimal superstring. ...
We consider the following problem: given a collection of strings s 1 ; .. .;s m , nd the shortest string s such that each s i appears as a substring (a consecutive block) of s. ...
of 4 approximation for the shortest-common-superstring problem. ...
doi:10.1145/103418.103455
dblp:conf/stoc/BlumJLTY91
fatcat:rrhuzscoezfe7o6vh42lte2bvy
Linear approximation of shortest superstrings
1994
Journal of the ACM
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Let n denote the length of the optimal superstring. ...
We consider the following problem: given a collection of strings s 1 ; .. .;s m , nd the shortest string s such that each s i appears as a substring (a consecutive block) of s. ...
of 4 approximation for the shortest-common-superstring problem. ...
doi:10.1145/179812.179818
fatcat:cc4wxhdpavd7bdjdxrjmxfycau
Greedy-reduction from Shortest Linear Superstring to Shortest Circular Superstring
[article]
2021
arXiv
pre-print
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The problem of finding the Shortest Linear Superstring is a well-know and well-studied problem in stringology. ...
Moreover, we propose a new conjecture on the approximation ratio of the Shortest Circular Superstring problem. ...
states that the approximation ratio of the greedy algorithm for the Shortest Linear Superstring problem is 2. ...
arXiv:2012.08878v2
fatcat:4cvkodoqdbd3hg7aie6ugtouly
Practical lower and upper bounds for the Shortest Linear Superstring
2018
Symposium on Experimental and Efficient Algorithms
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Given a set P of words, the Shortest Linear Superstring (SLS) problem is an optimisation problem that asks for a superstring of P of minimal length. ...
Here, we exhibit a linear time algorithm that reports an upper and a lower bound on the length of an optimal superstring. The upper bound is the length of an approximate superstring. ...
The Shortest Linear Superstring (SLS) problem -also known as Shortest Common Superstring -, asks for a superstring of P of minimal length. ...
doi:10.4230/lipics.sea.2018.18
dblp:conf/wea/CazauxJR18
fatcat:gqnpj3zq6vf5fjkkze6ehb3fgi
Approximating Shortest Superstring Problem Using de Bruijn Graphs
[chapter]
2013
Lecture Notes in Computer Science
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The best known approximation ratio for the shortest superstring problem is 2 11 23 (Mucha, 2012). ...
Such graphs are widely used in genome assembly (one of the most important practical applications of the shortest common superstring problem). ...
Introduction
Problem Statement The superstring problem (also known as shortest common superstring problem, SCS, or shortest superstring problem, SSP) is: given n strings s 1 , . . . , s n to find a shortest ...
doi:10.1007/978-3-642-38905-4_13
fatcat:lyoji5qipnh7xplz57u7zmivxu
Shortest DNA Cyclic Cover in Compressed Space
2016
2016 Data Compression Conference (DCC)
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Most approximation algorithms solve the Shortest Cyclic Cover problem before merging the cyclic strings into a linear superstring. ...
For a set of input words, finding a superstring (a string containing each word of the set as a substring) of minimal length is hard. ...
In the general case, shortest cyclic covers are used to compute approximate shortest superstrings. ...
doi:10.1109/dcc.2016.79
dblp:conf/dcc/CazauxCR16
fatcat:nexwiczs2rfbdanbejpxj6nbee
A linear time algorithm for Shortest Cyclic Cover of Strings
2016
Journal of Discrete Algorithms
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This has implications for solving certain instances of the Shortest linear or cyclic Superstring problems. ...
SCCS is used as a crucial step in polynomial time approximation algorithms for the notably hard Shortest Superstring problem, but it is solved in cubic time. ...
Consequences of the topology of the Superstring Graph The characterisation of the SG can also be applied to solve or approximate the "classical" shortest superstring problem (SLiS -for Shortest Linear ...
doi:10.1016/j.jda.2016.05.001
fatcat:3azou2obczffjpwcge7nh6jjj4
Approximating Shortest Superstrings
1997
SIAM journal on computing (Print)
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We present a new algorithm which always finds a superstring that is at most 2.89 times as long as the shortest superstring. Our result improves the 3-approximation result of Blum et al. ...
Since the problem is NP-hard and MAX SNP-hard, approximation algorithms are of interest. ...
Let |s| denote the length of a string s, and let |S| = s∈S |s|. We use opt(S) to denote the length of the shortest superstring of S. ...
doi:10.1137/s0097539794286125
fatcat:6wc2ntk3brdr5jq6i5ynmw42fu
Approximating shortest superstrings with constraints
1994
Theoretical Computer Science
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Li, Approximating shortest superstrings with constraints, Theoretical Computer Science 134 (1994) 473-491. ...
