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Volume

LIPIcs, Volume 181

31st International Symposium on Algorithms and Computation (ISAAC 2020)

ISAAC 2020, December 14-18, 2020, Hong Kong, China (Virtual Conference)

Editors: Yixin Cao, Siu-Wing Cheng, and Minming Li

Document

DOI: 10.4230/DagRep.13.5.165

Computational Geometry (Dagstuhl Seminar 23221)

Authors: Siu-Wing Cheng, Maarten Löffler, Jeff M. Phillips, and Aleksandr Popov

Published in: Dagstuhl Reports, Volume 13, Issue 5 (2023)

Abstract

This report documents the program and the outcomes of the Dagstuhl Seminar 23221 "Computational Geometry". The seminar was held from May 29th to June 2nd, 2023, and 39 participants from various countries attended it, including two remote participants. Recent advances in computational geometry were presented and discussed, and new challenges were identified. This report collects the abstracts of the talks and the open problems presented at the seminar.

Cite as

Siu-Wing Cheng, Maarten Löffler, Jeff M. Phillips, and Aleksandr Popov. Computational Geometry (Dagstuhl Seminar 23221). In Dagstuhl Reports, Volume 13, Issue 5, pp. 165-181, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@Article{cheng_et_al:DagRep.13.5.165,
  author =	{Cheng, Siu-Wing and L\"{o}ffler, Maarten and Phillips, Jeff M. and Popov, Aleksandr},
  title =	{{Computational Geometry (Dagstuhl Seminar 23221)}},
  pages =	{165--181},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{5},
  editor =	{Cheng, Siu-Wing and L\"{o}ffler, Maarten and Phillips, Jeff M. and Popov, Aleksandr},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.5.165},
  URN =		{urn:nbn:de:0030-drops-193692},
  doi =		{10.4230/DagRep.13.5.165},
  annote =	{Keywords: Algorithms, Combinatorics, Geometric Computing, Reconfiguration, Uncertainty}
}

Document

Abstract

DOI: 10.4230/LIPIcs.WABI.2023.3

BATCH-SCAMPP: Scaling Phylogenetic Placement Methods to Place Many Sequences (Abstract)

Authors: Eleanor Wedell, Chengze Shen, and Tandy Warnow

Published in: LIPIcs, Volume 273, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)

Abstract

Phylogenetic placement is the problem of placing one or more query sequences into a phylogenetic "backbone" tree, which may be a maximum likelihood tree on a multiple sequence alignment for a single gene, a taxonomy with leaves labeled by sequences for a single gene [Nidhi Shah et al., 2021], or a species tree [Jiang et al., 2023]. When the backbone tree is a tree estimated on a single gene, the most accurate techniques for phylogenetic placement are likelihood-based, and can be computationally intensive when the backbone trees are large [Chu and Warnow, 2023]. Phylogenetic placement into gene trees occurs when updating existing gene trees with newly observed sequences, but can also be applied in the "bulk" context, where many sequences are placed at the same time into the backbone tree. For example, phylogenetic placement can be used to taxonomically characterize shotgun sequencing reads generated for an environmental sample in metagenomic analysis [Nidhi Shah et al., 2021; Barbera et al., 2019]. The two most well known maximum likelihood phylogenetic placement methods are pplacer [Chu and Warnow, 2023] and EPA-ng [Barbera et al., 2019]. Of these two, EPA-ng is optimized for scaling the number of query sequences and is capable of placing millions of sequences into phylogenetic trees of up to a few thousand sequences [Barbera et al., 2019], and achieves sublinear runtime in the number of query sequences (see Figure 2 from [Balaban et al., 2022]). Previously we introduced the SCAMPP framework [Wedell et al., 2022] to enable both pplacer and EPA-ng to perform phylogenetic placement into ultra-large backbone trees, and we demonstrated its utility for placing into backbone trees with up to 200,000 sequences. By using maximum likelihood methods pplacer or EPA-ng within the SCAMPP framework, the resulting placements are more accurate than with APPLES-2 [Balaban et al., 2022], with the most notable accuracy improvement for fragmentary sequences, and are computationally similar for single query sequence placement [Wedell et al., 2022]. However, SCAMPP was designed to incrementally update a large tree, one query sequence at a time, and was not optimized for the other uses of phylogenetic placement, where batch placement of many sequencing reads is required. Here we introduce BATCH-SCAMPP, a technique that improves scalability in both dimensions: the number of query sequences being placed into the backbone tree and the size of the backbone tree. Furthermore, BATCH-SCAMPP is specifically designed to improve EPA-ng’s scalability to large backbone trees. Although BATCH-SCAMPP is based on SCAMPP, it uses a substantially modified design in order to be able to take advantage of EPA-ng’s ability to place many query sequences efficiently. The BATCH-SCAMPP method operates by allowing the input set of query sequences to suggest and then vote on placement subtrees, thus enabling many query sequences to select the same placement subtree. We pair BATCH-SCAMPP with EPA-ng to explore the capability of this approach for scaling to many query sequences. We show that this combination of techniques (which we call BSCAMPP+EPA-ng, or BSCAMPP(e)) not only provides high accuracy and scalability to large backbone trees, matching that of SCAMPP used with EPA-ng (i.e., SCAMPP(e)), but also achieves the goal of scaling sublinearly in the number of query sequences. Moreover, it is much more scalable than EPA-ng and faster than SCAMPP+EPA-ng: when placing 10,000 sequences into a backbone tree of 50,000 leaves, EPA-ng is unable to run due to memory issues, SCAMPP+EPA-ng requires 1421 minutes, and BSCAMPP(e) places all sequences in 7 minutes (all given the same computational resources. Figure 1 gives an example of this performance advantage on the nt78 [Chu and Warnow, 2023] simulated dataset.

Cite as

Eleanor Wedell, Chengze Shen, and Tandy Warnow. BATCH-SCAMPP: Scaling Phylogenetic Placement Methods to Place Many Sequences (Abstract). In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 3:1-3:2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{wedell_et_al:LIPIcs.WABI.2023.3,
  author =	{Wedell, Eleanor and Shen, Chengze and Warnow, Tandy},
  title =	{{BATCH-SCAMPP: Scaling Phylogenetic Placement Methods to Place Many Sequences}},
  booktitle =	{23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)},
  pages =	{3:1--3:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-294-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{273},
  editor =	{Belazzougui, Djamal and Ouangraoua, A\"{i}da},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2023.3},
  URN =		{urn:nbn:de:0030-drops-186296},
  doi =		{10.4230/LIPIcs.WABI.2023.3},
  annote =	{Keywords: Phylogenetic Placement, EPA-ng, Phylogenetics}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.40

Approximate Nearest Neighbor for Polygonal Curves Under Fréchet Distance

Authors: Siu-Wing Cheng and Haoqiang Huang

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract

We propose κ-approximate nearest neighbor (ANN) data structures for n polygonal curves under the Fréchet distance in ℝ^d, where κ ∈ {1+ε,3+ε} and d ≥ 2. We assume that every input curve has at most m vertices, every query curve has at most k vertices, k ≪ m, and k is given for preprocessing. The query times are Õ(k(mn)^{0.5+ε}/ε^d+ k(d/ε)^O(dk)) for (1+ε)-ANN and Õ(k(mn)^{0.5+ε}/ε^d) for (3+ε)-ANN. The space and expected preprocessing time are Õ(k(mnd^d/ε^d)^O(k+1/ε²)) in both cases. In two and three dimensions, we improve the query times to O(1/ε)^O(k) ⋅ Õ(k) for (1+ε)-ANN and Õ(k) for (3+ε)-ANN. The space and expected preprocessing time improve to O(mn/ε)^O(k) ⋅ Õ(k) in both cases. For ease of presentation, we treat factors in our bounds that depend purely on d as O(1). The hidden polylog factors in the big-Õ notation have powers dependent on d.

Cite as

Siu-Wing Cheng and Haoqiang Huang. Approximate Nearest Neighbor for Polygonal Curves Under Fréchet Distance. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 40:1-40:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cheng_et_al:LIPIcs.ICALP.2023.40,
  author =	{Cheng, Siu-Wing and Huang, Haoqiang},
  title =	{{Approximate Nearest Neighbor for Polygonal Curves Under Fr\'{e}chet Distance}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{40:1--40:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.40},
  URN =		{urn:nbn:de:0030-drops-180929},
  doi =		{10.4230/LIPIcs.ICALP.2023.40},
  annote =	{Keywords: Polygonal curves, Fr\'{e}chet distance, approximate nearest neighbor}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2021.8

Self-Improving Voronoi Construction for a Hidden Mixture of Product Distributions

Authors: Siu-Wing Cheng and Man Ting Wong

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract

We propose a self-improving algorithm for computing Voronoi diagrams under a given convex distance function with constant description complexity. The n input points are drawn from a hidden mixture of product distributions; we are only given an upper bound m = o(√n) on the number of distributions in the mixture, and the property that for each distribution, an input instance is drawn from it with a probability of Ω(1/n). For any ε ∈ (0,1), after spending O(mn log^O(1)(mn) + m^ε n^(1+ε) log(mn)) time in a training phase, our algorithm achieves an O(1/ε n log m + 1/ε n 2^O(log^* n) + 1/ε H) expected running time with probability at least 1 - O(1/n), where H is the entropy of the distribution of the Voronoi diagram output. The expectation is taken over the input distribution and the randomized decisions of the algorithm. For the Euclidean metric, the expected running time improves to O(1/ε n log m + 1/ε H).

Cite as

Siu-Wing Cheng and Man Ting Wong. Self-Improving Voronoi Construction for a Hidden Mixture of Product Distributions. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 8:1-8:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cheng_et_al:LIPIcs.ISAAC.2021.8,
  author =	{Cheng, Siu-Wing and Wong, Man Ting},
  title =	{{Self-Improving Voronoi Construction for a Hidden Mixture of Product Distributions}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{8:1--8:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.8},
  URN =		{urn:nbn:de:0030-drops-154418},
  doi =		{10.4230/LIPIcs.ISAAC.2021.8},
  annote =	{Keywords: entropy, Voronoi diagram, convex distance function, hidden mixture of product distributions}
}

Document

DOI: 10.4230/DagRep.11.4.1

Computational Geometry (Dagstuhl Seminar 21181)

Authors: Siu-Wing Cheng, Anne Driemel, and Jeff M. Phillips

Published in: Dagstuhl Reports, Volume 11, Issue 4 (2021)

Abstract

This report documents the program and the outcomes of Dagstuhl Seminar 21181 "Computational Geometry". The seminar was held from May 2 to May 7, 2021. Because of COVID, the seminar was held online in a virtual manner, and 36 participants from various countries attended it. New advances and directions in computational geometry were presented and discussed. The report collects the abstracts of talks and open problems presented in the seminar.

Cite as

Siu-Wing Cheng, Anne Driemel, and Jeff M. Phillips. Computational Geometry (Dagstuhl Seminar 21181). In Dagstuhl Reports, Volume 11, Issue 4, pp. 1-19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@Article{cheng_et_al:DagRep.11.4.1,
  author =	{Cheng, Siu-Wing and Driemel, Anne and Phillips, Jeff M.},
  title =	{{Computational Geometry (Dagstuhl Seminar 21181)}},
  pages =	{1--19},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2021},
  volume =	{11},
  number =	{4},
  editor =	{Cheng, Siu-Wing and Driemel, Anne and Phillips, Jeff M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.11.4.1},
  URN =		{urn:nbn:de:0030-drops-147963},
  doi =		{10.4230/DagRep.11.4.1},
  annote =	{Keywords: algorithms, computational geometry, Computational topology, data structures, Discrete geometry}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.ISAAC.2020

LIPIcs, Volume 181, ISAAC 2020, Complete Volume

Authors: Yixin Cao, Siu-Wing Cheng, and Minming Li

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

LIPIcs, Volume 181, ISAAC 2020, Complete Volume

Cite as

Yixin Cao, Siu-Wing Cheng, and Minming Li. LIPIcs, Volume 181, ISAAC 2020, Complete Volume. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 1-1012, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@Proceedings{cao_et_al:LIPIcs.ISAAC.2020,
  title =	{{LIPIcs, Volume 181, ISAAC 2020, Complete Volume}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{1--1012},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020},
  URN =		{urn:nbn:de:0030-drops-133439},
  doi =		{10.4230/LIPIcs.ISAAC.2020},
  annote =	{Keywords: LIPIcs, Volume 181, ISAAC 2020, Complete Volume}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.ISAAC.2020.0

Front Matter, Table of Contents, Preface, Conference Organization

Authors: Yixin Cao, Siu-Wing Cheng, and Minming Li

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

Front Matter, Table of Contents, Preface, Conference Organization

Cite as

Yixin Cao, Siu-Wing Cheng, and Minming Li. Front Matter, Table of Contents, Preface, Conference Organization. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 0:i-0:xviii, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cao_et_al:LIPIcs.ISAAC.2020.0,
  author =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.0},
  URN =		{urn:nbn:de:0030-drops-133448},
  doi =		{10.4230/LIPIcs.ISAAC.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.ISAAC.2020.1

How to Decompose a Graph into a Tree-Like Structure (Invited Talk)

Authors: Sang-il Oum

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

Many NP-hard problems on graphs are known to be tractable if we restrict the input to have a certain decomposition into a tree-like structure. Width parameters of graphs are measures on how easy it is to decompose the input graph into a tree-like structure. The tree-width is one of the most well-studied width parameters of graphs and the rank-width is a generalization of tree-width into dense graphs. This talk will present a survey on width parameters of graphs such as tree-width and rank-width and discuss known algorithms to find a decomposition of an input graph into such tree-like structures efficiently.

Cite as

Sang-il Oum. How to Decompose a Graph into a Tree-Like Structure (Invited Talk). In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, p. 1:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{oum:LIPIcs.ISAAC.2020.1,
  author =	{Oum, Sang-il},
  title =	{{How to Decompose a Graph into a Tree-Like Structure}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.1},
  URN =		{urn:nbn:de:0030-drops-133458},
  doi =		{10.4230/LIPIcs.ISAAC.2020.1},
  annote =	{Keywords: tree-width, rank-width}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.ISAAC.2020.2

Worst-Case Optimal Join Algorithms (Invited Talk)

Authors: Ke Yi

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

Join is the most important operator in relational databases, and remains the most expensive one despite years of research and engineering efforts. Following the ground-breaking work of Atserias, Grohe, and Marx in 2008, worst-case optimal join algorithms have been discovered, which has led to not only a series of beautiful theoretical results, but also new database systems based on drastically different query evaluation techniques. In this talk, I will present an overview of this topic, including algorithms in various computation models (sequential and parallel), variants of the problem (full, Boolean, and counting), and approximate solutions.

Cite as

Ke Yi. Worst-Case Optimal Join Algorithms (Invited Talk). In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, p. 2:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{yi:LIPIcs.ISAAC.2020.2,
  author =	{Yi, Ke},
  title =	{{Worst-Case Optimal Join Algorithms}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.2},
  URN =		{urn:nbn:de:0030-drops-133462},
  doi =		{10.4230/LIPIcs.ISAAC.2020.2},
  annote =	{Keywords: query evaluation}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2020.3

(In)approximability of Maximum Minimal FVS

Authors: Louis Dublois, Tesshu Hanaka, Mehdi Khosravian Ghadikolaei, Michael Lampis, and Nikolaos Melissinos

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

We study the approximability of the NP-complete Maximum Minimal Feedback Vertex Set problem. Informally, this natural problem seems to lie in an intermediate space between two more well-studied problems of this type: Maximum Minimal Vertex Cover, for which the best achievable approximation ratio is √n, and Upper Dominating Set, which does not admit any n^{1-ε} approximation. We confirm and quantify this intuition by showing the first non-trivial polynomial time approximation for Max Min FVS with a ratio of O(n^{2/3}), as well as a matching hardness of approximation bound of n^{2/3-ε}, improving the previous known hardness of n^{1/2-ε}. Along the way, we also obtain an O(Δ)-approximation and show that this is asymptotically best possible, and we improve the bound for which the problem is NP-hard from Δ ≥ 9 to Δ ≥ 6. Having settled the problem’s approximability in polynomial time, we move to the context of super-polynomial time. We devise a generalization of our approximation algorithm which, for any desired approximation ratio r, produces an r-approximate solution in time n^O(n/r^{3/2}). This time-approximation trade-off is essentially tight: we show that under the ETH, for any ratio r and ε > 0, no algorithm can r-approximate this problem in time n^{O((n/r^{3/2})^{1-ε})}, hence we precisely characterize the approximability of the problem for the whole spectrum between polynomial and sub-exponential time, up to an arbitrarily small constant in the second exponent.

