4 Search Results for "Revsb�k, Morten"

Document
DOI: 10.4230/LIPIcs.SWAT.2020.6
Sea-Rise Flooding on Massive Dynamic Terrains

Authors: Lars Arge, Mathias Rav, Morten Revsbæk, Yujin Shin, and Jungwoo Yang

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
Predicting floods caused by storm surges is a crucial task. Since the rise of ocean water can create floods that extend far onto land, the flood damage can be severe. By developing efficient flood prediction algorithms that use very detailed terrain models and accurate sea-level forecasts, users can plan mitigations such as flood walls and gates to minimize the damage from storm surge flooding. In this paper we present a data structure for predicting floods from dynamic sea-level forecast data on dynamic massive terrains. The forecast data is dynamic in the sense that new forecasts are released several times per day; the terrain is dynamic in the sense that the terrain model may be updated to plan flood mitigations. Since accurate flood risk computations require using very detailed terrain models, and such terrain models can easily exceed the size of the main memory in a regular computer, our data structure is I/O-efficient, that is, it minimizes the number of I/Os (i.e. block transfers) between main memory and disk. For a terrain represented as a raster of N cells, it can be constructed using O(N/B log_M/B N/B) I/Os, it can compute the flood risk in a given small region using O(log_B N) I/Os, and it can handle updating the terrain elevation in a given small region using O(log²_B N) I/Os, where B is the block size and M is the capacity of main memory.
Cite as

Lars Arge, Mathias Rav, Morten Revsbæk, Yujin Shin, and Jungwoo Yang. Sea-Rise Flooding on Massive Dynamic Terrains. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{arge_et_al:LIPIcs.SWAT.2020.6,
  author =	{Arge, Lars and Rav, Mathias and Revsb{\ae}k, Morten and Shin, Yujin and Yang, Jungwoo},
  title =	{{Sea-Rise Flooding on Massive Dynamic Terrains}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.6},
  URN =		{urn:nbn:de:0030-drops-122539},
  doi =		{10.4230/LIPIcs.SWAT.2020.6},
  annote =	{Keywords: Computational geometry, I/O-algorithms, merge tree, dynamic terrain}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.4
Constructing Light Spanners Deterministically in Near-Linear Time

Authors: Stephen Alstrup, Søren Dahlgaard, Arnold Filtser, Morten Stöckel, and Christian Wulff-Nilsen

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
Graph spanners are well-studied and widely used both in theory and practice. In a recent breakthrough, Chechik and Wulff-Nilsen [Shiri Chechik and Christian Wulff-Nilsen, 2018] improved the state-of-the-art for light spanners by constructing a (2k-1)(1+epsilon)-spanner with O(n^(1+1/k)) edges and O_epsilon(n^(1/k)) lightness. Soon after, Filtser and Solomon [Arnold Filtser and Shay Solomon, 2016] showed that the classic greedy spanner construction achieves the same bounds. The major drawback of the greedy spanner is its running time of O(mn^(1+1/k)) (which is faster than [Shiri Chechik and Christian Wulff-Nilsen, 2018]). This makes the construction impractical even for graphs of moderate size. Much faster spanner constructions do exist but they only achieve lightness Omega_epsilon(kn^(1/k)), even when randomization is used. The contribution of this paper is deterministic spanner constructions that are fast, and achieve similar bounds as the state-of-the-art slower constructions. Our first result is an O_epsilon(n^(2+1/k+epsilon')) time spanner construction which achieves the state-of-the-art bounds. Our second result is an O_epsilon(m + n log n) time construction of a spanner with (2k-1)(1+epsilon) stretch, O(log k * n^(1+1/k) edges and O_epsilon(log k * n^(1/k)) lightness. This is an exponential improvement in the dependence on k compared to the previous result with such running time. Finally, for the important special case where k=log n, for every constant epsilon>0, we provide an O(m+n^(1+epsilon)) time construction that produces an O(log n)-spanner with O(n) edges and O(1) lightness which is asymptotically optimal. This is the first known sub-quadratic construction of such a spanner for any k = omega(1). To achieve our constructions, we show a novel deterministic incremental approximate distance oracle. Our new oracle is crucial in our construction, as known randomized dynamic oracles require the assumption of a non-adaptive adversary. This is a strong assumption, which has seen recent attention in prolific venues. Our new oracle allows the order of the edge insertions to not be fixed in advance, which is critical as our spanner algorithm chooses which edges to insert based on the answers to distance queries. We believe our new oracle is of independent interest.
Cite as

Stephen Alstrup, Søren Dahlgaard, Arnold Filtser, Morten Stöckel, and Christian Wulff-Nilsen. Constructing Light Spanners Deterministically in Near-Linear Time. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 4:1-4:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{alstrup_et_al:LIPIcs.ESA.2019.4,
  author =	{Alstrup, Stephen and Dahlgaard, S{\o}ren and Filtser, Arnold and St\"{o}ckel, Morten and Wulff-Nilsen, Christian},
  title =	{{Constructing Light Spanners Deterministically in Near-Linear Time}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{4:1--4:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.4},
  URN =		{urn:nbn:de:0030-drops-111255},
  doi =		{10.4230/LIPIcs.ESA.2019.4},
  annote =	{Keywords: Spanners, Light Spanners, Efficient Construction, Deterministic Dynamic Distance Oracle}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.128
Near-Optimal Induced Universal Graphs for Bounded Degree Graphs

