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Linear approximation of shortest superstrings

Avrim Blum, Tao Jiang, Ming Li, John Tromp, Mihalis Yannakakis
1991 Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91  
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

Avrim Blum, Tao Jiang, Ming Li, John Tromp, Mihalis Yannakakis
1994 Journal of the ACM  
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]

Bastien Cazaux, Eric Rivals
2021 arXiv   pre-print
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

Bastien Cazaux, Samuel Juhel, Eric Rivals, Marc Herbstritt
2018 Symposium on Experimental and Efficient Algorithms  
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]

Alexander Golovnev, Alexander S. Kulikov, Ivan Mihajlin
2013 Lecture Notes in Computer Science  
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

Bastien Cazaux, Rodrigo Canovas, Eric Rivals
2016 2016 Data Compression Conference (DCC)  
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

Bastien Cazaux, Eric Rivals
2016 Journal of Discrete Algorithms  
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

Shang-Hua Teng, Frances F. Yao
1997 SIAM journal on computing (Print)  
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

Tao Jiang, Ming Li
1994 Theoretical Computer Science  
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]

Tao Jiang, Ming Li
1993 Lecture Notes in Computer Science  
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

Bastien Cazaux, Eric Rivals
2016 Discrete Applied Mathematics  
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

Bastien Cazaux, Eric Rivals, Marc Herbstritt
2018 Annual Symposium on Combinatorial Pattern Matching  
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]

Bastien Cazaux, Gustavo Sacomoto, Eric Rivals
2016 Lecture Notes in Computer Science  
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

Dany Breslauer, Tao Jiang, Zhigen Jiang
1996 BRICS Report Series  
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

Gabriele Fici, Tomasz Kociumaka, Jakub Radoszewski, Wojciech Rytter, Tomasz Waleń
2016 Information Processing Letters  
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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