TY - GEN
T1 - Exact Algorithms for the Bounded Repetition Longest Common Subsequence Problem
AU - Asahiro, Yuichi
AU - Jansson, Jesper Andreas
AU - Lin, Guohui
AU - Miyano, Eiji
AU - Ono, Hirotaka
AU - Utashima, Tadatoshi
PY - 2019/1/1
Y1 - 2019/1/1
N2 - In this paper, we study exact, exponential-time algorithms for a variant of the classic Longest Common Subsequence problem called the r-Repetition Longest Common Subsequence problem (or r-RLCS, for short): Given two sequences X and Y over an alphabet S, find a longest common subsequence of X and Y such that each symbol appears at most r times in the obtained subsequence. Without loss of generality, we will assume that from here on. The special case of 1-RLCS, also known as the Repetition-Free Longest Common Subsequence problem (RFLCS), has been studied previously; e.g., in [1], Adi et al. presented an (exponential-time) integer linear programming-based exact algorithm for 1-RLCS. However, they did not analyze its time complexity, and to the best of our knowledge, there are no previous results on the running times of any exact algorithms for this problem. In this paper, we first propose a simple algorithm for 1-RLCS based on the strategy used in [1] and show explicitly that its running time is bounded by. Next, we provide a DP-based algorithm for r-RLCS and prove that its running time is for any. In particular, our new algorithm runs in time for 1-RLCS, which is faster than the previous one.
AB - In this paper, we study exact, exponential-time algorithms for a variant of the classic Longest Common Subsequence problem called the r-Repetition Longest Common Subsequence problem (or r-RLCS, for short): Given two sequences X and Y over an alphabet S, find a longest common subsequence of X and Y such that each symbol appears at most r times in the obtained subsequence. Without loss of generality, we will assume that from here on. The special case of 1-RLCS, also known as the Repetition-Free Longest Common Subsequence problem (RFLCS), has been studied previously; e.g., in [1], Adi et al. presented an (exponential-time) integer linear programming-based exact algorithm for 1-RLCS. However, they did not analyze its time complexity, and to the best of our knowledge, there are no previous results on the running times of any exact algorithms for this problem. In this paper, we first propose a simple algorithm for 1-RLCS based on the strategy used in [1] and show explicitly that its running time is bounded by. Next, we provide a DP-based algorithm for r-RLCS and prove that its running time is for any. In particular, our new algorithm runs in time for 1-RLCS, which is faster than the previous one.
UR - http://www.scopus.com/inward/record.url?scp=85078537609&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-36412-0_1
DO - 10.1007/978-3-030-36412-0_1
M3 - Conference article published in proceeding or book
AN - SCOPUS:85078537609
SN - 9783030364113
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 1
EP - 12
BT - Combinatorial Optimization and Applications - 13th International Conference, COCOA 2019, Proceedings
A2 - Li, Yingshu
A2 - Cardei, Mihaela
A2 - Huang, Yan
PB - Springer
T2 - 13th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2019
Y2 - 13 December 2019 through 15 December 2019
ER -