Remember a linear approximation algorithm for the shortest consistent superstring problem is also a linear approximation algorithm for the shortest common superstring problem. ...
Hence the resulting superstring is of length O(n) following the proof of Theorem 7. 0
Concluding remarks We have given polynomial-time linear approximation algorithms for two special cases of the shortest ...
doi:10.1016/0304-3975(94)90249-6
fatcat:2bv6azxsivf7jfyqamasynbmxm
Approximating shortest superstrings with constraints
[chapter]
1993
Lecture Notes in Computer Science
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Li, Approximating shortest superstrings with constraints, Theoretical Computer Science 134 (1994) 473-491. ...
Remember a linear approximation algorithm for the shortest consistent superstring problem is also a linear approximation algorithm for the shortest common superstring problem. ...
Hence the resulting superstring is of length O(n) following the proof of Theorem 7. 0
Concluding remarks We have given polynomial-time linear approximation algorithms for two special cases of the shortest ...
doi:10.1007/3-540-57155-8_264
fatcat:cnkgz7fbfbhfpaul5fze3idnv4
The power of greedy algorithms for approximating Max-ATSP, Cyclic Cover, and superstrings
2016
Discrete Applied Mathematics
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P := {s 1 , . . . , s p }, asks for w, a superstring of P minimising ∑ s i ∈S |s i | − |w|, are both difficult to approximate (Max-SNP hard). ...
The best approximation algorithms use the Shortest Cyclic Cover of Strings (SCCS) as a procedure, which asks for a set of cyclic strings of total minimum length that collectively contain the input words ...
A preliminary version of this work was published in the proceedings of the Prague Stringology Conference in 2014 ...
doi:10.1016/j.dam.2015.06.003
fatcat:ry7weg4olfb4nidlsodpjgw6py
Superstrings with multiplicities
2018
Annual Symposium on Combinatorial Pattern Matching
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Given P , the well known Shortest Linear Superstring problem (SLS), asks for a shortest superstring of P . ...
Here, we study the approximability of Multi-SLS and that of the companion problem Multi-SCCS, which asks for a shortest cyclic cover instead of shortest superstring. ...
The Shortest Linear Superstring (SLS) problem is an optimization problem that asks for a superstring of P of minimal length. ...
doi:10.4230/lipics.cpm.2018.21
dblp:conf/cpm/CazauxR18
fatcat:sgtq4vm6g5hqla7cscicfridgu
Superstring Graph: A New Approach for Genome Assembly
[chapter]
2016
Lecture Notes in Computer Science
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In linear time and space, it combines the efficiency of a greedy approach to the advantages of using a single graph. ...
Here, we present a novel approach based on a digraph, the Superstring Graph, that captures all desired sizes of overlaps at once and allows to discard unreliable overlaps. ...
Thus, the problem of finding a shortest linear string cover is as hard and as difficult to approximate as the shortest linear superstring problem (NP-hard [7] and APX-hard [12] ). ...
doi:10.1007/978-3-319-41168-2_4
fatcat:cns7emg7tvcuvmeptkn746jlye
Rotation of Periodic Strings and Short Superstrings
1996
BRICS Report Series
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This paper presents two simple approximation algorithms for the shortest superstring problem, with approximation ratios 2.67 and 2.596, improving the best previously published 2.75<br />approximation. ...
In the previous shortest superstring algorithms p+q was used as the standard bound on overlap between two strings with periods p and q. ...
His proof uses properties of Lyndon words directly, in the spirit of the recent proofs of the Critical Factorization Theorem in [6, 7] , and exploiting the fact that the string in question α is infinite ...
doi:10.7146/brics.v3i21.19984
fatcat:dgzdejr5a5flphdwiyszq2bl74
On the greedy algorithm for the Shortest Common Superstring problem with reversals
2016
Information Processing Letters
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2015 pre-print arXiv:1511.08431v1 fatcat:wjtjc4zv55hjvmeul3lcq3rdziOther Versions
We study a variation of the classical Shortest Common Superstring (SCS) problem in which a shortest superstring of a finite set of strings $S$ is sought containing as a factor every string of $S$ or its ...
We also provide a linear-time implementation of our algorithm. ...
Acknowledgments The authors thank anonymous referees for a number of helpful comments and remarks. This ...
doi:10.1016/j.ipl.2015.11.015
fatcat:j77p6ecfmnhyfhq2i2nt6xvaie
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