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Documents authored by Mihalák, Matús

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Mihalák, Matús

Document
DOI: 10.4230/OASIcs.ATMOS.2019.3
On Sorting with a Network of Two Stacks

Authors: Matúš Mihalák and Marc Pont

Published in: OASIcs, Volume 75, 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)

Abstract
Sorting with stacks is a collection of problems that deal with sorting a sequence of numbers by pushing and popping the numbers to and from a given set of stacks. Multiple concrete decision or optimization questions are formed by restricting the access to the stacks. The motivation comes, e.g., from shunting train wagons in shunting yards, shunting trams in depots, or in stacking cargo containers on cargo ships or storage yards in transshipment terminals. We consider the problem of sorting a permutation of n integers 1,2,...,n using k >= 2 stacks. In this problem, elements from the input sequence are pushed one-by-one (in the order of the elements in the sequence) to one of the k stacks. At any time, an element from a stack can be popped and pushed to another stack; such an operation is called a shuffle. Also, at any time, an element can be popped from a stack and placed to the output sequence. We can only place the elements to the output in the increasing order of their value such that at the end the output is the ordered sequence of the elements. The problem asks to minimize the number of shuffles in the process. It is known that for k >= 4, the problem is NP-hard, and that there is no approximation algorithm unless P=NP. For k >= 3, it is known that at most O(n log n) shuffles are needed for any input sequence. For the case when k=2, there exist input sequences that require Omega(n^{2-epsilon}) shuffles, for any epsilon>0. Nothing substantially more is known for the case of k=2. In this paper, we study the following variant of the problem with k=2 stacks: no shuffle and no placement to the output sequence can happen before every element is in one of the two stacks. We show that our problem can be seen as the MinUnCut problem by providing a polynomial-time reduction, and thus we show that there exists a randomized O(sqrt{log n})-approximation algorithm and a deterministic O(log n)-approximation algorithm for our problem.
Cite as

Matúš Mihalák and Marc Pont. On Sorting with a Network of Two Stacks. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 3:1-3:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mihalak_et_al:OASIcs.ATMOS.2019.3,
  author =	{Mihal\'{a}k, Mat\'{u}\v{s} and Pont, Marc},
  title =	{{On Sorting with a Network of Two Stacks}},
  booktitle =	{19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)},
  pages =	{3:1--3:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-128-3},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{75},
  editor =	{Cacchiani, Valentina and Marchetti-Spaccamela, Alberto},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.3},
  URN =		{urn:nbn:de:0030-drops-114159},
  doi =		{10.4230/OASIcs.ATMOS.2019.3},
  annote =	{Keywords: Sorting, Stacks, Optimization, Algorithms, Reduction, MinUnCut}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.45
Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm

Authors: Annette M. C. Ficker, Thomas Erlebach, Matús Mihalák, and Frits C. R. Spieksma

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Consider a problem where 4k given vectors need to be partitioned into k clusters of four vectors each. A cluster of four vectors is called a quad, and the cost of a quad is the sum of the component-wise maxima of the four vectors in the quad. The problem is to partition the given 4k vectors into k quads with minimum total cost. We analyze a straightforward matching-based algorithm and prove that this algorithm is a 3/2-approximation algorithm for this problem. We further analyze the performance of this algorithm on a hierarchy of special cases of the problem and prove that, in one particular case, the algorithm is a 5/4-approximation algorithm. Our analysis is tight in all cases except one.
Cite as

Annette M. C. Ficker, Thomas Erlebach, Matús Mihalák, and Frits C. R. Spieksma. Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 45:1-45:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ficker_et_al:LIPIcs.ISAAC.2018.45,
  author =	{Ficker, Annette M. C. and Erlebach, Thomas and Mihal\'{a}k, Mat\'{u}s and Spieksma, Frits C. R.},
  title =	{{Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{45:1--45:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.45},
  URN =		{urn:nbn:de:0030-drops-99933},
  doi =		{10.4230/LIPIcs.ISAAC.2018.45},
  annote =	{Keywords: approximation algorithm, matching, clustering problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.56
Collective Fast Delivery by Energy-Efficient Agents

Authors: Andreas Bärtschi, Daniel Graf, and Matús Mihalák

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
We consider k mobile agents initially located at distinct nodes of an undirected graph (on n nodes, with edge lengths). The agents have to deliver a single item from a given source node s to a given target node t. The agents can move along the edges of the graph, starting at time 0, with respect to the following: Each agent i has a weight omega_i that defines the rate of energy consumption while travelling a distance in the graph, and a velocity upsilon_i with which it can move. We are interested in schedules (operating the k agents) that result in a small delivery time T (time when the item arrives at t), and small total energy consumption E. Concretely, we ask for a schedule that: either (i) Minimizes T, (ii) Minimizes lexicographically (T,E) (prioritizing fast delivery), or (iii) Minimizes epsilon * T + (1-epsilon)* E, for a given epsilon in (0,1). We show that (i) is solvable in polynomial time, and show that (ii) is polynomial-time solvable for uniform velocities and solvable in time O(n+k log k) for arbitrary velocities on paths, but in general is NP-hard even on planar graphs. As a corollary of our hardness result, (iii) is NP-hard, too. We show that there is a 2-approximation algorithm for (iii) using a single agent.
Cite as

Andreas Bärtschi, Daniel Graf, and Matús Mihalák. Collective Fast Delivery by Energy-Efficient Agents. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 56:1-56:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bartschi_et_al:LIPIcs.MFCS.2018.56,
  author =	{B\"{a}rtschi, Andreas and Graf, Daniel and Mihal\'{a}k, Mat\'{u}s},
  title =	{{Collective Fast Delivery by Energy-Efficient Agents}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{56:1--56:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.56},
  URN =		{urn:nbn:de:0030-drops-96381},
  doi =		{10.4230/LIPIcs.MFCS.2018.56},
  annote =	{Keywords: delivery, mobile agents, time/energy optimization, complexity, algorithms}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.68
Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past

Authors: Katerina Böhmová, Matúš Mihalák, Peggy Neubert, Tobias Pröger, and Peter Widmayer

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
Given an urban public transportation network and historic delay information, we consider the problem of computing reliable journeys. We propose new algorithms based on our recently presented solution concept (Böhmová et al., ATMOS 2013), and perform an experimental evaluation using real-world delay data from Zürich, Switzerland. We compare these methods to natural approaches as well as to our recently proposed method which can also be used to measure typicality of past observations. Moreover, we demonstrate how this measure relates to the predictive quality of the individual methods. In particular, if the past observations are typical, then the learning- based methods are able to produce solutions that perform well on typical days, even in the presence of large delays.
Cite as

Katerina Böhmová, Matúš Mihalák, Peggy Neubert, Tobias Pröger, and Peter Widmayer. Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 68-81, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{bohmova_et_al:OASIcs.ATMOS.2015.68,
  author =	{B\"{o}hmov\'{a}, Katerina and Mihal\'{a}k, Mat\'{u}\v{s} and Neubert, Peggy and Pr\"{o}ger, Tobias and Widmayer, Peter},
  title =	{{Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{68--81},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.68},
  URN =		{urn:nbn:de:0030-drops-54542},
  doi =		{10.4230/OASIcs.ATMOS.2015.68},
  annote =	{Keywords: public transportation, route planning, robustness, optimization, experiments}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.82
Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks

Authors: Matúš Mihalák and Sandro Montanari

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
Based on time-dependent travel times for N past days, we consider the computation of robust routes according to the min-max relative regret criterion. For this method we seek a path minimizing its maximum weight in any one of the N days, normalized by the weight of an optimum for the respective day. In order to speed-up this computationally demanding approach, we observe that its output belongs to the Pareto front of the network with time-dependent multi-criteria edge weights. We adapt a well-known algorithm for computing Pareto fronts in time-dependent graphs and apply the bi-directional search technique to it. We also show how to parametrize this algorithm by a value K to compute a K-approximate Pareto front. An experimental evaluation for the cases N = 2 and N = 3 indicates a considerable speed-up of the bi-directional search over the uni-directional.
Cite as

Matúš Mihalák and Sandro Montanari. Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 82-94, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{mihalak_et_al:OASIcs.ATMOS.2015.82,
  author =	{Mihal\'{a}k, Mat\'{u}\v{s} and Montanari, Sandro},
  title =	{{Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{82--94},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.82},
  URN =		{urn:nbn:de:0030-drops-54561},
  doi =		{10.4230/OASIcs.ATMOS.2015.82},
  annote =	{Keywords: shortest path, time-dependent, bi-criteria, bi-directional search, min-max relative regret}
}
Document
Complete Volume
DOI: 10.4230/OASIcs.ATMOS.2014
OASIcs, Volume 42, ATMOS'14, Complete Volume

Authors: Stefan Funke and Matúš Mihalák

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Abstract
OASIcs, Volume 42, ATMOS'14, Complete Volume
Cite as

14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Proceedings{funke_et_al:OASIcs.ATMOS.2014,
  title =	{{OASIcs, Volume 42, ATMOS'14, Complete Volume}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014},
  URN =		{urn:nbn:de:0030-drops-47613},
  doi =		{10.4230/OASIcs.ATMOS.2014},
  annote =	{Keywords: Analysis of Algorithms and Problem Complexity, Optimization, Combinatorics, Graph Theory, Applications}
}
Document
Front Matter
DOI: 10.4230/OASIcs.ATMOS.2014.i
Frontmatter, Table of Contents, Preface, Workshop Organization

Authors: Stefan Funke and Matús Mihalák

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Abstract
Frontmatter, Table of Contents, Preface, Workshop Organization
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14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. i-ix, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{funke_et_al:OASIcs.ATMOS.2014.i,
  author =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  title =	{{Frontmatter, Table of Contents, Preface, Workshop Organization}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{i--ix},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014.i},
  URN =		{urn:nbn:de:0030-drops-47470},
  doi =		{10.4230/OASIcs.ATMOS.2014.i},
  annote =	{Keywords: Frontmatter, Table of Contents, Preface, Workshop Organization}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2013.27
Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations

Authors: Katerina Böhmová, Matús Mihalák, Tobias Pröger, Rastislav Srámek, and Peter Widmayer

Published in: OASIcs, Volume 33, 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2013)

Abstract
We study the problem of robust routing in urban public transportation networks. In order to propose solutions that are robust for typical delays, we assume that we have past observations of real traffic situations available. In particular, we assume that we have "daily records" containing the observed travel times in the whole network for a few past days. We introduce a new concept to express a solution that is feasible in any record of a given public transportation network. We adapt the method of Buhmann et al. [Buhmann et al., ITCS 2013] for optimization under uncertainty, and develop algorithms that allow its application for finding a robust journey from a given source to a given destination. The performance of the algorithms and the quality of the predicted journey are evaluated in a preliminary experimental study. We furthermore introduce a measure of reliability of a given journey, and develop algorithms for its computation. The robust routing concepts presented in this work are suited specially for public transportation networks of large cities that lack clear hierarchical structure and contain services that run with high frequencies.
Cite as

Katerina Böhmová, Matús Mihalák, Tobias Pröger, Rastislav Srámek, and Peter Widmayer. Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations. In 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 33, pp. 27-41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{bohmova_et_al:OASIcs.ATMOS.2013.27,
  author =	{B\"{o}hmov\'{a}, Katerina and Mihal\'{a}k, Mat\'{u}s and Pr\"{o}ger, Tobias and Sr\'{a}mek, Rastislav and Widmayer, Peter},
  title =	{{Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations}},
  booktitle =	{13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{27--41},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-58-3},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{33},
  editor =	{Frigioni, Daniele and Stiller, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2013.27},
  URN =		{urn:nbn:de:0030-drops-42428},
  doi =		{10.4230/OASIcs.ATMOS.2013.27},
  annote =	{Keywords: Algorithms, Optimization, Robustness, Route planning, Public transportation}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2011.38
Track Allocation in Freight-Train Classification with Mixed Tracks

Authors: Markus Bohlin, Holger Flier, Jens Maue, and Matús Mihalák

Published in: OASIcs, Volume 20, 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2011)

Abstract
We consider the process of forming outbound trains from cars of inbound trains at rail-freight hump yards. Given the arrival and departure times as well as the composition of the trains, we study the problem of allocating classification tracks to outbound trains such that every outbound train can be built on a separate classification track. We observe that the core problem can be formulated as a special list coloring problem in interval graphs, which is known to be NP-complete. We focus on an extension where individual cars of different trains can temporarily be stored on a special subset of the tracks. This problem induces several new variants of the list-coloring problem, in which the given intervals can be shortened by cutting off a prefix of the interval. We show that in case of uniform and sufficient track lengths, the corresponding coloring problem can be solved in polynomial time, if the goal is to minimize the total cost associated with cutting off prefixes of the intervals. Based on these results, we devise two heuristics as well as an integer program to tackle the problem. As a case study, we consider a real-world problem instance from the Hallsberg Rangerbangard hump yard in Sweden. Planning over horizons of seven days, we obtain feasible solutions from the integer program in all scenarios, and from the heuristics in most scenarios.
Cite as

Markus Bohlin, Holger Flier, Jens Maue, and Matús Mihalák. Track Allocation in Freight-Train Classification with Mixed Tracks. In 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 20, pp. 38-51, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{bohlin_et_al:OASIcs.ATMOS.2011.38,
  author =	{Bohlin, Markus and Flier, Holger and Maue, Jens and Mihal\'{a}k, Mat\'{u}s},
  title =	{{Track Allocation in Freight-Train Classification with Mixed Tracks}},
  booktitle =	{11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{38--51},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-33-0},
  ISSN =	{2190-6807},
  year =	{2011},
  volume =	{20},
  editor =	{Caprara, Alberto and Kontogiannis, Spyros},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2011.38},
  URN =		{urn:nbn:de:0030-drops-32658},
  doi =		{10.4230/OASIcs.ATMOS.2011.38},
  annote =	{Keywords: algorithms, complexity, graph theory, railways, scheduling, shunting, train classification, train marshalling, transportation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2011.153
Telling convex from reflex allows to map a polygon

Authors: Jeremie Chalopin, Shantanu Das, Yann Disser, Matus Mihalak, and Peter Widmayer

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract
We consider the exploration of a simple polygon P by a robot that moves from vertex to vertex along edges of the visibility graph of P. The visibility graph has a vertex for every vertex of P and an edge between two vertices if they see each other, i.e.~if the line segment connecting them lies inside $P$ entirely. While located at a vertex, the robot is capable of ordering the vertices it sees in counter-clockwise order as they appear on the boundary, and for every two such vertices, it can distinguish whether the angle between them is convex (<= pi) or reflex (> pi). Other than that, distant vertices are indistinguishable to the robot. We assume that an upper bound on the number of vertices is known and show that the robot is always capable of reconstructing the visibility graph of P. We also show that multiple identical, indistinguishable and deterministic such robots can always position themselves such that they mutually see each other, i.e. such that they form a clique in the visibility graph.
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Jeremie Chalopin, Shantanu Das, Yann Disser, Matus Mihalak, and Peter Widmayer. Telling convex from reflex allows to map a polygon. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 153-164, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{chalopin_et_al:LIPIcs.STACS.2011.153,
  author =	{Chalopin, Jeremie and Das, Shantanu and Disser, Yann and Mihalak, Matus and Widmayer, Peter},
  title =	{{Telling convex from reflex allows to map a polygon}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{153--164},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.153},
  URN =		{urn:nbn:de:0030-drops-30077},
  doi =		{10.4230/LIPIcs.STACS.2011.153},
  annote =	{Keywords: polygon mapping, map construction, autonomous agent, simple robot, visibility graph reconstruction}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2010.61
Vertex Disjoint Paths for Dispatching in Railways

