Filters








6,707 Hits in 2.1 sec

The Minimum Substring Cover problem

Danny Hermelin, Dror Rawitz, Romeo Rizzi, Stéphane Vialette
2008 Information and Computation  
In this paper we consider the problem of covering a set of strings S with a set C of substrings in S, where C is said to cover S if every string in S can be written as a concatenation of the substrings  ...  We then proceed to show that this problem is at least as hard as the Minimum Set Cover problem.  ...  In our covering problem, the base elements are strings and the covering elements are their substrings.  ... 
doi:10.1016/j.ic.2008.06.002 fatcat:wvpjnp5fjzhphkbl37nb3btt3m

The Minimum Substring Cover Problem [chapter]

Danny Hermelin, Dror Rawitz, Romeo Rizzi, Stéphane Vialette
Approximation and Online Algorithms  
In this paper we consider the problem of covering a set of strings S with a set C of substrings in S, where C is said to cover S if every string in S can be written as a concatenation of the substrings  ...  We then proceed to show that this problem is at least as hard as the Minimum Set Cover problem.  ...  In our covering problem, the base elements are strings and the covering elements are their substrings.  ... 
doi:10.1007/978-3-540-77918-6_14 dblp:conf/waoa/HermelinRRV07 fatcat:wpreleq5lrbztjkyk7liynwtyq

Generalized approximate regularities in strings

Hui Zhang, Qing Guo, Costas S. Iliopoulos
2008 International Journal of Computer Mathematics  
Given a string x of length n and an integer λ, the minimum approximate λ-cover (resp. seed) problem is to find a set of λ substrings each of equal length that covers x (resp. a superstring of x) with the  ...  We concentrate on the generalized string regularities and study the minimum approximate λ-cover problem and the minimum approximate λ-seed problem of a string.  ...  Solving the Minimum Approximate λ-cover Problem Now we turn to investigate the minimum approximate λ-cover problem.  ... 
doi:10.1080/00207160701389168 fatcat:qnrb7ega45fdjidtz6yqwwlopa

New complexity results for the k-covers problem

Costas S. Iliopoulos, Manal Mohamed, W.F. Smyth
2011 Information Sciences  
The k-covers problem (kCP) asks us to compute a minimum cardinality set of strings of given length k > 1 that covers a given string.  ...  It was shown in a recent paper, by reduction to 3-SAT, that the k-covers problem is NP-complete.  ...  Open Problems We have shown that for k ≥ 2, the k-covers problem kCP is equivalent to RVCP k , hence that efficient algorithms can be used to approximate a minimum k-cover as specified in Section 3.  ... 
doi:10.1016/j.ins.2011.02.009 fatcat:fttao4tnbvcdxhour2ninukjma

Solving the Minimum String Cover Problem [chapter]

Stefan Canzar, Tobias Marschall, Sven Rahmann, Chris Schwiegelshohn
2012 2012 Proceedings of the Fourteenth Workshop on Algorithm Engineering and Experiments (ALENEX)  
Given costs assigned to each substring from S, the Minimum String Cover (MSC) problem asks for a cover of minimum total cost.  ...  A string cover C of a set of strings S is a set of substrings from S such that every string in S can be written as a concatenation of the strings in C.  ...  In the basic Minimum String Cover (MSC) problem, we want to find a cover with minimal cardinality. In a more general version, we assign a costs to substrings and aim at a cover of minimal total cost.  ... 
doi:10.1137/1.9781611972924.8 dblp:conf/alenex/CanzarMRS12 fatcat:irvnjdjjbfabjh33zjnxu7ailm

COVERING A CIRCULAR STRING WITH SUBSTRINGS OF FIXED LENGTH

ART M. DUVAL, W.F. SMYTH
1996 International Journal of Foundations of Computer Science  
In this paper we consider the problem of determining the minimum cardinality of a set U k which guarantees that every circular string C(x) of length n k can be covered.  ...  m , where u k = jU k j and is the size of the alphabet on which the strings are de ned. The problem has application to DNA sequencing by hybridization using oligonucleotide probes.  ...  Clearly each such chip, or set of substrings, guarantees that every position in x is contained in a substring which matches one of the substrings on the chip: we say then that U k covers (or is a cover  ... 
doi:10.1142/s0129054196000075 fatcat:zfvdma7rcjd4tpxzg2m4nlowjm

Genomic Distances under Deletions and Insertions

Mark Marron, Krister M. Swenson, Bernard M.E. Moret
2004 Theoretical Computer Science  
As more and more genomes are sequenced, evolutionary biologists are becoming increasingly interested in evolution at the level of whole genomes, in scenarios in which the genome evolves through insertions  ...  In the mathematical model pioneered by Sankoff and others, a unichromosomal genome is represented by a signed permutation of a multi-set of genes; Hannenhalli and Pevzner showed that the edit distance  ...  This work is supported by the National Science Foundation under grants ACI 00-81404, DEB 01-20709, EIA 01-13095, EIA 01-21377, and EIA 02-03584.  ... 
doi:10.1016/j.tcs.2004.02.039 fatcat:6hjzacvhpbbmdbxzfyxmy2y3tu

Genomic Distances under Deletions and Insertions [chapter]

