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Documents authored by Disser, Yann

Document
DOI: 10.4230/LIPIcs.ESA.2024.15
A (5/3+ε)-Approximation for Tricolored Non-Crossing Euclidean TSP

Authors: Júlia Baligács, Yann Disser, Andreas Emil Feldmann, and Anna Zych-Pawlewicz

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
In the Tricolored Euclidean Traveling Salesperson problem, we are given k = 3 sets of points in the plane and are looking for disjoint tours, each covering one of the sets. Arora (1998) famously gave a PTAS based on "patching" for the case k = 1 and, recently, Dross et al. (2023) generalized this result to k = 2. Our contribution is a (5/3+ε)-approximation algorithm for k = 3 that further generalizes Arora’s approach. It is believed that patching is generally no longer possible for more than two tours. We circumvent this issue by either applying a conditional patching scheme for three tours or using an alternative approach based on a weighted solution for k = 2.
Cite as

Júlia Baligács, Yann Disser, Andreas Emil Feldmann, and Anna Zych-Pawlewicz. A (5/3+ε)-Approximation for Tricolored Non-Crossing Euclidean TSP. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baligacs_et_al:LIPIcs.ESA.2024.15,
  author =	{Balig\'{a}cs, J\'{u}lia and Disser, Yann and Feldmann, Andreas Emil and Zych-Pawlewicz, Anna},
  title =	{{A (5/3+\epsilon)-Approximation for Tricolored Non-Crossing Euclidean TSP}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.15},
  URN =		{urn:nbn:de:0030-drops-210862},
  doi =		{10.4230/LIPIcs.ESA.2024.15},
  annote =	{Keywords: Approximation Algorithms, geometric Network Optimization, Euclidean TSP, non-crossing Structures}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.47
Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem

Authors: Yann Disser, Svenja M. Griesbach, Max Klimm, and Annette Lutz

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We consider an incremental variant of the rooted prize-collecting Steiner-tree problem with a growing budget constraint. While no incremental solution exists that simultaneously approximates the optimum for all budgets, we show that a bicriterial (α,μ)-approximation is possible, i.e., a solution that with budget B+α for all B ∈ ℝ_{≥ 0} is a multiplicative μ-approximation compared to the optimum solution with budget B. For the case that the underlying graph is a tree, we present a polynomial-time density-greedy algorithm that computes a (χ,1)-approximation, where χ denotes the eccentricity of the root vertex in the underlying graph, and show that this is best possible. An adaptation of the density-greedy algorithm for general graphs is (γ,2)-competitive where γ is the maximal length of a vertex-disjoint path starting in the root. While this algorithm does not run in polynomial time, it can be adapted to a (γ,3)-competitive algorithm that runs in polynomial time. We further devise a capacity-scaling algorithm that guarantees a (3χ,8)-approximation and, more generally, a ((4𝓁 - 1)χ, (2^{𝓁 + 2})/(2^𝓁 -1))-approximation for every fixed 𝓁 ∈ ℕ.
Cite as

Yann Disser, Svenja M. Griesbach, Max Klimm, and Annette Lutz. Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{disser_et_al:LIPIcs.ESA.2024.47,
  author =	{Disser, Yann and Griesbach, Svenja M. and Klimm, Max and Lutz, Annette},
  title =	{{Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{47:1--47:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.47},
  URN =		{urn:nbn:de:0030-drops-211188},
  doi =		{10.4230/LIPIcs.ESA.2024.47},
  annote =	{Keywords: incremental optimization, competitive analysis, prize-collecting Steiner-tree}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.27
A Unified Worst Case for Classical Simplex and Policy Iteration Pivot Rules

Authors: Yann Disser and Nils Mosis

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
We construct a family of Markov decision processes for which the policy iteration algorithm needs an exponential number of improving switches with Dantzig’s rule, with Bland’s rule, and with the Largest Increase pivot rule. This immediately translates to a family of linear programs for which the simplex algorithm needs an exponential number of pivot steps with the same three pivot rules. Our results yield a unified construction that simultaneously reproduces well-known lower bounds for these classical pivot rules, and we are able to infer that any (deterministic or randomized) combination of them cannot avoid an exponential worst-case behavior. Regarding the policy iteration algorithm, pivot rules typically switch multiple edges simultaneously and our lower bound for Dantzig’s rule and the Largest Increase rule, which perform only single switches, seem novel. Regarding the simplex algorithm, the individual lower bounds were previously obtained separately via deformed hypercube constructions. In contrast to previous bounds for the simplex algorithm via Markov decision processes, our rigorous analysis is reasonably concise.
Cite as

Yann Disser and Nils Mosis. A Unified Worst Case for Classical Simplex and Policy Iteration Pivot Rules. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{disser_et_al:LIPIcs.ISAAC.2023.27,
  author =	{Disser, Yann and Mosis, Nils},
  title =	{{A Unified Worst Case for Classical Simplex and Policy Iteration Pivot Rules}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.27},
  URN =		{urn:nbn:de:0030-drops-193292},
  doi =		{10.4230/LIPIcs.ISAAC.2023.27},
  annote =	{Keywords: Bland’s pivot rule, Dantzig’s pivot rule, Largest Increase pivot rule, Markov decision process, policy iteration, simplex algorithm}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.11
Exploration of Graphs with Excluded Minors

Authors: Júlia Baligács, Yann Disser, Irene Heinrich, and Pascal Schweitzer

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

Abstract
We study the online graph exploration problem proposed by Kalyanasundaram and Pruhs (1994) and prove a constant competitive ratio on minor-free graphs. This result encompasses and significantly extends the graph classes that were previously known to admit a constant competitive ratio. The main ingredient of our proof is that we find a connection between the performance of the particular exploration algorithm Blocking and the existence of light spanners. Conversely, we exploit this connection to construct light spanners of bounded genus graphs. In particular, we achieve a lightness that improves on the best known upper bound for genus g ≥ 1 and recovers the known tight bound for the planar case (g = 0).
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Júlia Baligács, Yann Disser, Irene Heinrich, and Pascal Schweitzer. Exploration of Graphs with Excluded Minors. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baligacs_et_al:LIPIcs.ESA.2023.11,
  author =	{Balig\'{a}cs, J\'{u}lia and Disser, Yann and Heinrich, Irene and Schweitzer, Pascal},
  title =	{{Exploration of Graphs with Excluded Minors}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.11},
  URN =		{urn:nbn:de:0030-drops-186644},
  doi =		{10.4230/LIPIcs.ESA.2023.11},
  annote =	{Keywords: online algorithms, competitive analysis, graph exploration, graph spanners, minor-free graphs, bounded genus graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.47
Incremental Maximization via Continuization

Authors: Yann Disser, Max Klimm, Kevin Schewior, and David Weckbecker

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

Abstract
We consider the problem of finding an incremental solution to a cardinality-constrained maximization problem that not only captures the solution for a fixed cardinality, but also describes how to gradually grow the solution as the cardinality bound increases. The goal is to find an incremental solution that guarantees a good competitive ratio against the optimum solution for all cardinalities simultaneously. The central challenge is to characterize maximization problems where this is possible, and to determine the best-possible competitive ratio that can be attained. A lower bound of 2.18 and an upper bound of φ + 1 ≈ 2.618 are known on the competitive ratio for monotone and accountable objectives [Bernstein et al., Math. Prog., 2022], which capture a wide range of maximization problems. We introduce a continuization technique and identify an optimal incremental algorithm that provides strong evidence that φ + 1 is the best-possible competitive ratio. Using this continuization, we obtain an improved lower bound of 2.246 by studying a particular recurrence relation whose characteristic polynomial has complex roots exactly beyond the lower bound. Based on the optimal continuous algorithm combined with a scaling approach, we also provide a 1.772-competitive randomized algorithm. We complement this by a randomized lower bound of 1.447 via Yao’s principle.
Cite as

Yann Disser, Max Klimm, Kevin Schewior, and David Weckbecker. Incremental Maximization via Continuization. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 47:1-47:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{disser_et_al:LIPIcs.ICALP.2023.47,
  author =	{Disser, Yann and Klimm, Max and Schewior, Kevin and Weckbecker, David},
  title =	{{Incremental Maximization via Continuization}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{47:1--47:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.47},
  URN =		{urn:nbn:de:0030-drops-180992},
  doi =		{10.4230/LIPIcs.ICALP.2023.47},
  annote =	{Keywords: incremental optimization, competitive analysis, robust matching, submodular function}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.5
On Sparse Hitting Sets: From Fair Vertex Cover to Highway Dimension

Authors: Johannes Blum, Yann Disser, Andreas Emil Feldmann, Siddharth Gupta, and Anna Zych-Pawlewicz

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
We consider the Sparse Hitting Set (Sparse-HS) problem, where we are given a set system (V,ℱ,ℬ) with two families ℱ,ℬ of subsets of the universe V. The task is to find a hitting set for ℱ that minimizes the maximum number of elements in any of the sets of ℬ. This generalizes several problems that have been studied in the literature. Our focus is on determining the complexity of some of these special cases of Sparse-HS with respect to the sparseness k, which is the optimum number of hitting set elements in any set of ℬ (i.e., the value of the objective function). For the Sparse Vertex Cover (Sparse-VC) problem, the universe is given by the vertex set V of a graph, and ℱ is its edge set. We prove NP-hardness for sparseness k ≥ 2 and polynomial time solvability for k = 1. We also provide a polynomial-time 2-approximation algorithm for any k. A special case of Sparse-VC is Fair Vertex Cover (Fair-VC), where the family ℬ is given by vertex neighbourhoods. For this problem it was open whether it is FPT (or even XP) parameterized by the sparseness k. We answer this question in the negative, by proving NP-hardness for constant k. We also provide a polynomial-time (2-1/k)-approximation algorithm for Fair-VC, which is better than any approximation algorithm possible for Sparse-VC or the Vertex Cover problem (under the Unique Games Conjecture). We then switch to a different set of problems derived from Sparse-HS related to the highway dimension, which is a graph parameter modelling transportation networks. In recent years a growing literature has shown interesting algorithms for graphs of low highway dimension. To exploit the structure of such graphs, most of them compute solutions to the r-Shortest Path Cover (r-SPC) problem, where r > 0, ℱ contains all shortest paths of length between r and 2r, and ℬ contains all balls of radius 2r. It is known that there is an XP algorithm that computes solutions to r-SPC of sparseness at most h if the input graph has highway dimension h. However it was not known whether a corresponding FPT algorithm exists as well. We prove that r-SPC and also the related r-Highway Dimension (r-HD) problem, which can be used to formally define the highway dimension of a graph, are both W[1]-hard. Furthermore, by the result of Abraham et al. [ICALP 2011] there is a polynomial-time O(log k)-approximation algorithm for r-HD, but for r-SPC such an algorithm is not known. We prove that r-SPC admits a polynomial-time O(log n)-approximation algorithm.
Cite as

Johannes Blum, Yann Disser, Andreas Emil Feldmann, Siddharth Gupta, and Anna Zych-Pawlewicz. On Sparse Hitting Sets: From Fair Vertex Cover to Highway Dimension. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 5:1-5:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blum_et_al:LIPIcs.IPEC.2022.5,
  author =	{Blum, Johannes and Disser, Yann and Feldmann, Andreas Emil and Gupta, Siddharth and Zych-Pawlewicz, Anna},
  title =	{{On Sparse Hitting Sets: From Fair Vertex Cover to Highway Dimension}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{5:1--5:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.5},
  URN =		{urn:nbn:de:0030-drops-173612},
  doi =		{10.4230/LIPIcs.IPEC.2022.5},
  annote =	{Keywords: sparse hitting set, fair vertex cover, highway dimension}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2020.17
Recoloring Interval Graphs with Limited Recourse Budget

Authors: Bartłomiej Bosek, Yann Disser, Andreas Emil Feldmann, Jakub Pawlewicz, and Anna Zych-Pawlewicz

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

Abstract
We consider the problem of coloring an interval graph dynamically. Intervals arrive one after the other and have to be colored immediately such that no two intervals of the same color overlap. In each step only a limited number of intervals may be recolored to maintain a proper coloring (thus interpolating between the well-studied online and offline settings). The number of allowed recolorings per step is the so-called recourse budget. Our main aim is to prove both upper and lower bounds on the required recourse budget for interval graphs, given a bound on the allowed number of colors. For general interval graphs with n vertices and chromatic number k it is known that some recoloring is needed even if we have 2k colors available. We give an algorithm that maintains a 2k-coloring with an amortized recourse budget of 𝒪(log n). For maintaining a k-coloring with k ≤ n, we give an amortized upper bound of 𝒪(k⋅ k! ⋅ √n), and a lower bound of Ω(k) for k ∈ 𝒪(√n), which can be as large as Ω(√n). For unit interval graphs it is known that some recoloring is needed even if we have k+1 colors available. We give an algorithm that maintains a (k+1)-coloring with at most 𝒪(k²) recolorings per step in the worst case. We also give a lower bound of Ω(log n) on the amortized recourse budget needed to maintain a k-coloring. Additionally, for general interval graphs we show that if one does not insist on maintaining an explicit coloring, one can have a k-coloring algorithm which does not incur a factor of 𝒪(k ⋅ k! ⋅ √n) in the running time. For this we provide a data structure, which allows for adding intervals in 𝒪(k² log³ n) amortized time per update and querying for the color of a particular interval in 𝒪(log n) time. Between any two updates, the data structure answers consistently with some optimal coloring. The data structure maintains the coloring implicitly, so the notion of recourse budget does not apply to it.
Cite as

