License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2023.2
URN: urn:nbn:de:0030-drops-179560
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17956/
Go to the corresponding LIPIcs Volume Portal

Asahiro, Yuichi ; Eto, Hiroshi ; Gong, Mingyang ; Jansson, Jesper ; Lin, Guohui ; Miyano, Eiji ; Ono, Hirotaka ; Tanaka, Shunichi

Approximation Algorithms for the Longest Run Subsequence Problem

pdf-format:
LIPIcs-CPM-2023-2.pdf (0.8 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{asahiro_et_al:LIPIcs.CPM.2023.2,
  author =	{Asahiro, Yuichi and Eto, Hiroshi and Gong, Mingyang and Jansson, Jesper and Lin, Guohui and Miyano, Eiji and Ono, Hirotaka and Tanaka, Shunichi},
  title =	{{Approximation Algorithms for the Longest Run Subsequence Problem}},
  booktitle =	{34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)},
  pages =	{2:1--2:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-276-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{259},
  editor =	{Bulteau, Laurent and Lipt\'{a}k, Zsuzsanna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17956},
  URN =		{urn:nbn:de:0030-drops-179560},
  doi =		{10.4230/LIPIcs.CPM.2023.2},
  annote =	{Keywords: Longest run subsequence problem, bounded occurrence, approximation algorithm}
}

Keywords: Longest run subsequence problem, bounded occurrence, approximation algorithm
Collection: 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)
Issue Date: 2023
Date of publication: 21.06.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI