Search Results

Documents authored by Tanaka, Shunichi

Document
DOI: 10.4230/LIPIcs.WABI.2025.3
Approximability of Longest Run Subsequence and Complementary Minimization Problems

Authors: Yuichi Asahiro, Mingyang Gong, Jesper Jansson, Guohui Lin, Sichen Lu, Eiji Miyano, Hirotaka Ono, Toshiki Saitoh, and Shunichi Tanaka

Published in: LIPIcs, Volume 344, 25th International Conference on Algorithms for Bioinformatics (WABI 2025)

Abstract
We study the polynomial-time approximability of the Longest Run Subsequence problem (LRS for short) and its complementary minimization variant Minimum Run Subsequence Deletion problem (MRSD for short). For a string S = s₁ ⋯ s_n over an alphabet Σ, a subsequence S' of S is S' = s_{i₁} ⋯ s_{i_p}, such that 1 ≤ i₁ < i₂ < … < i_p ≤ |S|. 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 subsequence of S in which every symbol σ ∈ Σ occurs in at most one run. The co-subsequence ̅{S'} of the subsequence S' = s_{i₁} ⋯ s_{i_p} in S is the subsequence obtained by deleting all the characters in S' from S, i.e., ̅{S'} = s_{j₁} ⋯ s_{j_{n-p}} such that j₁ < j₂ < … < j_{n-p} and {j₁, …, j_{n-p}} = {1, …, n}⧵ {i₁, …, i_p}. Given a string S, the goal of LRS (resp., MRSD) is to find a run subsequence S^* of S such that the length |S^*| is maximized (resp., the number | ̅{S^*}| of deleted symbols from S is minimized) over all the run subsequences of S. Let k be the maximum number of symbol occurrences in the input S. It is known that LRS and MRSD are APX-hard even if k = 2. In this paper, we show that LRS can be approximated in polynomial time within factors of (k+2)/3 for k = 2 or 3, and 2(k+1)/5 for every k ≥ 4. Furthermore, we show that MRSD can be approximated in linear time within a factor of (k+4)/4 if k is even and (k+3)/4 if k is odd.
Cite as

Yuichi Asahiro, Mingyang Gong, Jesper Jansson, Guohui Lin, Sichen Lu, Eiji Miyano, Hirotaka Ono, Toshiki Saitoh, and Shunichi Tanaka. Approximability of Longest Run Subsequence and Complementary Minimization Problems. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{asahiro_et_al:LIPIcs.WABI.2025.3,
  author =	{Asahiro, Yuichi and Gong, Mingyang and Jansson, Jesper and Lin, Guohui and Lu, Sichen and Miyano, Eiji and Ono, Hirotaka and Saitoh, Toshiki and Tanaka, Shunichi},
  title =	{{Approximability of Longest Run Subsequence and Complementary Minimization Problems}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.3},
  URN =		{urn:nbn:de:0030-drops-239290},
  doi =		{10.4230/LIPIcs.WABI.2025.3},
  annote =	{Keywords: Longest run subsequence, minimum run subsequence deletion, approximation algorithm}
}
Document
DOI: 10.4230/LIPIcs.CPM.2023.2
Approximation Algorithms for the Longest Run Subsequence Problem

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

Published in: LIPIcs, Volume 259, 34th Annual Symposium on Combinatorial Pattern Matching (CPM 2023)

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

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)

Copy BibTex To Clipboard

@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/entities/document/10.4230/LIPIcs.CPM.2023.2},
  URN =		{urn:nbn:de:0030-drops-179560},
  doi =		{10.4230/LIPIcs.CPM.2023.2},
  annote =	{Keywords: Longest run subsequence problem, bounded occurrence, approximation algorithm}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact