4 Search Results for "D�ck, Viktor"

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.18
Sketching Distances in Monotone Graph Classes

Authors: Louis Esperet, Nathaniel Harms, and Andrey Kupavskii

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
We study the problems of adjacency sketching, small-distance sketching, and approximate distance threshold (ADT) sketching for monotone classes of graphs. The algorithmic problem is to assign random sketches to the vertices of any graph G in the class, so that adjacency, exact distance thresholds, or approximate distance thresholds of two vertices u,v can be decided (with probability at least 2/3) from the sketches of u and v, by a decoder that does not know the graph. The goal is to determine when sketches of constant size exist. Our main results are that, for monotone classes of graphs: constant-size adjacency sketches exist if and only if the class has bounded arboricity; constant-size small-distance sketches exist if and only if the class has bounded expansion; constant-size ADT sketches imply that the class has bounded expansion; any class of constant expansion (i.e. any proper minor closed class) has a constant-size ADT sketch; and a class may have arbitrarily small expansion without admitting a constant-size ADT sketch.
Cite as

Louis Esperet, Nathaniel Harms, and Andrey Kupavskii. Sketching Distances in Monotone Graph Classes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 18:1-18:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{esperet_et_al:LIPIcs.APPROX/RANDOM.2022.18,
  author =	{Esperet, Louis and Harms, Nathaniel and Kupavskii, Andrey},
  title =	{{Sketching Distances in Monotone Graph Classes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{18:1--18:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.18},
  URN =		{urn:nbn:de:0030-drops-171406},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.18},
  annote =	{Keywords: adjacency labelling, informative labelling, distance sketching, adjacency sketching, communication complexity}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.148
Temporal Vertex Cover with a Sliding Time Window

Authors: Eleni C. Akrida, George B. Mertzios, Paul G. Spirakis, and Viktor Zamaraev

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
Modern, inherently dynamic systems are usually characterized by a network structure, i.e. an underlying graph topology, which is subject to discrete changes over time. Given a static underlying graph G, a temporal graph can be represented via an assignment of a set of integer time-labels to every edge of G, indicating the discrete time steps when this edge is active. While most of the recent theoretical research on temporal graphs has focused on the notion of a temporal path and other "path-related" temporal notions, only few attempts have been made to investigate "non-path" temporal graph problems. In this paper, motivated by applications in sensor and in transportation networks, we introduce and study two natural temporal extensions of the classical problem Vertex Cover. In our first problem, Temporal Vertex Cover, the aim is to cover every edge at least once during the lifetime of the temporal graph, where an edge can only be covered by one of its endpoints at a time step when it is active. In our second, more pragmatic variation Sliding Window Temporal Vertex Cover, we are also given a natural number Delta, and our aim is to cover every edge at least once at every Delta consecutive time steps. In both cases we wish to minimize the total number of "vertex appearances" that are needed to cover the whole graph. We present a thorough investigation of the computational complexity and approximability of these two temporal covering problems. In particular, we provide strong hardness results, complemented by various approximation and exact algorithms. Some of our algorithms are polynomial-time, while others are asymptotically almost optimal under the Exponential Time Hypothesis (ETH) and other plausible complexity assumptions.
Cite as

Eleni C. Akrida, George B. Mertzios, Paul G. Spirakis, and Viktor Zamaraev. Temporal Vertex Cover with a Sliding Time Window. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 148:1-148:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{akrida_et_al:LIPIcs.ICALP.2018.148,
  author =	{Akrida, Eleni C. and Mertzios, George B. and Spirakis, Paul G. and Zamaraev, Viktor},
  title =	{{Temporal Vertex Cover with a Sliding Time Window}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{148:1--148:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.148},
  URN =		{urn:nbn:de:0030-drops-91522},
  doi =		{10.4230/LIPIcs.ICALP.2018.148},
  annote =	{Keywords: Temporal networks, temporal vertex cover, APX-hard, approximation algorithm, Exponential Time Hypothesis}
}
Document
DOI: 10.4230/DagSemProc.09261.12
Increasing Stability of Crew Schedules in Airlines