Authors: Mikkel Abrahamsen, Stephen Alstrup, Jacob Holm, Mathias Bæk Tejs Knudsen, and Morten Stöckel

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
A graph U is an induced universal graph for a family F of graphs if every graph in F is a vertex-induced subgraph of U. We give upper and lower bounds for the size of induced universal graphs for the family of graphs with n vertices of maximum degree D. Our new bounds improve several previous results except for the special cases where D is either near-constant or almost n/2. For constant even D Butler [Graphs and Combinatorics 2009] has shown O(n^(D/2)) and recently Alon and Nenadov [SODA 2017] showed the same bound for constant odd D. For constant D Butler also gave a matching lower bound. For generals graphs, which corresponds to D = n, Alon [Geometric and Functional Analysis, to appear] proved the existence of an induced universal graph with (1+o(1)) \cdot 2^((n-1)/2) vertices, leading to a smaller constant than in the previously best known bound of 16 * 2^(n/2) by Alstrup, Kaplan, Thorup, and Zwick [STOC 2015]. In this paper we give the following lower and upper bound of binom(floor(n/2))(floor(D/2)) * n^(-O(1)) and binom(floor(n/2))(floor(D/2)) * 2^(O(sqrt(D log D) * log(n/D))), respectively, where the upper bound is the main contribution. The proof that it is an induced universal graph relies on a randomized argument. We also give a deterministic upper bound of O(n^k / (k-1)!). These upper bounds are the best known when D <= n/2 - tilde-Omega(n^(3/4)) and either D is even and D = omega(1) or D is odd and D = omega(log n/log log n). In this range we improve asymptotically on the previous best known results by Butler [Graphs and Combinatorics 2009], Esperet, Arnaud and Ochem [IPL 2008], Adjiashvili and Rotbart [ICALP 2014], Alon and Nenadov [SODA 2017], and Alon [Geometric and Functional Analysis, to appear].
Cite as

Mikkel Abrahamsen, Stephen Alstrup, Jacob Holm, Mathias Bæk Tejs Knudsen, and Morten Stöckel. Near-Optimal Induced Universal Graphs for Bounded Degree Graphs. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 128:1-128:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{abrahamsen_et_al:LIPIcs.ICALP.2017.128,
  author =	{Abrahamsen, Mikkel and Alstrup, Stephen and Holm, Jacob and Knudsen, Mathias B{\ae}k Tejs and St\"{o}ckel, Morten},
  title =	{{Near-Optimal Induced Universal Graphs for Bounded Degree Graphs}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{128:1--128:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.128},
  URN =		{urn:nbn:de:0030-drops-74114},
  doi =		{10.4230/LIPIcs.ICALP.2017.128},
  annote =	{Keywords: Adjacency labeling schemes, Bounded degree graphs, Induced universal graphs, Distributed computing}
}
Document
DOI: 10.4230/LIPIcs.SOCG.2015.796
Maintaining Contour Trees of Dynamic Terrains

Authors: Pankaj K. Agarwal, Thomas Mølhave, Morten Revsbæk, Issam Safa, Yusu Wang, and Jungwoo Yang

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

Abstract
We study the problem of maintaining the contour tree T of a terrain Sigma, represented as a triangulated xy-monotone surface, as the heights of its vertices vary continuously with time. We characterize the combinatorial changes in T and how they relate to topological changes in Sigma. We present a kinetic data structure (KDS) for maintaining T efficiently. It maintains certificates that fail, i.e., an event occurs, only when the heights of two adjacent vertices become equal or two saddle vertices appear on the same contour. Assuming that the heights of two vertices of Sigma become equal only O(1) times and these instances can be computed in O(1) time, the KDS processes O(kappa + n) events, where n is the number of vertices in Sigma and kappa is the number of events at which the combinatorial structure of T changes, and processes each event in O(log n) time. The KDS can be extended to maintain an augmented contour tree and a join/split tree.
Cite as

Pankaj K. Agarwal, Thomas Mølhave, Morten Revsbæk, Issam Safa, Yusu Wang, and Jungwoo Yang. Maintaining Contour Trees of Dynamic Terrains. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 796-811, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{agarwal_et_al:LIPIcs.SOCG.2015.796,
  author =	{Agarwal, Pankaj K. and M{\o}lhave, Thomas and Revsb{\ae}k, Morten and Safa, Issam and Wang, Yusu and Yang, Jungwoo},
  title =	{{Maintaining Contour Trees of Dynamic Terrains}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{796--811},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.796},
  URN =		{urn:nbn:de:0030-drops-51406},
  doi =		{10.4230/LIPIcs.SOCG.2015.796},
  annote =	{Keywords: Contour tree, dynamic terrain, kinetic data structure}
}
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