Abstract
In Discrete Applied Mathematics 2010, Adi et al. introduce and study a variant of the well known Longest Common Subsequence problem, named Repetition Free Longest Common Subsequence (RFLCS). In RFLCS the input consists of two strings A and B over an alphabet Σ and the goal is to find the longest common subsequence containing only distinct characters from Σ. Adi et al. prove that the problem is APX -hard and show three approximation algorithms. Castelli et al. (Operations Research Letters 2013) propose a heuristic genetic algorithm and Blum and Blesa introduce metaheuristic algorithms (International Conference on Artificial Evolution 2013 and Evolutionary Computation in Combinatorial Optimization 2016). In this paper we design and test several new heuristic algorithms for RFLCS. The first algorithm, uses dynamic programming and in our testing setup outperforms the algorithms of Adi et al. The second heuristic algorithm improves upon the first and becomes comparable to the state-of-the-art algorithms of Blum and Blesa. The third algorithm transforms the RFLCS instance into an instance of the Maximum Independent Set (MIS) problem with the same value of the optimum solution. Then, we apply known algorithms for the MIS problem. We also augment one of the approximation algorithms of Adi et al. and we prove that we achieve an approximation of factor (Formula presented). Finally, we introduce a new variant of the LCS problem, named Multiset Restricted Common Subsequence (MRCS), that is a generalization of RFLCS. We present an exact polynomial time algorithm for MRCS for constant size alphabet. Additionally, we show that MRCS admits a (Formula presented) approximation.
| Original language | English |
|---|---|
| Title of host publication | String Processing and Information Retrieval - 25th International Symposium, SPIRE 2018, Proceedings |
| Editors | Travis Gagie, Alistair Moffat, Gonzalo Navarro, Ernesto Cuadros-Vargas |
| Publisher | Springer Verlag |
| Pages | 297-310 |
| Number of pages | 14 |
| ISBN (Print) | 9783030004781 |
| DOIs | |
| Publication status | Published - Jan 1 2018 |
| Event | 25th International Symposium on String Processing and Information Retrieval, SPIRE 2018 - Lima, Peru Duration: Oct 9 2018 → Oct 11 2018 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 11147 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Other
| Other | 25th International Symposium on String Processing and Information Retrieval, SPIRE 2018 |
|---|---|
| Country | Peru |
| City | Lima |
| Period | 10/9/18 → 10/11/18 |
Fingerprint
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)
Cite this
Better heuristic algorithms for the repetition free LCS and other variants. / Mincu, Radu Stefan; Popa, Alexandru.
String Processing and Information Retrieval - 25th International Symposium, SPIRE 2018, Proceedings. ed. / Travis Gagie; Alistair Moffat; Gonzalo Navarro; Ernesto Cuadros-Vargas. Springer Verlag, 2018. p. 297-310 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11147 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Better heuristic algorithms for the repetition free LCS and other variants
AU - Mincu, Radu Stefan
AU - Popa, Alexandru
PY - 2018/1/1
Y1 - 2018/1/1
N2 - In Discrete Applied Mathematics 2010, Adi et al. introduce and study a variant of the well known Longest Common Subsequence problem, named Repetition Free Longest Common Subsequence (RFLCS). In RFLCS the input consists of two strings A and B over an alphabet Σ and the goal is to find the longest common subsequence containing only distinct characters from Σ. Adi et al. prove that the problem is APX -hard and show three approximation algorithms. Castelli et al. (Operations Research Letters 2013) propose a heuristic genetic algorithm and Blum and Blesa introduce metaheuristic algorithms (International Conference on Artificial Evolution 2013 and Evolutionary Computation in Combinatorial Optimization 2016). In this paper we design and test several new heuristic algorithms for RFLCS. The first algorithm, uses dynamic programming and in our testing setup outperforms the algorithms of Adi et al. The second heuristic algorithm improves upon the first and becomes comparable to the state-of-the-art algorithms of Blum and Blesa. The third algorithm transforms the RFLCS instance into an instance of the Maximum Independent Set (MIS) problem with the same value of the optimum solution. Then, we apply known algorithms for the MIS problem. We also augment one of the approximation algorithms of Adi et al. and we prove that we achieve an approximation of factor (Formula presented). Finally, we introduce a new variant of the LCS problem, named Multiset Restricted Common Subsequence (MRCS), that is a generalization of RFLCS. We present an exact polynomial time algorithm for MRCS for constant size alphabet. Additionally, we show that MRCS admits a (Formula presented) approximation.
AB - In Discrete Applied Mathematics 2010, Adi et al. introduce and study a variant of the well known Longest Common Subsequence problem, named Repetition Free Longest Common Subsequence (RFLCS). In RFLCS the input consists of two strings A and B over an alphabet Σ and the goal is to find the longest common subsequence containing only distinct characters from Σ. Adi et al. prove that the problem is APX -hard and show three approximation algorithms. Castelli et al. (Operations Research Letters 2013) propose a heuristic genetic algorithm and Blum and Blesa introduce metaheuristic algorithms (International Conference on Artificial Evolution 2013 and Evolutionary Computation in Combinatorial Optimization 2016). In this paper we design and test several new heuristic algorithms for RFLCS. The first algorithm, uses dynamic programming and in our testing setup outperforms the algorithms of Adi et al. The second heuristic algorithm improves upon the first and becomes comparable to the state-of-the-art algorithms of Blum and Blesa. The third algorithm transforms the RFLCS instance into an instance of the Maximum Independent Set (MIS) problem with the same value of the optimum solution. Then, we apply known algorithms for the MIS problem. We also augment one of the approximation algorithms of Adi et al. and we prove that we achieve an approximation of factor (Formula presented). Finally, we introduce a new variant of the LCS problem, named Multiset Restricted Common Subsequence (MRCS), that is a generalization of RFLCS. We present an exact polynomial time algorithm for MRCS for constant size alphabet. Additionally, we show that MRCS admits a (Formula presented) approximation.
UR - http://www.scopus.com/inward/record.url?scp=85054885077&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85054885077&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-00479-8_24
DO - 10.1007/978-3-030-00479-8_24
M3 - Conference contribution
AN - SCOPUS:85054885077
SN - 9783030004781
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 297
EP - 310
BT - String Processing and Information Retrieval - 25th International Symposium, SPIRE 2018, Proceedings
A2 - Gagie, Travis
A2 - Moffat, Alistair
A2 - Navarro, Gonzalo
A2 - Cuadros-Vargas, Ernesto
PB - Springer Verlag
ER -