eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-06-21
2:1
2:12
10.4230/LIPIcs.CPM.2023.2
article
Approximation Algorithms for the Longest Run Subsequence Problem
Asahiro, Yuichi
1
https://orcid.org/0000-0002-9801-3285
Eto, Hiroshi
2
https://orcid.org/0000-0003-1456-1987
Gong, Mingyang
3
Jansson, Jesper
4
https://orcid.org/0000-0001-6859-8932
Lin, Guohui
3
https://orcid.org/0000-0003-4283-3396
Miyano, Eiji
2
https://orcid.org/0000-0002-4260-7818
Ono, Hirotaka
5
https://orcid.org/0000-0003-0845-3947
Tanaka, Shunichi
2
Kyushu Sangyo University, Fukuoka, Japan
Kyushu Institute of Technology, Iizuka, Japan
Uniersity of Alberta, Edmonton, Canada
Kyoto University, Kyoto, Japan
Nagoya University, Nagoya, Japan
We study the approximability of the Longest Run Subsequence problem (LRS for short). For a string S = s_1 ⋯ s_n over an alphabet Σ, a run of a symbol σ ∈ Σ in S is a maximal substring of consecutive occurrences of σ. A run subsequence S' of S is a sequence in which every symbol σ ∈ Σ occurs in at most one run. Given a string S, the goal of LRS is to find a longest run subsequence S^* of S such that the length |S^*| is maximized over all the run subsequences of S. It is known that LRS is APX-hard even if each symbol has at most two occurrences in the input string, and that LRS admits a polynomial-time k-approximation algorithm if the number of occurrences of every symbol in the input string is bounded by k. In this paper, we design a polynomial-time (k+1)/2-approximation algorithm for LRS under the k-occurrence constraint on input strings. For the case k = 2, we further improve the approximation ratio from 3/2 to 4/3.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol259-cpm2023/LIPIcs.CPM.2023.2/LIPIcs.CPM.2023.2.pdf
Longest run subsequence problem
bounded occurrence
approximation algorithm