Authors: Leena Suhl, Viktor Dück, and Natalia Kliewer

Published in: Dagstuhl Seminar Proceedings, Volume 9261, Models and Algorithms for Optimization in Logistics (2009)

Abstract
In airline traffic disruptions occur frequently and cannot be totally avoided. They may lead to infeasible aircraft and crew schedules during the day of operations, due to absence of resources or violation of crew rules. The process of finding new schedules in such cases is called recovery or disruption management. The short-term recovery actions usually imply additional costs meaning that the total operational costs of a crew schedule can be significantly higher than the original planned costs. It is generally desirable to construct the schedule already in the planning phase in such a way that not just the planned costs, but the total operational costs are minimized. The goal is thus to construct schedules which remain feasible or can be recovered without high costs in cases of disturbances. This approach is generally called robust scheduling.
Cite as

Leena Suhl, Viktor Dück, and Natalia Kliewer. Increasing Stability of Crew Schedules in Airlines. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{suhl_et_al:DagSemProc.09261.12,
  author =	{Suhl, Leena and D\"{u}ck, Viktor and Kliewer, Natalia},
  title =	{{Increasing Stability of Crew Schedules in Airlines}},
  booktitle =	{Models and Algorithms for Optimization in Logistics},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9261},
  editor =	{Cynthia Barnhart and Uwe Clausen and Ulrich Lauther and Rolf H. M\"{o}hring},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09261.12},
  URN =		{urn:nbn:de:0030-drops-21786},
  doi =		{10.4230/DagSemProc.09261.12},
  annote =	{Keywords: Robust planning, crew scheduling, airlines}
}
Document
DOI: 10.4230/DagSemProc.09061.12
Low-Memory Tour Reversal in Directed Graphs

Authors: Viktor Mosenkis, Uwe Naumann, and Elmar Peise

Published in: Dagstuhl Seminar Proceedings, Volume 9061, Combinatorial Scientific Computing (2009)

Abstract
We consider the problem of reversing a {em tour} $(i_1,i_2,ldots,i_l)$ in a directed graph $G=(V,E)$ with positive integer vertices $V$ and edges $E subseteq V imes V$, where $i_j in V$ and $(i_j,i_{j+1}) in E$ for all $j=1,ldots,l-1.$ The tour can be processed in last-in-first-out order as long as the size of the corresponding stack does not exceed the available memory. This constraint is violated in most cases when considering control-flow graphs of large-scale numerical simulation programs. The tour reversal problem also arises in adjoint programs used, for example, in the context of derivative-based nonlinear optimization, sensitivity analysis, or other, often inverse, problems. The intention is to compress the tour in order not to run out of memory. As the general optimal compression problem was proven to be NP-hard and big control-flow graphs results from loops in programs we do not want to use general purpose algorithms to compress the tour. We want rather to compress the tour by finding loops and replace the redundant information by proper representation of the loops.
Cite as

Viktor Mosenkis, Uwe Naumann, and Elmar Peise. Low-Memory Tour Reversal in Directed Graphs. In Combinatorial Scientific Computing. Dagstuhl Seminar Proceedings, Volume 9061, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{mosenkis_et_al:DagSemProc.09061.12,
  author =	{Mosenkis, Viktor and Naumann, Uwe and Peise, Elmar},
  title =	{{Low-Memory Tour Reversal in Directed Graphs}},
  booktitle =	{Combinatorial Scientific Computing},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9061},
  editor =	{Uwe Naumann and Olaf Schenk and Horst D. Simon and Sivan Toledo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09061.12},
  URN =		{urn:nbn:de:0030-drops-20924},
  doi =		{10.4230/DagSemProc.09061.12},
  annote =	{Keywords: Directed graph, tour reversal, offline algorithm, dynamic programming, online algorithm, control-flow reversal, adjoint program}
}
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