24 Search Results for "Röglin, Heiko"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.66
A Parameterized-Complexity Framework for Finding Local Optima

Authors: Robert Ganian, Hung P. Hoang, Christian Komusiewicz, and Nils Morawietz

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood. The traditional frameworks, PLS and the standard algorithm problem, introduced by Johnson, Papadimitriou, and Yannakakis (1988) fail to capture the methodology of local search algorithms: PLS is concerned with finding a local optimum and not with using local search, while the standard algorithm problem restricts each improvement step to follow a fixed pivoting rule. In this work, we introduce a novel formulation of local search which provides a middle ground between these models. In particular, the task is to output not only a local optimum but also a chain of local improvements leading to it. With this framework, we aim to capture the challenge in designing a good pivoting rule. Especially, when combined with the parameterized complexity paradigm, it enables both strong lower bounds and meaningful tractability results. Unlike previous works that combined parameterized complexity with local search, our framework targets the whole task of finding a local optimum and not only a single improvement step. Focusing on two representative meta-problems - Subset Weight Optimization Problem with the c-swap neighborhood and Weighted Circuit with the flip neighborhood - we establish fixed-parameter tractability results related to the number of distinct weights, while ruling out an analogous result when parameterizing by the distance to the nearest optimum via a new type of reduction.
Cite as

Robert Ganian, Hung P. Hoang, Christian Komusiewicz, and Nils Morawietz. A Parameterized-Complexity Framework for Finding Local Optima. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 66:1-66:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ganian_et_al:LIPIcs.ITCS.2026.66,
  author =	{Ganian, Robert and Hoang, Hung P. and Komusiewicz, Christian and Morawietz, Nils},
  title =	{{A Parameterized-Complexity Framework for Finding Local Optima}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{66:1--66:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.66},
  URN =		{urn:nbn:de:0030-drops-253532},
  doi =		{10.4230/LIPIcs.ITCS.2026.66},
  annote =	{Keywords: Local Search, Parameterized Complexity, PLS}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.16
Designing Compact ILPs via Fast Witness Verification

Authors: Michał Włodarczyk

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
The standard formalization of preprocessing in parameterized complexity is given by kernelization. In this work, we depart from this paradigm and study a different type of preprocessing for problems without polynomial kernels, still aiming at producing instances that are easily solvable in practice. Specifically, we ask for which parameterized problems an instance (I,k) can be reduced in polynomial time to an integer linear program (ILP) with poly(k) constraints. We show that this property coincides with the parameterized complexity class WK[1], previously studied in the context of Turing kernelization lower bounds. In turn, the class WK[1] enjoys an elegant characterization in terms of witness verification protocols: a yes-instance should admit a witness of size poly(k) that can be verified in time poly(k). By combining known data structures with new ideas, we design such protocols for several problems, such as r-Way Cut, Vertex Multiway Cut, Steiner Tree, and Minimum Common String Partition, thus showing that they can be modeled by compact ILPs. We also present explicit ILP and MILP formulations for Weighted Vertex Cover on graphs with small (unweighted) vertex cover number. We believe that these results will provide a background for a systematic study of ILP-oriented preprocessing procedures for parameterized problems.
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Michał Włodarczyk. Designing Compact ILPs via Fast Witness Verification. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wlodarczyk:LIPIcs.IPEC.2025.16,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Designing Compact ILPs via Fast Witness Verification}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{16:1--16:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.16},
  URN =		{urn:nbn:de:0030-drops-251481},
  doi =		{10.4230/LIPIcs.IPEC.2025.16},
  annote =	{Keywords: integer programming, kernelization, nondeterminism, multiway cut}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.8
Parameterized Algorithms for the Drone Delivery Problem