Authors: Holger Flier, Matús Mihalák, Anita Schöbel, Peter Widmayer, and Anna Zych

Published in: OASIcs, Volume 14, 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10) (2010)

Abstract
We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routing-in-rounds problem. Although all considered variants are NP-hard in planar graphs, restrictions on the location of the terminals, motivated by railway applications, lead to polynomially solvable cases for the decision and maximization versions of the problem, and to a $p$-approximation algorithm for the routing-in-rounds problem, where $p$ is the maximum number of alternative paths for a terminal pair.
Cite as

Holger Flier, Matús Mihalák, Anita Schöbel, Peter Widmayer, and Anna Zych. Vertex Disjoint Paths for Dispatching in Railways. In 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10). Open Access Series in Informatics (OASIcs), Volume 14, pp. 61-73, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{flier_et_al:OASIcs.ATMOS.2010.61,
  author =	{Flier, Holger and Mihal\'{a}k, Mat\'{u}s and Sch\"{o}bel, Anita and Widmayer, Peter and Zych, Anna},
  title =	{{Vertex Disjoint Paths for Dispatching in Railways}},
  booktitle =	{10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10)},
  pages =	{61--73},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-20-0},
  ISSN =	{2190-6807},
  year =	{2010},
  volume =	{14},
  editor =	{Erlebach, Thomas and L\"{u}bbecke, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2010.61},
  URN =		{urn:nbn:de:0030-drops-27508},
  doi =		{10.4230/OASIcs.ATMOS.2010.61},
  annote =	{Keywords: algorithms, approximation, complexity, graph theory, railways, routing, transportation}
}
Document
DOI: 10.4230/DagSemProc.05031.17
Network Discovery and Verification

Authors: Zuzana Beerliova, Felix Eberhard, Thomas Erlebach, Alexander Hall, Michael Hoffmann, Matus Mihalak, and L. Shankar Ram

Published in: Dagstuhl Seminar Proceedings, Volume 5031, Algorithms for Optimization with Incomplete Information (2005)

Abstract
Consider the problem of discovering (or verifying) the edges and non-edges of a network, modelled as a connected undirected graph, using a minimum number of queries. A query at a vertex v discovers (or verifies) all edges and non-edges whose endpoints have different distance from v. In the network discovery problem, the edges and non-edges are initially unknown, and the algorithm must select the next query based only on the results of previous queries. We study the problem using competitive analysis and give a randomized on-line algorithm with competitive ratio O(sqrt(n*log n)) for graphs with n vertices. We also show that no deterministic algorithm can have competitive ratio better than 3. In the network verification problem, the graph is known in advance and the goal is to compute a minimum number of queries that verify all edges and non-edges. This problem has previously been studied as the problem of placing landmarks in graphs or determining the metric dimension of a graph. We show that there is no approximation algorithm for this problem with ratio o(log n) unless P=NP. Furthermore, we prove that the optimal number of queries for d-dimensional hypercubes is Theta(d/log d).
Cite as

Zuzana Beerliova, Felix Eberhard, Thomas Erlebach, Alexander Hall, Michael Hoffmann, Matus Mihalak, and L. Shankar Ram. Network Discovery and Verification. In Algorithms for Optimization with Incomplete Information. Dagstuhl Seminar Proceedings, Volume 5031, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{beerliova_et_al:DagSemProc.05031.17,
  author =	{Beerliova, Zuzana and Eberhard, Felix and Erlebach, Thomas and Hall, Alexander and Hoffmann, Michael and Mihalak, Matus and Ram, L. Shankar},
  title =	{{Network Discovery and Verification}},
  booktitle =	{Algorithms for Optimization with Incomplete Information},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5031},
  editor =	{Susanne Albers and Rolf H. M\"{o}hring and Georg Ch. Pflug and R\"{u}diger Schultz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05031.17},
  URN =		{urn:nbn:de:0030-drops-594},
  doi =		{10.4230/DagSemProc.05031.17},
  annote =	{Keywords: on-line algorithms , set cover , landmarks , metric dimension}
}

Mihalák, Matúš

Document
DOI: 10.4230/OASIcs.ATMOS.2019.3
On Sorting with a Network of Two Stacks

Authors: Matúš Mihalák and Marc Pont

Published in: OASIcs, Volume 75, 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)

Abstract
Sorting with stacks is a collection of problems that deal with sorting a sequence of numbers by pushing and popping the numbers to and from a given set of stacks. Multiple concrete decision or optimization questions are formed by restricting the access to the stacks. The motivation comes, e.g., from shunting train wagons in shunting yards, shunting trams in depots, or in stacking cargo containers on cargo ships or storage yards in transshipment terminals. We consider the problem of sorting a permutation of n integers 1,2,...,n using k >= 2 stacks. In this problem, elements from the input sequence are pushed one-by-one (in the order of the elements in the sequence) to one of the k stacks. At any time, an element from a stack can be popped and pushed to another stack; such an operation is called a shuffle. Also, at any time, an element can be popped from a stack and placed to the output sequence. We can only place the elements to the output in the increasing order of their value such that at the end the output is the ordered sequence of the elements. The problem asks to minimize the number of shuffles in the process. It is known that for k >= 4, the problem is NP-hard, and that there is no approximation algorithm unless P=NP. For k >= 3, it is known that at most O(n log n) shuffles are needed for any input sequence. For the case when k=2, there exist input sequences that require Omega(n^{2-epsilon}) shuffles, for any epsilon>0. Nothing substantially more is known for the case of k=2. In this paper, we study the following variant of the problem with k=2 stacks: no shuffle and no placement to the output sequence can happen before every element is in one of the two stacks. We show that our problem can be seen as the MinUnCut problem by providing a polynomial-time reduction, and thus we show that there exists a randomized O(sqrt{log n})-approximation algorithm and a deterministic O(log n)-approximation algorithm for our problem.
Cite as

Matúš Mihalák and Marc Pont. On Sorting with a Network of Two Stacks. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 3:1-3:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mihalak_et_al:OASIcs.ATMOS.2019.3,
  author =	{Mihal\'{a}k, Mat\'{u}\v{s} and Pont, Marc},
  title =	{{On Sorting with a Network of Two Stacks}},
  booktitle =	{19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)},
  pages =	{3:1--3:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-128-3},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{75},
  editor =	{Cacchiani, Valentina and Marchetti-Spaccamela, Alberto},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.3},
  URN =		{urn:nbn:de:0030-drops-114159},
  doi =		{10.4230/OASIcs.ATMOS.2019.3},
  annote =	{Keywords: Sorting, Stacks, Optimization, Algorithms, Reduction, MinUnCut}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.45
Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm

Authors: Annette M. C. Ficker, Thomas Erlebach, Matús Mihalák, and Frits C. R. Spieksma

