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Approximation Algorithms for the Longest Run Subsequence Problem
Authors
Yuichi Asahiro 
,
Hiroshi Eto ,
Jesper Jansson ,
Guohui Lin ,
Eiji Miyano ,
Hirotaka Ono ,
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Volume:
34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Annual Symposium on Combinatorial Pattern Matching (CPM) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-06-21
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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.
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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
https://doi.org/10.4230/LIPIcs.CPM.2023.2
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.
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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