Authors: Simon Bartlmae, Andreas Hene, Joshua Könen, and Heiko Röglin

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Timely delivery and optimal routing remain fundamental challenges in the modern logistics industry. Building on prior work that considers single-package delivery across networks using multiple types of collaborative agents with restricted movement areas (e.g., drones or trucks), we examine the complexity of the problem under structural and operational constraints. Our focus is on minimizing total delivery time by coordinating agents that differ in speed and movement range across a graph. This problem formulation aligns with the recently proposed Drone Delivery Problem with respect to delivery time (DDT), introduced by Erlebach et al. [ISAAC 2022]. We first resolve an open question posed by Erlebach et al. [ISAAC 2022] by showing that even when the delivery network is a path graph, DDT admits no polynomial-time approximation within any polynomially encodable factor a(n), unless P=NP. Additionally, we identify the intersection graph of the agents, where nodes represent agents and edges indicate an overlap of the movement areas of two agents, as an important structural concept. For path graphs, we show that DDT becomes tractable when parameterized by the treewidth w of the intersection graph, and we present an exact FPT algorithm with running time f(w)⋅poly(n,k), for some computable function f. For general graphs, we give an FPT algorithm with running time f(Δ,w)⋅poly(n,k), where Δ is the maximum degree of the intersection graph. In the special case where the intersection graph is a tree, we provide a simple polynomial-time algorithm.
Cite as

Simon Bartlmae, Andreas Hene, Joshua Könen, and Heiko Röglin. Parameterized Algorithms for the Drone Delivery Problem. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bartlmae_et_al:LIPIcs.ISAAC.2025.8,
  author =	{Bartlmae, Simon and Hene, Andreas and K\"{o}nen, Joshua and R\"{o}glin, Heiko},
  title =	{{Parameterized Algorithms for the Drone Delivery Problem}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.8},
  URN =		{urn:nbn:de:0030-drops-249162},
  doi =		{10.4230/LIPIcs.ISAAC.2025.8},
  annote =	{Keywords: Complexity, Delivery, FPT algorithms, Graph Theory}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.63
Connected k-Median with Disjoint and Non-Disjoint Clusters

Authors: Jan Eube, Kelin Luo, Dorian Reineccius, Heiko Röglin, and Melanie Schmidt

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The connected k-median problem is a constrained clustering problem that combines distance-based k-clustering with connectivity information. The problem allows to input a metric space and an unweighted undirected connectivity graph that is completely unrelated to the metric space. The goal is to compute k centers and corresponding clusters such that each cluster forms a connected subgraph of G, and such that the k-median cost is minimized. The problem has applications in very different fields like geodesy (particularly districting), social network analysis (especially community detection), or bioinformatics. We study a version with overlapping clusters where points can be part of multiple clusters which is natural for the use case of community detection. This problem variant is Ω(log n)-hard to approximate, and our main result is an 𝒪(k² log n)-approximation algorithm for the problem. We complement it with an Ω(n^{1-ε})-hardness result for the case of disjoint clusters without overlap with general connectivity graphs, as well as an exact algorithm in this setting if the connectivity graph is a tree.
Cite as

Jan Eube, Kelin Luo, Dorian Reineccius, Heiko Röglin, and Melanie Schmidt. Connected k-Median with Disjoint and Non-Disjoint Clusters. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 63:1-63:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eube_et_al:LIPIcs.ESA.2025.63,
  author =	{Eube, Jan and Luo, Kelin and Reineccius, Dorian and R\"{o}glin, Heiko and Schmidt, Melanie},
  title =	{{Connected k-Median with Disjoint and Non-Disjoint Clusters}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{63:1--63:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.63},
  URN =		{urn:nbn:de:0030-drops-245317},
  doi =		{10.4230/LIPIcs.ESA.2025.63},
  annote =	{Keywords: Clustering, Connectivity constraints, Approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.115
Smoothed Analysis of Online Metric Problems

Authors: Christian Coester and Jack Umenberger

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We study three classical online problems - k-server, k-taxi, and chasing size k sets - through a lens of smoothed analysis. Our setting allows request locations to be adversarial up to small perturbations, interpolating between worst-case and average-case models. Specifically, we show that if the metric space is contained in a ball in any normed space and requests are drawn from distributions whose density functions are upper bounded by 1/σ times the uniform density over the ball, then all three problems admit polylog(k/σ)-competitive algorithms. Our approach is simple: it reduces smoothed instances to fully adversarial instances on finite metrics and leverages existing algorithms in a black-box manner. We also provide a lower bound showing that no algorithm can achieve a competitive ratio sub-polylogarithmic in k/σ, matching our upper bounds up to the exponent of the polylogarithm. In contrast, the best known competitive ratios for these problems in the fully adversarial setting are 2k-1, ∞ and Θ(k²), respectively.
Cite as