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Consider a problem where 4k given vectors need to be partitioned into k clusters of four vectors each. A cluster of four vectors is called a quad, and the cost of a quad is the sum of the component-wise maxima of the four vectors in the quad. The problem is to partition the given 4k vectors into k quads with minimum total cost. We analyze a straightforward matching-based algorithm and prove that this algorithm is a 3/2-approximation algorithm for this problem. We further analyze the performance of this algorithm on a hierarchy of special cases of the problem and prove that, in one particular case, the algorithm is a 5/4-approximation algorithm. Our analysis is tight in all cases except one.
Cite as

Annette M. C. Ficker, Thomas Erlebach, Matús Mihalák, and Frits C. R. Spieksma. Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 45:1-45:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ficker_et_al:LIPIcs.ISAAC.2018.45,
  author =	{Ficker, Annette M. C. and Erlebach, Thomas and Mihal\'{a}k, Mat\'{u}s and Spieksma, Frits C. R.},
  title =	{{Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{45:1--45:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.45},
  URN =		{urn:nbn:de:0030-drops-99933},
  doi =		{10.4230/LIPIcs.ISAAC.2018.45},
  annote =	{Keywords: approximation algorithm, matching, clustering problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.56
Collective Fast Delivery by Energy-Efficient Agents

Authors: Andreas Bärtschi, Daniel Graf, and Matús Mihalák

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
We consider k mobile agents initially located at distinct nodes of an undirected graph (on n nodes, with edge lengths). The agents have to deliver a single item from a given source node s to a given target node t. The agents can move along the edges of the graph, starting at time 0, with respect to the following: Each agent i has a weight omega_i that defines the rate of energy consumption while travelling a distance in the graph, and a velocity upsilon_i with which it can move. We are interested in schedules (operating the k agents) that result in a small delivery time T (time when the item arrives at t), and small total energy consumption E. Concretely, we ask for a schedule that: either (i) Minimizes T, (ii) Minimizes lexicographically (T,E) (prioritizing fast delivery), or (iii) Minimizes epsilon * T + (1-epsilon)* E, for a given epsilon in (0,1). We show that (i) is solvable in polynomial time, and show that (ii) is polynomial-time solvable for uniform velocities and solvable in time O(n+k log k) for arbitrary velocities on paths, but in general is NP-hard even on planar graphs. As a corollary of our hardness result, (iii) is NP-hard, too. We show that there is a 2-approximation algorithm for (iii) using a single agent.
Cite as

Andreas Bärtschi, Daniel Graf, and Matús Mihalák. Collective Fast Delivery by Energy-Efficient Agents. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 56:1-56:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bartschi_et_al:LIPIcs.MFCS.2018.56,
  author =	{B\"{a}rtschi, Andreas and Graf, Daniel and Mihal\'{a}k, Mat\'{u}s},
  title =	{{Collective Fast Delivery by Energy-Efficient Agents}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{56:1--56:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.56},
  URN =		{urn:nbn:de:0030-drops-96381},
  doi =		{10.4230/LIPIcs.MFCS.2018.56},
  annote =	{Keywords: delivery, mobile agents, time/energy optimization, complexity, algorithms}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.68
Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past

Authors: Katerina Böhmová, Matúš Mihalák, Peggy Neubert, Tobias Pröger, and Peter Widmayer

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
Given an urban public transportation network and historic delay information, we consider the problem of computing reliable journeys. We propose new algorithms based on our recently presented solution concept (Böhmová et al., ATMOS 2013), and perform an experimental evaluation using real-world delay data from Zürich, Switzerland. We compare these methods to natural approaches as well as to our recently proposed method which can also be used to measure typicality of past observations. Moreover, we demonstrate how this measure relates to the predictive quality of the individual methods. In particular, if the past observations are typical, then the learning- based methods are able to produce solutions that perform well on typical days, even in the presence of large delays.
Cite as

Katerina Böhmová, Matúš Mihalák, Peggy Neubert, Tobias Pröger, and Peter Widmayer. Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 68-81, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{bohmova_et_al:OASIcs.ATMOS.2015.68,
  author =	{B\"{o}hmov\'{a}, Katerina and Mihal\'{a}k, Mat\'{u}\v{s} and Neubert, Peggy and Pr\"{o}ger, Tobias and Widmayer, Peter},
  title =	{{Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{68--81},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.68},
  URN =		{urn:nbn:de:0030-drops-54542},
  doi =		{10.4230/OASIcs.ATMOS.2015.68},
  annote =	{Keywords: public transportation, route planning, robustness, optimization, experiments}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.82
Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks

Authors: Matúš Mihalák and Sandro Montanari

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
Based on time-dependent travel times for N past days, we consider the computation of robust routes according to the min-max relative regret criterion. For this method we seek a path minimizing its maximum weight in any one of the N days, normalized by the weight of an optimum for the respective day. In order to speed-up this computationally demanding approach, we observe that its output belongs to the Pareto front of the network with time-dependent multi-criteria edge weights. We adapt a well-known algorithm for computing Pareto fronts in time-dependent graphs and apply the bi-directional search technique to it. We also show how to parametrize this algorithm by a value K to compute a K-approximate Pareto front. An experimental evaluation for the cases N = 2 and N = 3 indicates a considerable speed-up of the bi-directional search over the uni-directional.
Cite as

Matúš Mihalák and Sandro Montanari. Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 82-94, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{mihalak_et_al:OASIcs.ATMOS.2015.82,
  author =	{Mihal\'{a}k, Mat\'{u}\v{s} and Montanari, Sandro},
  title =	{{Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{82--94},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.82},
  URN =		{urn:nbn:de:0030-drops-54561},
  doi =		{10.4230/OASIcs.ATMOS.2015.82},
  annote =	{Keywords: shortest path, time-dependent, bi-criteria, bi-directional search, min-max relative regret}
}
Document
Complete Volume
DOI: 10.4230/OASIcs.ATMOS.2014
OASIcs, Volume 42, ATMOS'14, Complete Volume

Authors: Stefan Funke and Matúš Mihalák

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Abstract
OASIcs, Volume 42, ATMOS'14, Complete Volume
Cite as

14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Proceedings{funke_et_al:OASIcs.ATMOS.2014,
  title =	{{OASIcs, Volume 42, ATMOS'14, Complete Volume}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014},
  URN =		{urn:nbn:de:0030-drops-47613},
  doi =		{10.4230/OASIcs.ATMOS.2014},
  annote =	{Keywords: Analysis of Algorithms and Problem Complexity, Optimization, Combinatorics, Graph Theory, Applications}
}
Document
Front Matter
DOI: 10.4230/OASIcs.ATMOS.2014.i
Frontmatter, Table of Contents, Preface, Workshop Organization

Authors: Stefan Funke and Matús Mihalák

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Abstract
Frontmatter, Table of Contents, Preface, Workshop Organization
Cite as

14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. i-ix, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{funke_et_al:OASIcs.ATMOS.2014.i,
  author =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  title =	{{Frontmatter, Table of Contents, Preface, Workshop Organization}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{i--ix},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014.i},
  URN =		{urn:nbn:de:0030-drops-47470},
  doi =		{10.4230/OASIcs.ATMOS.2014.i},
  annote =	{Keywords: Frontmatter, Table of Contents, Preface, Workshop Organization}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2013.27
Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations

Authors: Katerina Böhmová, Matús Mihalák, Tobias Pröger, Rastislav Srámek, and Peter Widmayer

Published in: OASIcs, Volume 33, 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2013)