Cite as

Louis Dublois, Tesshu Hanaka, Mehdi Khosravian Ghadikolaei, Michael Lampis, and Nikolaos Melissinos. (In)approximability of Maximum Minimal FVS. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 3:1-3:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dublois_et_al:LIPIcs.ISAAC.2020.3,
  author =	{Dublois, Louis and Hanaka, Tesshu and Khosravian Ghadikolaei, Mehdi and Lampis, Michael and Melissinos, Nikolaos},
  title =	{{(In)approximability of Maximum Minimal FVS}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.3},
  URN =		{urn:nbn:de:0030-drops-133477},
  doi =		{10.4230/LIPIcs.ISAAC.2020.3},
  annote =	{Keywords: Approximation Algorithms, ETH, Inapproximability}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2020.4

A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem

Authors: Anadi Agrawal and Paweł Gawrychowski

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

The Longest Common Increasing Subsequence (LCIS) is a variant of the classical Longest Common Subsequence (LCS), in which we additionally require the common subsequence to be strictly increasing. While the well-known "Four Russians" technique can be used to find LCS in subquadratic time, it does not seem directly applicable to LCIS. Recently, Duraj [STACS 2020] used a completely different method based on the combinatorial properties of LCIS to design an 𝒪(n²(log log n)²/log^{1/6}n) time algorithm. We show that an approach based on exploiting tabulation (more involved than "Four Russians") can be used to construct an asymptotically faster 𝒪(n² log log n/√{log n}) time algorithm. As our solution avoids using the specific combinatorial properties of LCIS, it can be also adapted for the Longest Common Weakly Increasing Subsequence (LCWIS).

Cite as

Anadi Agrawal and Paweł Gawrychowski. A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 4:1-4:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{agrawal_et_al:LIPIcs.ISAAC.2020.4,
  author =	{Agrawal, Anadi and Gawrychowski, Pawe{\l}},
  title =	{{A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{4:1--4:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.4},
  URN =		{urn:nbn:de:0030-drops-133487},
  doi =		{10.4230/LIPIcs.ISAAC.2020.4},
  annote =	{Keywords: Longest Common Increasing Subsequence, Four Russians}
}

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DOI: 10.4230/LIPIcs.ISAAC.2020.5

A Unified Framework of FPT Approximation Algorithms for Clustering Problems

Authors: Qilong Feng, Zhen Zhang, Ziyun Huang, Jinhui Xu, and Jianxin Wang

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

In this paper, we present a framework for designing FPT approximation algorithms for many k-clustering problems. Our results are based on a new technique for reducing search spaces. A reduced search space is a small subset of the input data that has the guarantee of containing k clients close to the facilities opened in an optimal solution for any clustering problem we consider. We show, somewhat surprisingly, that greedily sampling O(k) clients yields the desired reduced search space, based on which we obtain FPT(k)-time algorithms with improved approximation guarantees for problems such as capacitated clustering, lower-bounded clustering, clustering with service installation costs, fault tolerant clustering, and priority clustering.

Cite as

Qilong Feng, Zhen Zhang, Ziyun Huang, Jinhui Xu, and Jianxin Wang. A Unified Framework of FPT Approximation Algorithms for Clustering Problems. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 5:1-5:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{feng_et_al:LIPIcs.ISAAC.2020.5,
  author =	{Feng, Qilong and Zhang, Zhen and Huang, Ziyun and Xu, Jinhui and Wang, Jianxin},
  title =	{{A Unified Framework of FPT Approximation Algorithms for Clustering Problems}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{5:1--5:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.5},
  URN =		{urn:nbn:de:0030-drops-133495},
  doi =		{10.4230/LIPIcs.ISAAC.2020.5},
  annote =	{Keywords: clustering, approximation algorithms, fixed-parameter tractability}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2020.6