Christian Coester and Jack Umenberger. Smoothed Analysis of Online Metric Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 115:1-115:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{coester_et_al:LIPIcs.ESA.2025.115,
  author =	{Coester, Christian and Umenberger, Jack},
  title =	{{Smoothed Analysis of Online Metric Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{115:1--115:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.115},
  URN =		{urn:nbn:de:0030-drops-245847},
  doi =		{10.4230/LIPIcs.ESA.2025.115},
  annote =	{Keywords: Online Algorithms, Competitive Analysis, Smoothed Analysis, k-server, k-taxi, Metrical Service Systems}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.105
Parameterized Algorithms for Computing Pareto Sets

Authors: Joshua Marc Könen, Heiko Röglin, and Tarek Stuck

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
The problem of computing the set of Pareto-optimal solutions has been studied for a variety of multiobjective optimization problems. For many such problems, algorithms are known that compute the Pareto set in (weak) output-polynomial time. These algorithms are often based on dynamic programming and by weak output-polynomial time, we mean that the running time depends polynomially on the size of the Pareto set but also on the sizes of the Pareto sets of the subproblems that occur in the dynamic program. For some problems, like the multiobjective minimum spanning tree problem, such algorithms are not known to exist and for other problems, like multiobjective versions of many NP-hard problems, such algorithms cannot exist, unless 𝒫 = 𝒩𝒫. Dynamic programming over tree decompositions is a common technique in parameterized algorithms. In this paper, we study whether this technique can also be applied to compute Pareto sets of multiobjective optimization problems. We first derive an algorithm to compute the Pareto set for the multicriteria s-t cut problem and show how this result can be applied to a polygon aggregation problem arising in cartography that has recently been introduced by Rottmann et al. (GIScience 2021). We also show how to apply these techniques to also compute the Pareto set of the multiobjective minimum spanning tree problem and for the multiobjective TSP. The running time of our algorithms is O(f(w)⋅poly(n,p_{max})), where f is some function in the treewidth w, n is the input size, and p_{max} is an upper bound on the size of the Pareto sets of the subproblems that occur in the dynamic program. Finally, we present an experimental evaluation of computing Pareto sets on real-world instances of polygon aggregation problems. For this matter we devised a task-specific data structure that allows for efficient storage and modification of large sets of Pareto-optimal solutions. Throughout the implementation process, we incorporated several improved strategies and heuristics that significantly reduced both runtime and memory usage, enabling us to solve instances with treewidth of up to 22 within reasonable amount of time. Moreover, we conducted a preprocessing study to compare different tree decompositions in terms of their estimated overall runtime.
Cite as

Joshua Marc Könen, Heiko Röglin, and Tarek Stuck. Parameterized Algorithms for Computing Pareto Sets. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 105:1-105:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{konen_et_al:LIPIcs.ESA.2025.105,
  author =	{K\"{o}nen, Joshua Marc and R\"{o}glin, Heiko and Stuck, Tarek},
  title =	{{Parameterized Algorithms for Computing Pareto Sets}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{105:1--105:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.105},
  URN =		{urn:nbn:de:0030-drops-245749},
  doi =		{10.4230/LIPIcs.ESA.2025.105},
  annote =	{Keywords: parameterized algorithms, treewidth, multicriteria optimization problems, multicriteria MST, multicriteria TSP, polygon aggregation}
}
Artifact
Software
DOI: 10.4230/artifacts.24714
Bicriteria Aggregation

Authors: Joshua Marc Könen, Heiko Röglin, and Tarek Stuck

Abstract
Cite as

Joshua Marc Könen, Heiko Röglin, Tarek Stuck. Bicriteria Aggregation (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-24714,
   title = {{Bicriteria Aggregation}}, 
   author = {K\"{o}nen, Joshua Marc and R\"{o}glin, Heiko and Stuck, Tarek},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:b6eacf189792239e9115cf288be27c6753b8df17;origin=https://github.com/Tarek-pub/Bicriteria_Aggregation;visit=swh:1:snp:6062d834e514947614ecb3cd421cafb02a5cd7f5;anchor=swh:1:rev:029970db0ee7425b1739d3c87bfa94e3f9081dbd}{\texttt{swh:1:dir:b6eacf189792239e9115cf288be27c6753b8df17}} (visited on 2025-10-01)},
   url = {https://github.com/Tarek-pub/Bicriteria_Aggregation},
   doi = {10.4230/artifacts.24714},
}
Artifact
InteractiveResource
DOI: 10.4230/artifacts.24713
Bicriteria Aggregation Plotting