Abstract
We study the problem of robust routing in urban public transportation networks. In order to propose solutions that are robust for typical delays, we assume that we have past observations of real traffic situations available. In particular, we assume that we have "daily records" containing the observed travel times in the whole network for a few past days. We introduce a new concept to express a solution that is feasible in any record of a given public transportation network. We adapt the method of Buhmann et al. [Buhmann et al., ITCS 2013] for optimization under uncertainty, and develop algorithms that allow its application for finding a robust journey from a given source to a given destination. The performance of the algorithms and the quality of the predicted journey are evaluated in a preliminary experimental study. We furthermore introduce a measure of reliability of a given journey, and develop algorithms for its computation. The robust routing concepts presented in this work are suited specially for public transportation networks of large cities that lack clear hierarchical structure and contain services that run with high frequencies.
Cite as

Katerina Böhmová, Matús Mihalák, Tobias Pröger, Rastislav Srámek, and Peter Widmayer. Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations. In 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 33, pp. 27-41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{bohmova_et_al:OASIcs.ATMOS.2013.27,
  author =	{B\"{o}hmov\'{a}, Katerina and Mihal\'{a}k, Mat\'{u}s and Pr\"{o}ger, Tobias and Sr\'{a}mek, Rastislav and Widmayer, Peter},
  title =	{{Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations}},
  booktitle =	{13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{27--41},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-58-3},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{33},
  editor =	{Frigioni, Daniele and Stiller, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2013.27},
  URN =		{urn:nbn:de:0030-drops-42428},
  doi =		{10.4230/OASIcs.ATMOS.2013.27},
  annote =	{Keywords: Algorithms, Optimization, Robustness, Route planning, Public transportation}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2011.38
Track Allocation in Freight-Train Classification with Mixed Tracks

Authors: Markus Bohlin, Holger Flier, Jens Maue, and Matús Mihalák

Published in: OASIcs, Volume 20, 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2011)

Abstract
We consider the process of forming outbound trains from cars of inbound trains at rail-freight hump yards. Given the arrival and departure times as well as the composition of the trains, we study the problem of allocating classification tracks to outbound trains such that every outbound train can be built on a separate classification track. We observe that the core problem can be formulated as a special list coloring problem in interval graphs, which is known to be NP-complete. We focus on an extension where individual cars of different trains can temporarily be stored on a special subset of the tracks. This problem induces several new variants of the list-coloring problem, in which the given intervals can be shortened by cutting off a prefix of the interval. We show that in case of uniform and sufficient track lengths, the corresponding coloring problem can be solved in polynomial time, if the goal is to minimize the total cost associated with cutting off prefixes of the intervals. Based on these results, we devise two heuristics as well as an integer program to tackle the problem. As a case study, we consider a real-world problem instance from the Hallsberg Rangerbangard hump yard in Sweden. Planning over horizons of seven days, we obtain feasible solutions from the integer program in all scenarios, and from the heuristics in most scenarios.
Cite as

Markus Bohlin, Holger Flier, Jens Maue, and Matús Mihalák. Track Allocation in Freight-Train Classification with Mixed Tracks. In 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 20, pp. 38-51, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{bohlin_et_al:OASIcs.ATMOS.2011.38,
  author =	{Bohlin, Markus and Flier, Holger and Maue, Jens and Mihal\'{a}k, Mat\'{u}s},
  title =	{{Track Allocation in Freight-Train Classification with Mixed Tracks}},
  booktitle =	{11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{38--51},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-33-0},
  ISSN =	{2190-6807},
  year =	{2011},
  volume =	{20},
  editor =	{Caprara, Alberto and Kontogiannis, Spyros},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2011.38},
  URN =		{urn:nbn:de:0030-drops-32658},
  doi =		{10.4230/OASIcs.ATMOS.2011.38},
  annote =	{Keywords: algorithms, complexity, graph theory, railways, scheduling, shunting, train classification, train marshalling, transportation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2011.153
Telling convex from reflex allows to map a polygon

Authors: Jeremie Chalopin, Shantanu Das, Yann Disser, Matus Mihalak, and Peter Widmayer

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract
We consider the exploration of a simple polygon P by a robot that moves from vertex to vertex along edges of the visibility graph of P. The visibility graph has a vertex for every vertex of P and an edge between two vertices if they see each other, i.e.~if the line segment connecting them lies inside $P$ entirely. While located at a vertex, the robot is capable of ordering the vertices it sees in counter-clockwise order as they appear on the boundary, and for every two such vertices, it can distinguish whether the angle between them is convex (<= pi) or reflex (> pi). Other than that, distant vertices are indistinguishable to the robot. We assume that an upper bound on the number of vertices is known and show that the robot is always capable of reconstructing the visibility graph of P. We also show that multiple identical, indistinguishable and deterministic such robots can always position themselves such that they mutually see each other, i.e. such that they form a clique in the visibility graph.
Cite as

Jeremie Chalopin, Shantanu Das, Yann Disser, Matus Mihalak, and Peter Widmayer. Telling convex from reflex allows to map a polygon. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 153-164, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{chalopin_et_al:LIPIcs.STACS.2011.153,
  author =	{Chalopin, Jeremie and Das, Shantanu and Disser, Yann and Mihalak, Matus and Widmayer, Peter},
  title =	{{Telling convex from reflex allows to map a polygon}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{153--164},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.153},
  URN =		{urn:nbn:de:0030-drops-30077},
  doi =		{10.4230/LIPIcs.STACS.2011.153},
  annote =	{Keywords: polygon mapping, map construction, autonomous agent, simple robot, visibility graph reconstruction}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2010.61
Vertex Disjoint Paths for Dispatching in Railways

Authors: Holger Flier, Matús Mihalák, Anita Schöbel, Peter Widmayer, and Anna Zych

Published in: OASIcs, Volume 14, 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10) (2010)

Abstract
We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routing-in-rounds problem. Although all considered variants are NP-hard in planar graphs, restrictions on the location of the terminals, motivated by railway applications, lead to polynomially solvable cases for the decision and maximization versions of the problem, and to a $p$-approximation algorithm for the routing-in-rounds problem, where $p$ is the maximum number of alternative paths for a terminal pair.
Cite as

Holger Flier, Matús Mihalák, Anita Schöbel, Peter Widmayer, and Anna Zych. Vertex Disjoint Paths for Dispatching in Railways. In 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10). Open Access Series in Informatics (OASIcs), Volume 14, pp. 61-73, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{flier_et_al:OASIcs.ATMOS.2010.61,
  author =	{Flier, Holger and Mihal\'{a}k, Mat\'{u}s and Sch\"{o}bel, Anita and Widmayer, Peter and Zych, Anna},
  title =	{{Vertex Disjoint Paths for Dispatching in Railways}},
  booktitle =	{10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10)},
  pages =	{61--73},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-20-0},
  ISSN =	{2190-6807},
  year =	{2010},
  volume =	{14},
  editor =	{Erlebach, Thomas and L\"{u}bbecke, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2010.61},
  URN =		{urn:nbn:de:0030-drops-27508},
  doi =		{10.4230/OASIcs.ATMOS.2010.61},
  annote =	{Keywords: algorithms, approximation, complexity, graph theory, railways, routing, transportation}
}
Document
DOI: 10.4230/DagSemProc.05031.17
Network Discovery and Verification

Authors: Zuzana Beerliova, Felix Eberhard, Thomas Erlebach, Alexander Hall, Michael Hoffmann, Matus Mihalak, and L. Shankar Ram

Published in: Dagstuhl Seminar Proceedings, Volume 5031, Algorithms for Optimization with Incomplete Information (2005)