A Reduction of the Dynamic Time Warping Distance to the Longest Increasing Subsequence Length

Authors: Yoshifumi Sakai and Shunsuke Inenaga

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

The similarity between a pair of time series, i.e., sequences of indexed values in time order, is often estimated by the dynamic time warping (DTW) distance, instead of any in the well-studied family of measures including the longest common subsequence (LCS) length and the edit distance. Although it may seem as if the DTW and the LCS(-like) measures are essentially different, we reveal that the DTW distance can be represented by the longest increasing subsequence (LIS) length of a sequence of integers, which is the LCS length between the integer sequence and itself sorted. For a given pair of time series of n integers between zero and c, we propose an integer sequence that represents any substring-substring DTW distance as its band-substring LIS length. The length of the produced integer sequence is O(c⁴ n²) or O(c² n²) depending on the variant of the DTW distance used, both of which can be translated to O(n²) for constant cost functions. To demonstrate that techniques developed under the LCS(-like) measures are directly applicable to analysis of time series via our reduction of DTW to LIS, we present time-efficient algorithms for DTW-related problems utilizing the semi-local sequence comparison technique developed for LCS-related problems.

Cite as

Yoshifumi Sakai and Shunsuke Inenaga. A Reduction of the Dynamic Time Warping Distance to the Longest Increasing Subsequence Length. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 6:1-6:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{sakai_et_al:LIPIcs.ISAAC.2020.6,
  author =	{Sakai, Yoshifumi and Inenaga, Shunsuke},
  title =	{{A Reduction of the Dynamic Time Warping Distance to the Longest Increasing Subsequence Length}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.6},
  URN =		{urn:nbn:de:0030-drops-133508},
  doi =		{10.4230/LIPIcs.ISAAC.2020.6},
  annote =	{Keywords: algorithms, dynamic time warping distance, longest increasing subsequence, semi-local sequence comparison}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2020.7

Algorithms and Complexity for Geodetic Sets on Planar and Chordal Graphs

Authors: Dibyayan Chakraborty, Sandip Das, Florent Foucaud, Harmender Gahlawat, Dimitri Lajou, and Bodhayan Roy

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

We study the complexity of finding the geodetic number on subclasses of planar graphs and chordal graphs. A set S of vertices of a graph G is a geodetic set if every vertex of G lies in a shortest path between some pair of vertices of S. The Minimum Geodetic Set (MGS) problem is to find a geodetic set with minimum cardinality of a given graph. The problem is known to remain NP-hard on bipartite graphs, chordal graphs, planar graphs and subcubic graphs. We first study MGS on restricted classes of planar graphs: we design a linear-time algorithm for MGS on solid grids, improving on a 3-approximation algorithm by Chakraborty et al. (CALDAM, 2020) and show that MGS remains NP-hard even for subcubic partial grids of arbitrary girth. This unifies some results in the literature. We then turn our attention to chordal graphs, showing that MGS is fixed parameter tractable for inputs of this class when parameterized by their treewidth (which equals the clique number minus one). This implies a linear-time algorithm for k-trees, for fixed k. Then, we show that MGS is NP-hard on interval graphs, thereby answering a question of Ekim et al. (LATIN, 2012). As interval graphs are very constrained, to prove the latter result we design a rather sophisticated reduction technique to work around their inherent linear structure.

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Dibyayan Chakraborty, Sandip Das, Florent Foucaud, Harmender Gahlawat, Dimitri Lajou, and Bodhayan Roy. Algorithms and Complexity for Geodetic Sets on Planar and Chordal Graphs. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 7:1-7:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{chakraborty_et_al:LIPIcs.ISAAC.2020.7,
  author =	{Chakraborty, Dibyayan and Das, Sandip and Foucaud, Florent and Gahlawat, Harmender and Lajou, Dimitri and Roy, Bodhayan},
  title =	{{Algorithms and Complexity for Geodetic Sets on Planar and Chordal Graphs}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.7},
  URN =		{urn:nbn:de:0030-drops-133516},
  doi =		{10.4230/LIPIcs.ISAAC.2020.7},
  annote =	{Keywords: Geodetic set, Planar graph, Chordal graph, Interval graph, FPT algorithm}
}

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