Authors: Joshua Marc Könen, Heiko Röglin, and Tarek Stuck

Abstract
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Joshua Marc Könen, Heiko Röglin, Tarek Stuck. Bicriteria Aggregation Plotting (InteractiveResource). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-24713,
   title = {{Bicriteria Aggregation Plotting}}, 
   author = {K\"{o}nen, Joshua Marc and R\"{o}glin, Heiko and Stuck, Tarek},
   note = {InteractiveResource (visited on 2025-10-01)},
   url = {https://github.com/Tarek-pub/Bicriteria_Aggregation_plotting},
   doi = {10.4230/artifacts.24713},
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.21
On the Performance of Mildly Greedy Players in k-Coloring Games

Authors: Vittorio Bilò, Andrea D'Ascenzo, Mattia D'Emidio, and Giuseppe F. Italiano

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We study the performance of mildly greedy players in k-coloring games, a relevant subclass of anti-coordination games. A mildly greedy player is a selfish agent who is willing to deviate from a certain strategy profile only if her payoff improves by a factor of more than ε, for some given ε ≥ 0. In presence of mildly greedy players, stability is captured by the concept of (1+ε)-approximate Nash equilibrium. In this paper, we first show that, for any k-coloring game, the (1+ε)-approximate price of anarchy, i.e., the price of anarchy of (1+ε)-approximate pure Nash equilibria, is at least (k-1)/((k-1)ε +k), and that this bound is tight for any ε ≥ 0. Then, we evaluate the approximation ratio of the solutions achieved after a (1 + ϵ)-approximate one-round walk starting from any initial strategy profile, where a (1 + ϵ)-approximate one-round walk is a sequence of (1 + ε)-approximate best-responses, one for each player. We provide a lower bound of min{(k-2)/k, (k-1)/((k-1)ε+k)} on this ratio, for any ε ≥ 0 and k ≥ 5; for the cases of k = 3 and k = 4, we give finer bounds depending on ε. Our work generalizes the results known for cut games, the special case of k-coloring games restricted to k = 2.
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Vittorio Bilò, Andrea D'Ascenzo, Mattia D'Emidio, and Giuseppe F. Italiano. On the Performance of Mildly Greedy Players in k-Coloring Games. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bilo_et_al:LIPIcs.MFCS.2025.21,
  author =	{Bil\`{o}, Vittorio and D'Ascenzo, Andrea and D'Emidio, Mattia and Italiano, Giuseppe F.},
  title =	{{On the Performance of Mildly Greedy Players in k-Coloring Games}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{21:1--21:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.21},
  URN =		{urn:nbn:de:0030-drops-241287},
  doi =		{10.4230/LIPIcs.MFCS.2025.21},
  annote =	{Keywords: Coloring games, (Approximate) Nash Equilibria, Price of Anarchy}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.73
Counting Locally Optimal Tours in the TSP

Authors: Bodo Manthey and Jesse van Rhijn

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We show that the problem of counting 2-optimal tours in instances of the Travelling Salesperson Problem (TSP) on complete graphs is #P-complete. In addition, we show that the expected number of 2-optimal tours in random instances of the TSP on complete graphs is O(1.2098ⁿ √{n!}). Based on numerical experiments, we conjecture that the true bound is at most O(√{n!}), which is approximately the square root of the total number of tours.
Cite as

Bodo Manthey and Jesse van Rhijn. Counting Locally Optimal Tours in the TSP. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 73:1-73:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{manthey_et_al:LIPIcs.MFCS.2025.73,
  author =	{Manthey, Bodo and van Rhijn, Jesse},
  title =	{{Counting Locally Optimal Tours in the TSP}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{73:1--73:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.73},
  URN =		{urn:nbn:de:0030-drops-241807},
  doi =		{10.4230/LIPIcs.MFCS.2025.73},
  annote =	{Keywords: Travelling salesman problem, probabilistic analysis, local search, heuristics, 2-opt}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.15
When Distances Lie: Euclidean Embeddings in the Presence of Outliers and Distance Violations

Authors: Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, M. S. Ramanujan, and Saket Saurabh