Abstract
Consider the problem of discovering (or verifying) the edges and non-edges of a network, modelled as a connected undirected graph, using a minimum number of queries. A query at a vertex v discovers (or verifies) all edges and non-edges whose endpoints have different distance from v. In the network discovery problem, the edges and non-edges are initially unknown, and the algorithm must select the next query based only on the results of previous queries. We study the problem using competitive analysis and give a randomized on-line algorithm with competitive ratio O(sqrt(n*log n)) for graphs with n vertices. We also show that no deterministic algorithm can have competitive ratio better than 3. In the network verification problem, the graph is known in advance and the goal is to compute a minimum number of queries that verify all edges and non-edges. This problem has previously been studied as the problem of placing landmarks in graphs or determining the metric dimension of a graph. We show that there is no approximation algorithm for this problem with ratio o(log n) unless P=NP. Furthermore, we prove that the optimal number of queries for d-dimensional hypercubes is Theta(d/log d).
Cite as

Zuzana Beerliova, Felix Eberhard, Thomas Erlebach, Alexander Hall, Michael Hoffmann, Matus Mihalak, and L. Shankar Ram. Network Discovery and Verification. In Algorithms for Optimization with Incomplete Information. Dagstuhl Seminar Proceedings, Volume 5031, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{beerliova_et_al:DagSemProc.05031.17,
  author =	{Beerliova, Zuzana and Eberhard, Felix and Erlebach, Thomas and Hall, Alexander and Hoffmann, Michael and Mihalak, Matus and Ram, L. Shankar},
  title =	{{Network Discovery and Verification}},
  booktitle =	{Algorithms for Optimization with Incomplete Information},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5031},
  editor =	{Susanne Albers and Rolf H. M\"{o}hring and Georg Ch. Pflug and R\"{u}diger Schultz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05031.17},
  URN =		{urn:nbn:de:0030-drops-594},
  doi =		{10.4230/DagSemProc.05031.17},
  annote =	{Keywords: on-line algorithms , set cover , landmarks , metric dimension}
}

Mihalak, Matus

Document
DOI: 10.4230/OASIcs.ATMOS.2019.3
On Sorting with a Network of Two Stacks

Authors: Matúš Mihalák and Marc Pont

Published in: OASIcs, Volume 75, 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)

Abstract
Sorting with stacks is a collection of problems that deal with sorting a sequence of numbers by pushing and popping the numbers to and from a given set of stacks. Multiple concrete decision or optimization questions are formed by restricting the access to the stacks. The motivation comes, e.g., from shunting train wagons in shunting yards, shunting trams in depots, or in stacking cargo containers on cargo ships or storage yards in transshipment terminals. We consider the problem of sorting a permutation of n integers 1,2,...,n using k >= 2 stacks. In this problem, elements from the input sequence are pushed one-by-one (in the order of the elements in the sequence) to one of the k stacks. At any time, an element from a stack can be popped and pushed to another stack; such an operation is called a shuffle. Also, at any time, an element can be popped from a stack and placed to the output sequence. We can only place the elements to the output in the increasing order of their value such that at the end the output is the ordered sequence of the elements. The problem asks to minimize the number of shuffles in the process. It is known that for k >= 4, the problem is NP-hard, and that there is no approximation algorithm unless P=NP. For k >= 3, it is known that at most O(n log n) shuffles are needed for any input sequence. For the case when k=2, there exist input sequences that require Omega(n^{2-epsilon}) shuffles, for any epsilon>0. Nothing substantially more is known for the case of k=2. In this paper, we study the following variant of the problem with k=2 stacks: no shuffle and no placement to the output sequence can happen before every element is in one of the two stacks. We show that our problem can be seen as the MinUnCut problem by providing a polynomial-time reduction, and thus we show that there exists a randomized O(sqrt{log n})-approximation algorithm and a deterministic O(log n)-approximation algorithm for our problem.
Cite as

Matúš Mihalák and Marc Pont. On Sorting with a Network of Two Stacks. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 3:1-3:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{mihalak_et_al:OASIcs.ATMOS.2019.3,
  author =	{Mihal\'{a}k, Mat\'{u}\v{s} and Pont, Marc},
  title =	{{On Sorting with a Network of Two Stacks}},
  booktitle =	{19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019)},
  pages =	{3:1--3:12},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-128-3},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{75},
  editor =	{Cacchiani, Valentina and Marchetti-Spaccamela, Alberto},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2019.3},
  URN =		{urn:nbn:de:0030-drops-114159},
  doi =		{10.4230/OASIcs.ATMOS.2019.3},
  annote =	{Keywords: Sorting, Stacks, Optimization, Algorithms, Reduction, MinUnCut}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.45
Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm

Authors: Annette M. C. Ficker, Thomas Erlebach, Matús Mihalák, and Frits C. R. Spieksma

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Consider a problem where 4k given vectors need to be partitioned into k clusters of four vectors each. A cluster of four vectors is called a quad, and the cost of a quad is the sum of the component-wise maxima of the four vectors in the quad. The problem is to partition the given 4k vectors into k quads with minimum total cost. We analyze a straightforward matching-based algorithm and prove that this algorithm is a 3/2-approximation algorithm for this problem. We further analyze the performance of this algorithm on a hierarchy of special cases of the problem and prove that, in one particular case, the algorithm is a 5/4-approximation algorithm. Our analysis is tight in all cases except one.
Cite as

Annette M. C. Ficker, Thomas Erlebach, Matús Mihalák, and Frits C. R. Spieksma. Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 45:1-45:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ficker_et_al:LIPIcs.ISAAC.2018.45,
  author =	{Ficker, Annette M. C. and Erlebach, Thomas and Mihal\'{a}k, Mat\'{u}s and Spieksma, Frits C. R.},
  title =	{{Partitioning Vectors into Quadruples: Worst-Case Analysis of a Matching-Based Algorithm}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{45:1--45:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.45},
  URN =		{urn:nbn:de:0030-drops-99933},
  doi =		{10.4230/LIPIcs.ISAAC.2018.45},
  annote =	{Keywords: approximation algorithm, matching, clustering problem}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2018.56
Collective Fast Delivery by Energy-Efficient Agents

Authors: Andreas Bärtschi, Daniel Graf, and Matús Mihalák

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

Abstract
We consider k mobile agents initially located at distinct nodes of an undirected graph (on n nodes, with edge lengths). The agents have to deliver a single item from a given source node s to a given target node t. The agents can move along the edges of the graph, starting at time 0, with respect to the following: Each agent i has a weight omega_i that defines the rate of energy consumption while travelling a distance in the graph, and a velocity upsilon_i with which it can move. We are interested in schedules (operating the k agents) that result in a small delivery time T (time when the item arrives at t), and small total energy consumption E. Concretely, we ask for a schedule that: either (i) Minimizes T, (ii) Minimizes lexicographically (T,E) (prioritizing fast delivery), or (iii) Minimizes epsilon * T + (1-epsilon)* E, for a given epsilon in (0,1). We show that (i) is solvable in polynomial time, and show that (ii) is polynomial-time solvable for uniform velocities and solvable in time O(n+k log k) for arbitrary velocities on paths, but in general is NP-hard even on planar graphs. As a corollary of our hardness result, (iii) is NP-hard, too. We show that there is a 2-approximation algorithm for (iii) using a single agent.
Cite as

Andreas Bärtschi, Daniel Graf, and Matús Mihalák. Collective Fast Delivery by Energy-Efficient Agents. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 56:1-56:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bartschi_et_al:LIPIcs.MFCS.2018.56,
  author =	{B\"{a}rtschi, Andreas and Graf, Daniel and Mihal\'{a}k, Mat\'{u}s},
  title =	{{Collective Fast Delivery by Energy-Efficient Agents}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{56:1--56:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.56},
  URN =		{urn:nbn:de:0030-drops-96381},
  doi =		{10.4230/LIPIcs.MFCS.2018.56},
  annote =	{Keywords: delivery, mobile agents, time/energy optimization, complexity, algorithms}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.68
Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past

