73 Search Results for "Li, Minming"


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
Dynamic Maximal Matching in Clique Networks

Authors: Minming Li, Peter Robinson, and Xianbin Zhu

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
We consider the problem of computing a maximal matching with a distributed algorithm in the presence of batch-dynamic changes to the graph topology. We assume that a graph of n nodes is vertex-partitioned among k players that communicate via message passing. Our goal is to provide an efficient algorithm that quickly updates the matching even if an adversary determines batches of 𝓁 edge insertions or deletions. We first show a lower bound of Ω((𝓁 log k)/(k²log n)) rounds for recomputing a matching assuming an oblivious adversary who is unaware of the initial (random) vertex partition as well as the current state of the players, and a stronger lower bound of Ω(𝓁/(klog n)) rounds against an adaptive adversary, who may choose any balanced (but not necessarily random) vertex partition initially and who knows the current state of the players. We also present a randomized algorithm that has an initialization time of O(n/(k log n)) rounds, while achieving an update time that that is independent of n: In more detail, the update time is O(⌈𝓁/k⌉ log k) against an oblivious adversary, who must fix all updates in advance. If we consider the stronger adaptive adversary, the update time becomes O (⌈𝓁/√k⌉ log k) rounds.

Cite as

Minming Li, Peter Robinson, and Xianbin Zhu. Dynamic Maximal Matching in Clique Networks. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 73:1-73:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{li_et_al:LIPIcs.ITCS.2024.73,
  author =	{Li, Minming and Robinson, Peter and Zhu, Xianbin},
  title =	{{Dynamic Maximal Matching in Clique Networks}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{73:1--73:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.73},
  URN =		{urn:nbn:de:0030-drops-196017},
  doi =		{10.4230/LIPIcs.ITCS.2024.73},
  annote =	{Keywords: distributed graph algorithm, dynamic network, maximal matching, randomized algorithm, lower bound}
}
Document
Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings

Authors: Christoph Damerius, Peter Kling, Minming Li, Chenyang Xu, and Ruilong Zhang

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
Scheduling with testing falls under the umbrella of the research on optimization with explorable uncertainty. In this model, each job has an upper limit on its processing time that can be decreased to a lower limit (possibly unknown) by some preliminary action (testing). Recently, [Christoph Dürr et al., 2020] has studied a setting where testing a job takes a unit time, and the goal is to minimize total completion time or makespan on a single machine. In this paper, we extend their problem to the budget setting in which each test consumes a job-specific cost, and we require that the total testing cost cannot exceed a given budget. We consider the offline variant (the lower processing time is known) and the oblivious variant (the lower processing time is unknown) and aim to minimize the total completion time or makespan on a single machine. For the total completion time objective, we show NP-hardness and derive a PTAS for the offline variant based on a novel LP rounding scheme. We give a (4+ε)-competitive algorithm for the oblivious variant based on a framework inspired by the worst-case lower-bound instance. For the makespan objective, we give an FPTAS for the offline variant and a (2+ε)-competitive algorithm for the oblivious variant. Our algorithms for the oblivious variants under both objectives run in time 𝒪(poly(n/ε)). Lastly, we show that our results are essentially optimal by providing matching lower bounds.

Cite as

Christoph Damerius, Peter Kling, Minming Li, Chenyang Xu, and Ruilong Zhang. Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 38:1-38:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{damerius_et_al:LIPIcs.ESA.2023.38,
  author =	{Damerius, Christoph and Kling, Peter and Li, Minming and Xu, Chenyang and Zhang, Ruilong},
  title =	{{Scheduling with a Limited Testing Budget: Tight Results for the Offline and Oblivious Settings}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{38:1--38:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.38},
  URN =		{urn:nbn:de:0030-drops-186915},
  doi =		{10.4230/LIPIcs.ESA.2023.38},
  annote =	{Keywords: scheduling, total completion time, makespan, LP rounding, competitive analysis, approximation algorithm, NP hardness, PTAS}
}
Document
Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs

Authors: Enze Sun, Zonghan Yang, and Yuhao Zhang

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
We consider the Online Rent Minimization problem, where online jobs with release times, deadlines, and processing times must be scheduled on machines that can be rented for a fixed length period of T. The objective is to minimize the number of machine rents. This problem generalizes the Online Machine Minimization problem where machines can be rented for an infinite period, and both problems have an asymptotically optimal competitive ratio of O(log(p_max/p_min)) for general processing times, where p_max and p_min are the maximum and minimum processing times respectively. However, for small values of p_max/p_min, a better competitive ratio can be achieved by assuming unit-size jobs. Under this assumption, Devanur et al. (2014) gave an optimal e-competitive algorithm for Online Machine Minimization, and Chen and Zhang (2022) gave a (3e+7) ≈ 15.16-competitive algorithm for Online Rent Minimization. In this paper, we significantly improve the competitive ratio of the Online Rent Minimization problem under unit size to 6, by using a clean oracle-based online algorithm framework.