Bartłomiej Bosek, Yann Disser, Andreas Emil Feldmann, Jakub Pawlewicz, and Anna Zych-Pawlewicz. Recoloring Interval Graphs with Limited Recourse Budget. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 17:1-17:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bosek_et_al:LIPIcs.SWAT.2020.17,
  author =	{Bosek, Bart{\l}omiej and Disser, Yann and Feldmann, Andreas Emil and Pawlewicz, Jakub and Zych-Pawlewicz, Anna},
  title =	{{Recoloring Interval Graphs with Limited Recourse Budget}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{17:1--17:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.17},
  URN =		{urn:nbn:de:0030-drops-122649},
  doi =		{10.4230/LIPIcs.SWAT.2020.17},
  annote =	{Keywords: Colouring, Dynamic Algorithms, Recourse Budget, Interval Graphs}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.21
Improved Bounds for Open Online Dial-a-Ride on the Line

Authors: Alexander Birx, Yann Disser, and Kevin Schewior

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
We consider the open, non-preemptive online Dial-a-Ride problem on the real line, where transportation requests appear over time and need to be served by a single server. We give a lower bound of 2.0585 on the competitive ratio, which is the first bound that strictly separates online Dial-a-Ride on the line from online TSP on the line in terms of competitive analysis, and is the best currently known lower bound even for general metric spaces. On the other hand, we present an algorithm that improves the best known upper bound from 2.9377 to 2.6662. The analysis of our algorithm is tight.
Cite as

Alexander Birx, Yann Disser, and Kevin Schewior. Improved Bounds for Open Online Dial-a-Ride on the Line. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{birx_et_al:LIPIcs.APPROX-RANDOM.2019.21,
  author =	{Birx, Alexander and Disser, Yann and Schewior, Kevin},
  title =	{{Improved Bounds for Open Online Dial-a-Ride on the Line}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.21},
  URN =		{urn:nbn:de:0030-drops-112367},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.21},
  annote =	{Keywords: dial-a-ride on the line, elevator problem, online algorithms, competitive analysis, smartstart, competitive ratio}
}
Document
DOI: 10.4230/LIPIcs.STACS.2019.15
Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line

Authors: Alexander Birx and Yann Disser

Published in: LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

Abstract
The online Dial-a-Ride problem is a fundamental online problem in a metric space, where transportation requests appear over time and may be served in any order by a single server with unit speed. Restricted to the real line, online Dial-a-Ride captures natural problems like controlling a personal elevator. Tight results in terms of competitive ratios are known for the general setting and for online TSP on the line (where source and target of each request coincide). In contrast, online Dial-a-Ride on the line has resisted tight analysis so far, even though it is a very natural online problem. We conduct a tight competitive analysis of the Smartstart algorithm that gave the best known results for the general, metric case. In particular, our analysis yields a new upper bound of 2.94 for open, non-preemptive online Dial-a-Ride on the line, which improves the previous bound of 3.41 [Krumke'00]. The best known lower bound remains 2.04 [SODA'17]. We also show that the known upper bound of 2 [STACS'00] regarding Smartstart’s competitive ratio for closed, non-preemptive online Dial-a-Ride is tight on the line.
Cite as

Alexander Birx and Yann Disser. Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{birx_et_al:LIPIcs.STACS.2019.15,
  author =	{Birx, Alexander and Disser, Yann},
  title =	{{Tight Analysis of the Smartstart Algorithm for Online Dial-a-Ride on the Line}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{15:1--15:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Niedermeier, Rolf and Paul, Christophe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.15},
  URN =		{urn:nbn:de:0030-drops-102543},
  doi =		{10.4230/LIPIcs.STACS.2019.15},
  annote =	{Keywords: dial-a-ride on the line, elevator problem, online algorithms, competitive analysis, smartstart, competitive ratio}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.51
Distance-Preserving Graph Contractions

Authors: Aaron Bernstein, Karl Däubel, Yann Disser, Max Klimm, Torsten Mütze, and Frieder Smolny

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
Compression and sparsification algorithms are frequently applied in a preprocessing step before analyzing or optimizing large networks/graphs. In this paper we propose and study a new framework contracting edges of a graph (merging vertices into super-vertices) with the goal of preserving pairwise distances as accurately as possible. Formally, given an edge-weighted graph, the contraction should guarantee that for any two vertices at distance d, the corresponding super-vertices remain at distance at least \varphi(d) in the contracted graph, where \varphi is a tolerance function bounding the permitted distance distortion. We present a comprehensive picture of the algorithmic complexity of the contraction problem for affine tolerance functions \varphi(x)=x/\alpha-\beta, where \alpha \geq 1 and \beta \geq 0 are arbitrary real-valued parameters. Specifically, we present polynomial-time algorithms for trees as well as hardness and inapproximability results for different graph classes, precisely separating easy and hard cases. Further we analyze the asymptotic behavior of the size of contractions, and find efficient algorithms to compute (non-optimal) contractions despite our hardness results.
Cite as

Aaron Bernstein, Karl Däubel, Yann Disser, Max Klimm, Torsten Mütze, and Frieder Smolny. Distance-Preserving Graph Contractions. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 51:1-51:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bernstein_et_al:LIPIcs.ITCS.2018.51,
  author =	{Bernstein, Aaron and D\"{a}ubel, Karl and Disser, Yann and Klimm, Max and M\"{u}tze, Torsten and Smolny, Frieder},
  title =	{{Distance-Preserving Graph Contractions}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{51:1--51:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.51},
  URN =		{urn:nbn:de:0030-drops-83427},
  doi =		{10.4230/LIPIcs.ITCS.2018.51},
  annote =	{Keywords: distance oracle, contraction, spanner}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.43
General Bounds for Incremental Maximization

Authors: Aaron Bernstein, Yann Disser, and Martin Groß

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

Abstract
We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value k in N that grows over time, and we allow the solution to be extended one element at a time. We investigate the best-possible competitive ratio of such an incremental solution, i.e., the worst ratio over all k between the incremental solution after~$k$ steps and an optimum solution of cardinality k. We define a large class of problems that contains many important cardinality constrained maximization problems like maximum matching, knapsack, and packing/covering problems. We provide a general 2.618-competitive incremental algorithm for this class of problems, and show that no algorithm can have competitive ratio below 2.18 in general. In the second part of the paper, we focus on the inherently incremental greedy algorithm that increases the objective value as much as possible in each step. This algorithm is known to be 1.58-competitive for submodular objective functions, but it has unbounded competitive ratio for the class of incremental problems mentioned above. We define a relaxed submodularity condition for the objective function, capturing problems like maximum (weighted) (b-)matching and a variant of the maximum flow problem. We show that the greedy algorithm has competitive ratio (exactly) 2.313 for the class of problems that satisfy this relaxed submodularity condition. Note that our upper bounds on the competitive ratios translate to approximation ratios for the underlying cardinality constrained problems.
Cite as

Aaron Bernstein, Yann Disser, and Martin Groß. General Bounds for Incremental Maximization. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 43:1-43:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bernstein_et_al:LIPIcs.ICALP.2017.43,
  author =	{Bernstein, Aaron and Disser, Yann and Gro{\ss}, Martin},
  title =	{{General Bounds for Incremental Maximization}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{43:1--43:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.43},
  URN =		{urn:nbn:de:0030-drops-74650},
  doi =		{10.4230/LIPIcs.ICALP.2017.43},
  annote =	{Keywords: incremental optimization, maximization problems, greedy algorithm, competitive analysis, cardinality constraint}
}
Document
DOI: 10.4230/LIPIcs.STACS.2017.10
Energy-Efficient Delivery by Heterogeneous Mobile Agents

Authors: Andreas Bärtschi, Jérémie Chalopin, Shantanu Das, Yann Disser, Daniel Graf, Jan Hackfeld, and Paolo Penna

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract
We consider the problem of delivering m messages between specified source-target pairs in an undirected graph, by k mobile agents initially located at distinct nodes of the graph. Each edge has a designated length and each agent consumes energy proportional to the distance it travels in the graph. We are interested in optimizing the total energy consumption for the team of agents. Unlike previous related work, we consider heterogeneous agents with different rates of energy consumption (weights w_i). To solve the delivery problem, agents face three major challenges: Collaboration (how to work together on each message), Planning (which route to take) and Coordination (how to assign agents to messages). We first show that the delivery problem can be 2-approximated without collaborating and that this is best possible, i.e., we show that the benefit of collaboration is 2 in general. We also show that the benefit of collaboration for a single message is 1 / log 2 which is approximately 1.44. Planning turns out to be NP-hard to approximate even for a single agent, but can be 2-approximated in polynomial time if agents have unit capacities and do not collaborate. We further show that coordination is NP-hard even for agents with unit capacity, but can be efficiently solved exactly if they additionally have uniform weights. Finally, we give a polynomial-time c-approximation for message delivery with unit capacities.
Cite as

Andreas Bärtschi, Jérémie Chalopin, Shantanu Das, Yann Disser, Daniel Graf, Jan Hackfeld, and Paolo Penna. Energy-Efficient Delivery by Heterogeneous Mobile Agents. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bartschi_et_al:LIPIcs.STACS.2017.10,
  author =	{B\"{a}rtschi, Andreas and Chalopin, J\'{e}r\'{e}mie and Das, Shantanu and Disser, Yann and Graf, Daniel and Hackfeld, Jan and Penna, Paolo},
  title =	{{Energy-Efficient Delivery by Heterogeneous Mobile Agents}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.10},
  URN =		{urn:nbn:de:0030-drops-70233},
  doi =		{10.4230/LIPIcs.STACS.2017.10},
  annote =	{Keywords: message delivery, mobile agents, energy optimization, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2017.26
Robust and Adaptive Search

Authors: Yann Disser and Stefan Kratsch

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract
Binary search finds a given element in a sorted array with an optimal number of log n queries. However, binary search fails even when the array is only slightly disordered or access to its elements is subject to errors. We study the worst-case query complexity of search algorithms that are robust to imprecise queries and that adapt to perturbations of the order of the elements. We give (almost) tight results for various parameters that quantify query errors and that measure array disorder. In particular, we exhibit settings where query complexities of log n + ck, (1+epsilon) log n + ck, and sqrt(cnk)+o(nk) are best-possible for parameter value k, any epsilon > 0, and constant c.
Cite as

Yann Disser and Stefan Kratsch. Robust and Adaptive Search. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 26:1-26:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{disser_et_al:LIPIcs.STACS.2017.26,
  author =	{Disser, Yann and Kratsch, Stefan},
  title =	{{Robust and Adaptive Search}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{26:1--26:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.26},
  URN =		{urn:nbn:de:0030-drops-70077},
  doi =		{10.4230/LIPIcs.STACS.2017.26},
  annote =	{Keywords: searching, robustness, adaptive algorithms, memory faults, array disorder}
}
Document
DOI: 10.4230/LIPIcs.STACS.2014.276
Packing a Knapsack of Unknown Capacity

Authors: Yann Disser, Max Klimm, Nicole Megow, and Sebastian Stiller

Published in: LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

Abstract
We study the problem of packing a knapsack without knowing its capacity. Whenever we attempt to pack an item that does not fit, the item is discarded; if the item fits, we have to include it in the packing. We show that there is always a policy that packs a value within factor 2 of the optimum packing, irrespective of the actual capacity. If all items have unit density, we achieve a factor equal to the golden ratio. Both factors are shown to be best possible. In fact, we obtain the above factors using packing policies that are universal in the sense that they fix a particular order of the items and try to pack the items in this order, independent of the observations made while packing. We give efficient algorithms computing these policies. On the other hand, we show that, for any a>1, the problem of deciding whether a given universal policy achieves a factor of a is coNP-complete. If a is part of the input, the same problem is shown to be coNP-complete for items with unit densities. Finally, we show that it is coNP-hard to decide, for given a, whether a set of items admits a universal policy with factor a, even if all items have unit densities.
Cite as

Yann Disser, Max Klimm, Nicole Megow, and Sebastian Stiller. Packing a Knapsack of Unknown Capacity. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 276-287, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{disser_et_al:LIPIcs.STACS.2014.276,
  author =	{Disser, Yann and Klimm, Max and Megow, Nicole and Stiller, Sebastian},
  title =	{{Packing a Knapsack of Unknown Capacity}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{276--287},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Mayr, Ernst W. and Portier, Natacha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.276},
  URN =		{urn:nbn:de:0030-drops-44642},
  doi =		{10.4230/LIPIcs.STACS.2014.276},
  annote =	{Keywords: Knapsack, unknown capacity, robustness, approximation algorithms}
}
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}
}
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