Authors: Katerina Böhmová, Matúš Mihalák, Peggy Neubert, Tobias Pröger, and Peter Widmayer

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
Given an urban public transportation network and historic delay information, we consider the problem of computing reliable journeys. We propose new algorithms based on our recently presented solution concept (Böhmová et al., ATMOS 2013), and perform an experimental evaluation using real-world delay data from Zürich, Switzerland. We compare these methods to natural approaches as well as to our recently proposed method which can also be used to measure typicality of past observations. Moreover, we demonstrate how this measure relates to the predictive quality of the individual methods. In particular, if the past observations are typical, then the learning- based methods are able to produce solutions that perform well on typical days, even in the presence of large delays.
Cite as

Katerina Böhmová, Matúš Mihalák, Peggy Neubert, Tobias Pröger, and Peter Widmayer. Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 68-81, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{bohmova_et_al:OASIcs.ATMOS.2015.68,
  author =	{B\"{o}hmov\'{a}, Katerina and Mihal\'{a}k, Mat\'{u}\v{s} and Neubert, Peggy and Pr\"{o}ger, Tobias and Widmayer, Peter},
  title =	{{Robust Routing in Urban Public Transportation: Evaluating Strategies that Learn From the Past}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{68--81},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.68},
  URN =		{urn:nbn:de:0030-drops-54542},
  doi =		{10.4230/OASIcs.ATMOS.2015.68},
  annote =	{Keywords: public transportation, route planning, robustness, optimization, experiments}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2015.82
Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks

Authors: Matúš Mihalák and Sandro Montanari

Published in: OASIcs, Volume 48, 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)

Abstract
Based on time-dependent travel times for N past days, we consider the computation of robust routes according to the min-max relative regret criterion. For this method we seek a path minimizing its maximum weight in any one of the N days, normalized by the weight of an optimum for the respective day. In order to speed-up this computationally demanding approach, we observe that its output belongs to the Pareto front of the network with time-dependent multi-criteria edge weights. We adapt a well-known algorithm for computing Pareto fronts in time-dependent graphs and apply the bi-directional search technique to it. We also show how to parametrize this algorithm by a value K to compute a K-approximate Pareto front. An experimental evaluation for the cases N = 2 and N = 3 indicates a considerable speed-up of the bi-directional search over the uni-directional.
Cite as

Matúš Mihalák and Sandro Montanari. Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks. In 15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015). Open Access Series in Informatics (OASIcs), Volume 48, pp. 82-94, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{mihalak_et_al:OASIcs.ATMOS.2015.82,
  author =	{Mihal\'{a}k, Mat\'{u}\v{s} and Montanari, Sandro},
  title =	{{Bi-directional Search for Robust Routes in Time-dependent Bi-criteria Road Networks}},
  booktitle =	{15th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2015)},
  pages =	{82--94},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-99-6},
  ISSN =	{2190-6807},
  year =	{2015},
  volume =	{48},
  editor =	{Italiano, Giuseppe F. and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2015.82},
  URN =		{urn:nbn:de:0030-drops-54561},
  doi =		{10.4230/OASIcs.ATMOS.2015.82},
  annote =	{Keywords: shortest path, time-dependent, bi-criteria, bi-directional search, min-max relative regret}
}
Document
Complete Volume
DOI: 10.4230/OASIcs.ATMOS.2014
OASIcs, Volume 42, ATMOS'14, Complete Volume

Authors: Stefan Funke and Matúš Mihalák

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Abstract
OASIcs, Volume 42, ATMOS'14, Complete Volume
Cite as

14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Proceedings{funke_et_al:OASIcs.ATMOS.2014,
  title =	{{OASIcs, Volume 42, ATMOS'14, Complete Volume}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014},
  URN =		{urn:nbn:de:0030-drops-47613},
  doi =		{10.4230/OASIcs.ATMOS.2014},
  annote =	{Keywords: Analysis of Algorithms and Problem Complexity, Optimization, Combinatorics, Graph Theory, Applications}
}
Document
Front Matter
DOI: 10.4230/OASIcs.ATMOS.2014.i
Frontmatter, Table of Contents, Preface, Workshop Organization

Authors: Stefan Funke and Matús Mihalák

Published in: OASIcs, Volume 42, 14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2014)

Abstract
Frontmatter, Table of Contents, Preface, Workshop Organization
Cite as

14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 42, pp. i-ix, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{funke_et_al:OASIcs.ATMOS.2014.i,
  author =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  title =	{{Frontmatter, Table of Contents, Preface, Workshop Organization}},
  booktitle =	{14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{i--ix},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-75-0},
  ISSN =	{2190-6807},
  year =	{2014},
  volume =	{42},
  editor =	{Funke, Stefan and Mihal\'{a}k, Mat\'{u}s},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2014.i},
  URN =		{urn:nbn:de:0030-drops-47470},
  doi =		{10.4230/OASIcs.ATMOS.2014.i},
  annote =	{Keywords: Frontmatter, Table of Contents, Preface, Workshop Organization}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2013.27
Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations

Authors: Katerina Böhmová, Matús Mihalák, Tobias Pröger, Rastislav Srámek, and Peter Widmayer

Published in: OASIcs, Volume 33, 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2013)

Abstract
We study the problem of robust routing in urban public transportation networks. In order to propose solutions that are robust for typical delays, we assume that we have past observations of real traffic situations available. In particular, we assume that we have "daily records" containing the observed travel times in the whole network for a few past days. We introduce a new concept to express a solution that is feasible in any record of a given public transportation network. We adapt the method of Buhmann et al. [Buhmann et al., ITCS 2013] for optimization under uncertainty, and develop algorithms that allow its application for finding a robust journey from a given source to a given destination. The performance of the algorithms and the quality of the predicted journey are evaluated in a preliminary experimental study. We furthermore introduce a measure of reliability of a given journey, and develop algorithms for its computation. The robust routing concepts presented in this work are suited specially for public transportation networks of large cities that lack clear hierarchical structure and contain services that run with high frequencies.
Cite as

Katerina Böhmová, Matús Mihalák, Tobias Pröger, Rastislav Srámek, and Peter Widmayer. Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations. In 13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 33, pp. 27-41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{bohmova_et_al:OASIcs.ATMOS.2013.27,
  author =	{B\"{o}hmov\'{a}, Katerina and Mihal\'{a}k, Mat\'{u}s and Pr\"{o}ger, Tobias and Sr\'{a}mek, Rastislav and Widmayer, Peter},
  title =	{{Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations}},
  booktitle =	{13th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{27--41},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-58-3},
  ISSN =	{2190-6807},
  year =	{2013},
  volume =	{33},
  editor =	{Frigioni, Daniele and Stiller, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2013.27},
  URN =		{urn:nbn:de:0030-drops-42428},
  doi =		{10.4230/OASIcs.ATMOS.2013.27},
  annote =	{Keywords: Algorithms, Optimization, Robustness, Route planning, Public transportation}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2011.38
Track Allocation in Freight-Train Classification with Mixed Tracks

Authors: Markus Bohlin, Holger Flier, Jens Maue, and Matús Mihalák

Published in: OASIcs, Volume 20, 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (2011)