Cite as

Enze Sun, Zonghan Yang, and Yuhao Zhang. Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 97:1-97:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{sun_et_al:LIPIcs.ESA.2023.97,
  author =	{Sun, Enze and Yang, Zonghan and Zhang, Yuhao},
  title =	{{Improved Algorithms for Online Rent Minimization Problem Under Unit-Size Jobs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{97:1--97:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.97},
  URN =		{urn:nbn:de:0030-drops-187500},
  doi =		{10.4230/LIPIcs.ESA.2023.97},
  annote =	{Keywords: Online Algorithm, Scheduling, Machine Minimization, Rent Minimization}
}
Document
Complete Volume
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

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-dev.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
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

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-dev.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
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-dev.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
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-dev.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
(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-dev.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
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-dev.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}
}
Document
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-dev.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
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-dev.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
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.

Cite as

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)


Copy BibTex To Clipboard

@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-dev.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}
}
Document
An SPQR-Tree-Like Embedding Representation for Level Planarity

Authors: Guido Brückner and Ignaz Rutter

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


Abstract
An SPQR-tree is a data structure that efficiently represents all planar embeddings of a biconnected planar graph. It is a key tool in a number of constrained planarity testing algorithms, which seek a planar embedding of a graph subject to some given set of constraints. We develop an SPQR-tree-like data structure that represents all level-planar embeddings of a biconnected level graph with a single source, called the LP-tree, and give a simple algorithm to compute it in linear time. Moreover, we show that LP-trees can be used to adapt three constrained planarity algorithms to the level-planar case by using them as a drop-in replacement for SPQR-trees.

Cite as

Guido Brückner and Ignaz Rutter. An SPQR-Tree-Like Embedding Representation for Level Planarity. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{bruckner_et_al:LIPIcs.ISAAC.2020.8,
  author =	{Br\"{u}ckner, Guido and Rutter, Ignaz},
  title =	{{An SPQR-Tree-Like Embedding Representation for Level Planarity}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{8:1--8:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.8},
  URN =		{urn:nbn:de:0030-drops-133526},
  doi =		{10.4230/LIPIcs.ISAAC.2020.8},
  annote =	{Keywords: SPQR-tree, Level planarity, Partial drawings, Simultaneous drawings}
}
Document
Approximating the Packedness of Polygonal Curves

Authors: Joachim Gudmundsson, Yuan Sha, and Sampson Wong

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


Abstract
In 2012 Driemel et al. [Anne Driemel et al., 2012] introduced the concept of c-packed curves as a realistic input model. In the case when c is a constant they gave a near linear time (1+ε)-approximation algorithm for computing the Fréchet distance between two c-packed polygonal curves. Since then a number of papers have used the model. In this paper we consider the problem of computing the smallest c for which a given polygonal curve in ℝ^d is c-packed. We present two approximation algorithms. The first algorithm is a 2-approximation algorithm and runs in O(dn² log n) time. In the case d = 2 we develop a faster algorithm that returns a (6+ε)-approximation and runs in O((n/ε³)^{4/3} polylog (n/ε))) time. We also implemented the first algorithm and computed the approximate packedness-value for 16 sets of real-world trajectories. The experiments indicate that the notion of c-packedness is a useful realistic input model for many curves and trajectories.

Cite as

Joachim Gudmundsson, Yuan Sha, and Sampson Wong. Approximating the Packedness of Polygonal Curves. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{gudmundsson_et_al:LIPIcs.ISAAC.2020.9,
  author =	{Gudmundsson, Joachim and Sha, Yuan and Wong, Sampson},
  title =	{{Approximating the Packedness of Polygonal Curves}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{9:1--9:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.9},
  URN =		{urn:nbn:de:0030-drops-133530},
  doi =		{10.4230/LIPIcs.ISAAC.2020.9},
  annote =	{Keywords: Computational geometry, trajectories, realistic input models}
}
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