Mark Marron, Krister M. Swenson, Bernard M. E. Moret
2003 Lecture Notes in Computer Science  
As more and more genomes are sequenced, evolutionary biologists are becoming increasingly interested in evolution at the level of whole genomes, in scenarios in which the genome evolves through insertions  ...  In the mathematical model pioneered by Sankoff and others, a unichromosomal genome is represented by a signed permutation of a multi-set of genes; Hannenhalli and Pevzner showed that the edit distance  ...  This work is supported by the National Science Foundation under grants ACI 00-81404, DEB 01-20709, EIA 01-13095, EIA 01-21377, and EIA 02-03584.  ... 
doi:10.1007/3-540-45071-8_54 fatcat:tfee3g6jd5fjhdtifksjaqecma

Computing regularities in strings: A survey

W.F. Smyth
2013 European journal of combinatorics (Print)  
The aim of this survey is to provide insight into the sequential algorithms that have been proposed to compute exact "regularities" in strings; that is, covers (or quasiperiods), seeds, repetitions, runs  ...  After outlining and evaluating the algorithms that have been proposed for their computation, I suggest possibly productive future directions of research.  ...  It was shown further that the decision problem is a special case of the set cover problem, hence the minimum k-cover can be computed to within a logarithmic factor by an efficient greedy algorithm.  ... 
doi:10.1016/j.ejc.2012.07.010 fatcat:4vdmvekfpngu3csv4zbz5sa4jy

Implementing approximate regularities

M. Christodoulakis, C.S. Iliopoulos, Kunsoo Park, Jeong Seop Sim
2005 Mathematical and computer modelling  
We explore their similarities and differences and we implement algorithms for solving the smallest distance approximate period/cover/seed problem and the restricted smallest approximate period/cover/seed  ...  problem in polynomial time, under a variety of distance rules (the Hamming distance, the edit distance, and the weighted edit distance).  ...  Step 1 Step Restricted Smallest Approximate Period/Cover/Seed Problem Definition 5 Given a string x of length n, the Restricted Smallest Approximate Period/Cover/Seed problem is to find a substring  ... 
doi:10.1016/j.mcm.2005.09.013 fatcat:w2cxwl2jjvc7nc4a7mhm4skmoa

Memory efficient minimum substring partitioning

Yang Li, Pegah Kamousi, Fangqiu Han, Shengqi Yang, Xifeng Yan, Subhash Suri
2013 Proceedings of the VLDB Endowment  
We propose a disk-based partition method, called Minimum Substring Partitioning (MSP), to complete the task using less than 10 gigabytes memory, without runtime slowdown.  ...  By leveraging the overlaps among the k-mers (substring of length k), MSP achieves astonishing compression ratio: The total size of partitions is reduced from Θ(kn) to Θ(n), where n is the size of the short  ...  Here the p-substrings are sorted according to the percentage of k-mers they cover. The figure uses logarithm on both axes.  ... 
doi:10.14778/2535569.2448951 fatcat:qqjxkmuqcfexpjqcw4mhrca63m

Memory Efficient De Bruijn Graph Construction [article]

Yang Li, Pegah Kamousi, Fangqiu Han, Shengqi Yang, Xifeng Yan, Subhash Suri
2012 arXiv   pre-print
We propose a disk-based partition method, called Minimum Substring Partitioning (MSP), to complete the task using less than 10 gigabytes memory, without runtime slowdown.  ...  By leveraging the overlaps among the k-mers (substring of length k), MSP achieves astonishing compression ratio: The total size of partitions is reduced from Θ(kn) to Θ(n), where n is the size of the short  ...  In this study, we resort to another approach to bypass this problem. Definition 3 (Minimum Substring [20] ).  ... 
arXiv:1207.3532v1 fatcat:7f75zvbmofbfhann652zph2ztq

Approximate Periods of Strings [chapter]

Jeong Seop Sim, Kunsoo Park, Costas S. Iliopoulos, William F. Smyth
1999 Lecture Notes in Computer Science  
We consider three related problems, for two of which we derive polynomial-time algorithms; we then show that the third problem is NP-complete.  ...  The study of approximately periodic strings is relevant to diverse applications such as molecular biology, data compression, and computer-assisted music analysis.  ...  A two-dimensional variant of the covering problem was studied in [11, 14] , and minimum covering by substrings of a given length in [19] . • Seeds: Iliopoulos et al.  ... 
doi:10.1007/3-540-48452-3_10 fatcat:gvcnmruo5zdvja4yn3r6so4qb4

Approximate periods of strings

Jeong Seop Sim, Costas S. Iliopoulos, Kunsoo Park, W.F. Smyth
2001 Theoretical Computer Science  
We consider three related problems, for two of which we derive polynomial-time algorithms; we then show that the third problem is NP-complete.  ...  The study of approximately periodic strings is relevant to diverse applications such as molecular biology, data compression, and computer-assisted music analysis.  ...  A two-dimensional variant of the covering problem was studied in [11, 14] , and minimum covering by substrings of a given length in [19] . • Seeds: Iliopoulos et al.  ... 
doi:10.1016/s0304-3975(00)00365-0 fatcat:nf6c26kezralldevgqiophx66i

At the roots of dictionary compression: string attractors

Dominik Kempa, Nicola Prezza
2018 Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2018  
CCS CONCEPTS • Theory of computation → Data compression; Packing and covering problems; Problems, reductions and completeness; Cell probe models and lower bounds;  ...  In this paper, we show that these techniques are different solutions to the same, elegant, combinatorial problem: to find a small set of positions capturing all distinct text's substrings.  ...  ACKNOWLEDGMENTS We received useful suggestions from many people during the writeup of this paper.  ... 
doi:10.1145/3188745.3188814 dblp:conf/stoc/KempaP18 fatcat:pr67vs6oynhkdlcpbqcwrb5qmu
« Previous Showing results 1 — 15 out of 6,707 results