Abstract
We consider the process of forming outbound trains from cars of inbound trains at rail-freight hump yards. Given the arrival and departure times as well as the composition of the trains, we study the problem of allocating classification tracks to outbound trains such that every outbound train can be built on a separate classification track. We observe that the core problem can be formulated as a special list coloring problem in interval graphs, which is known to be NP-complete. We focus on an extension where individual cars of different trains can temporarily be stored on a special subset of the tracks. This problem induces several new variants of the list-coloring problem, in which the given intervals can be shortened by cutting off a prefix of the interval. We show that in case of uniform and sufficient track lengths, the corresponding coloring problem can be solved in polynomial time, if the goal is to minimize the total cost associated with cutting off prefixes of the intervals. Based on these results, we devise two heuristics as well as an integer program to tackle the problem. As a case study, we consider a real-world problem instance from the Hallsberg Rangerbangard hump yard in Sweden. Planning over horizons of seven days, we obtain feasible solutions from the integer program in all scenarios, and from the heuristics in most scenarios.
Cite as

Markus Bohlin, Holger Flier, Jens Maue, and Matús Mihalák. Track Allocation in Freight-Train Classification with Mixed Tracks. In 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems. Open Access Series in Informatics (OASIcs), Volume 20, pp. 38-51, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{bohlin_et_al:OASIcs.ATMOS.2011.38,
  author =	{Bohlin, Markus and Flier, Holger and Maue, Jens and Mihal\'{a}k, Mat\'{u}s},
  title =	{{Track Allocation in Freight-Train Classification with Mixed Tracks}},
  booktitle =	{11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems},
  pages =	{38--51},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-33-0},
  ISSN =	{2190-6807},
  year =	{2011},
  volume =	{20},
  editor =	{Caprara, Alberto and Kontogiannis, Spyros},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2011.38},
  URN =		{urn:nbn:de:0030-drops-32658},
  doi =		{10.4230/OASIcs.ATMOS.2011.38},
  annote =	{Keywords: algorithms, complexity, graph theory, railways, scheduling, shunting, train classification, train marshalling, transportation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2011.153
Telling convex from reflex allows to map a polygon

Authors: Jeremie Chalopin, Shantanu Das, Yann Disser, Matus Mihalak, and Peter Widmayer

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract
We consider the exploration of a simple polygon P by a robot that moves from vertex to vertex along edges of the visibility graph of P. The visibility graph has a vertex for every vertex of P and an edge between two vertices if they see each other, i.e.~if the line segment connecting them lies inside $P$ entirely. While located at a vertex, the robot is capable of ordering the vertices it sees in counter-clockwise order as they appear on the boundary, and for every two such vertices, it can distinguish whether the angle between them is convex (<= pi) or reflex (> pi). Other than that, distant vertices are indistinguishable to the robot. We assume that an upper bound on the number of vertices is known and show that the robot is always capable of reconstructing the visibility graph of P. We also show that multiple identical, indistinguishable and deterministic such robots can always position themselves such that they mutually see each other, i.e. such that they form a clique in the visibility graph.
Cite as

Jeremie Chalopin, Shantanu Das, Yann Disser, Matus Mihalak, and Peter Widmayer. Telling convex from reflex allows to map a polygon. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 153-164, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{chalopin_et_al:LIPIcs.STACS.2011.153,
  author =	{Chalopin, Jeremie and Das, Shantanu and Disser, Yann and Mihalak, Matus and Widmayer, Peter},
  title =	{{Telling convex from reflex allows to map a polygon}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{153--164},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.153},
  URN =		{urn:nbn:de:0030-drops-30077},
  doi =		{10.4230/LIPIcs.STACS.2011.153},
  annote =	{Keywords: polygon mapping, map construction, autonomous agent, simple robot, visibility graph reconstruction}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2010.61
Vertex Disjoint Paths for Dispatching in Railways

Authors: Holger Flier, Matús Mihalák, Anita Schöbel, Peter Widmayer, and Anna Zych

Published in: OASIcs, Volume 14, 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10) (2010)

Abstract
We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routing-in-rounds problem. Although all considered variants are NP-hard in planar graphs, restrictions on the location of the terminals, motivated by railway applications, lead to polynomially solvable cases for the decision and maximization versions of the problem, and to a $p$-approximation algorithm for the routing-in-rounds problem, where $p$ is the maximum number of alternative paths for a terminal pair.
Cite as

Holger Flier, Matús Mihalák, Anita Schöbel, Peter Widmayer, and Anna Zych. Vertex Disjoint Paths for Dispatching in Railways. In 10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10). Open Access Series in Informatics (OASIcs), Volume 14, pp. 61-73, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{flier_et_al:OASIcs.ATMOS.2010.61,
  author =	{Flier, Holger and Mihal\'{a}k, Mat\'{u}s and Sch\"{o}bel, Anita and Widmayer, Peter and Zych, Anna},
  title =	{{Vertex Disjoint Paths for Dispatching in Railways}},
  booktitle =	{10th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS'10)},
  pages =	{61--73},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-20-0},
  ISSN =	{2190-6807},
  year =	{2010},
  volume =	{14},
  editor =	{Erlebach, Thomas and L\"{u}bbecke, Marco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2010.61},
  URN =		{urn:nbn:de:0030-drops-27508},
  doi =		{10.4230/OASIcs.ATMOS.2010.61},
  annote =	{Keywords: algorithms, approximation, complexity, graph theory, railways, routing, transportation}
}
Document
DOI: 10.4230/DagSemProc.05031.17
Network Discovery and Verification

Authors: Zuzana Beerliova, Felix Eberhard, Thomas Erlebach, Alexander Hall, Michael Hoffmann, Matus Mihalak, and L. Shankar Ram

Published in: Dagstuhl Seminar Proceedings, Volume 5031, Algorithms for Optimization with Incomplete Information (2005)

Abstract
Consider the problem of discovering (or verifying) the edges and non-edges of a network, modelled as a connected undirected graph, using a minimum number of queries. A query at a vertex v discovers (or verifies) all edges and non-edges whose endpoints have different distance from v. In the network discovery problem, the edges and non-edges are initially unknown, and the algorithm must select the next query based only on the results of previous queries. We study the problem using competitive analysis and give a randomized on-line algorithm with competitive ratio O(sqrt(n*log n)) for graphs with n vertices. We also show that no deterministic algorithm can have competitive ratio better than 3. In the network verification problem, the graph is known in advance and the goal is to compute a minimum number of queries that verify all edges and non-edges. This problem has previously been studied as the problem of placing landmarks in graphs or determining the metric dimension of a graph. We show that there is no approximation algorithm for this problem with ratio o(log n) unless P=NP. Furthermore, we prove that the optimal number of queries for d-dimensional hypercubes is Theta(d/log d).
Cite as

Zuzana Beerliova, Felix Eberhard, Thomas Erlebach, Alexander Hall, Michael Hoffmann, Matus Mihalak, and L. Shankar Ram. Network Discovery and Verification. In Algorithms for Optimization with Incomplete Information. Dagstuhl Seminar Proceedings, Volume 5031, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{beerliova_et_al:DagSemProc.05031.17,
  author =	{Beerliova, Zuzana and Eberhard, Felix and Erlebach, Thomas and Hall, Alexander and Hoffmann, Michael and Mihalak, Matus and Ram, L. Shankar},
  title =	{{Network Discovery and Verification}},
  booktitle =	{Algorithms for Optimization with Incomplete Information},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5031},
  editor =	{Susanne Albers and Rolf H. M\"{o}hring and Georg Ch. Pflug and R\"{u}diger Schultz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05031.17},
  URN =		{urn:nbn:de:0030-drops-594},
  doi =		{10.4230/DagSemProc.05031.17},
  annote =	{Keywords: on-line algorithms , set cover , landmarks , metric dimension}
}
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