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Approximation Algorithms for the Longest Run Subsequence Problem

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

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Longest run subsequence problem
  • bounded occurrence
  • approximation algorithm

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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.

Cite As Get BibTex

Yuichi Asahiro, Hiroshi Eto, Mingyang Gong, Jesper Jansson, Guohui Lin, Eiji Miyano, Hirotaka Ono, and Shunichi Tanaka. Approximation Algorithms for the Longest Run Subsequence Problem. In 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 259, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CPM.2023.2

Author Details

Yuichi Asahiro
  • Kyushu Sangyo University, Fukuoka, Japan
Hiroshi Eto
  • Kyushu Institute of Technology, Iizuka, Japan
Mingyang Gong
  • Uniersity of Alberta, Edmonton, Canada
Jesper Jansson
  • Kyoto University, Kyoto, Japan
Guohui Lin
  • Uniersity of Alberta, Edmonton, Canada
Eiji Miyano
  • Kyushu Institute of Technology, Iizuka, Japan
Hirotaka Ono
  • Nagoya University, Nagoya, Japan
Shunichi Tanaka
  • Kyushu Institute of Technology, Iizuka, Japan

Funding

This work is partially supported by NSERC Canada, and JSPS KAKENHI Grant Numbers JP17K00024, JP20H05967, JP21K11755, JP21K19765, JP22H00513, JP22H03550, and JP22K11915.

Acknowledgements

The authors would like to thank the anonymous reviewers for their suggestions and detailed comments that helped to improve the presentation of the paper.

References

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