3 Search Results for "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)

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@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.2025.1
Representing Paths in Digraphs

Authors: Riccardo Dondi and Alexandru Popa

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
In this contribution we consider two combinatorial problems related to graph string matching, motivated by recent approaches in computational genomics. Given a DAG where each node is labeled by a symbol, the problems aim to find a path in the DAG whose nodes contain all (or the maximum number of) symbols of the alphabet. We introduce a decision problem, Σ-Representing Path, that asks whether there exists a path that contains all the symbols of the alphabet, and an optimization problem, called Maximum Representing Path, that asks for a path that contains the maximum number of symbols. We analyze the complexity of the problems, showing the NP-completeness of {Σ-Representing Path} when each symbol labels at most three nodes in the DAG, and showing the APX-hardness of Maximum Representing Path when each symbol labels at most two nodes in the DAG. We complement the first result by giving a polynomial-time algorithm for Σ-Representing Path when each symbol labels at most two nodes in the DAG. Then we investigate the parameterized complexity of the two problems when the DAG has a limited distance from a set of disjoint paths and we show that both problems are W[1]-hard for this parameter. We consider the approximation of Maximum Representing Path, giving an approximation algorithm of factor √OPT, where OPT is the value of an optimal solution of the problem. We also show that Maximum Representing Path cannot be approximated within factor e/(e-1) - α, for any constant α > 0, unless NP ⊆ DTIME(|V|^{O(log log |V|)}) (V is the set of nodes of the DAG).
Cite as

Riccardo Dondi and Alexandru Popa. Representing Paths in Digraphs. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dondi_et_al:LIPIcs.CPM.2025.1,
  author =	{Dondi, Riccardo and Popa, Alexandru},
  title =	{{Representing Paths in Digraphs}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{1:1--1:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.1},
  URN =		{urn:nbn:de:0030-drops-230954},
  doi =		{10.4230/LIPIcs.CPM.2025.1},
  annote =	{Keywords: Graph String Matching, Computational Complexity, Parameterized Complexity, Algorithms}
}
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)

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@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}
}
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