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
Distance geometry explores the properties of distance spaces that can be exactly represented as the pairwise Euclidean distances between points in ℝ^d (d ≥ 1), or equivalently, distance spaces that can be isometrically embedded in ℝ^d. In this work, we investigate whether a distance space can be isometrically embedded in ℝ^d after applying a limited number of modifications. Specifically, we focus on two types of modifications: outlier deletion (removing points) and distance modification (adjusting distances between points). The central problem, Euclidean Embedding Editing, asks whether an input distance space on n points can be transformed, using at most k modifications, into a space that is isometrically embeddable in ℝ^d. We present several fixed-parameter tractable (FPT) and approximation algorithms for this problem. Our first result is an algorithm that solves Euclidean Embedding Editing in time (dk)^𝒪(d+k) + n^𝒪(1). The core subroutine of this algorithm, which is of independent interest, is a polynomial-time method for compressing the input distance space into an equivalent instance of Euclidean Embedding Editing with 𝒪((dk)²) points. For the special but important case of Euclidean Embedding Editing where only outlier deletions are allowed, we improve the parameter dependence of the FPT algorithm and obtain a running time of min{(d+3)^k, 2^{d+k}} ⋅ n^𝒪(1). Additionally, we provide an FPT-approximation algorithm for this problem, which outputs a set of at most 2 ⋅ Opt outliers in time 2^d ⋅ n^{𝒪(1)}. This 2-approximation algorithm improves upon the previous (3+ε)-approximation algorithm by Sidiropoulos, Wang, and Wang [SODA '17]. Furthermore, we complement our algorithms with hardness results motivating our choice of parameterizations.
Cite as

Matthias Bentert, Fedor V. Fomin, Petr A. Golovach, M. S. Ramanujan, and Saket Saurabh. When Distances Lie: Euclidean Embeddings in the Presence of Outliers and Distance Violations. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 15:1-15:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.SoCG.2025.15,
  author =	{Bentert, Matthias and Fomin, Fedor V. and Golovach, Petr A. and Ramanujan, M. S. and Saurabh, Saket},
  title =	{{When Distances Lie: Euclidean Embeddings in the Presence of Outliers and Distance Violations}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{15:1--15:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.15},
  URN =		{urn:nbn:de:0030-drops-231672},
  doi =		{10.4230/LIPIcs.SoCG.2025.15},
  annote =	{Keywords: Parameterized Complexity, Euclidean Embedding, FPT-approximation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.57
Approximate Minimum Tree Cover in All Symmetric Monotone Norms Simultaneously

Authors: Matthias Kaul, Kelin Luo, Matthias Mnich, and Heiko Röglin

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
We study the problem of partitioning a set of n objects in a metric space into k clusters V₁,...,V_k. The quality of the clustering is measured by considering the vector of cluster costs and then minimizing some monotone symmetric norm of that vector (in particular, this includes the 𝓁_p-norms). For the costs of the clusters we take the weight of a minimum-weight spanning tree on the objects in V_i, which may serve as a proxy for the cost of traversing all objects in the cluster, for example in the context of Multirobot Coverage as studied by Zheng, Koenig, Kempe, Jain (IROS 2005), but also as a shape-invariant measure of cluster density similar to Single-Linkage Clustering. This problem has been studied by Even, Garg, Könemann, Ravi, Sinha (Oper. Res. Lett., 2004) for the setting of minimizing the weight of the largest cluster (i.e., using 𝓁_∞) as Min-Max Tree Cover, for which they gave a constant-factor approximation algorithm. We provide a careful adaptation of their algorithm to compute solutions which are approximately optimal with respect to all monotone symmetric norms simultaneously, and show how to find them in polynomial time. In fact, our algorithm is purely combinatorial and can process metric spaces with 10,000 points in less than a second. As an extension, we also consider the case where instead of a target number of clusters we are provided with a set of depots in the space such that every cluster should contain at least one such depot. One can consider these as the fixed starting points of some agents that will traverse all points of a cluster. For this setting also we are able to give a polynomial-time algorithm computing a constant-factor approximation with respect to all monotone symmetric norms simultaneously. To show that the algorithmic results are tight up to the precise constant of approximation attainable, we also prove that such clustering problems are already APX-hard when considering only one single 𝓁_p norm for the objective.
Cite as

Matthias Kaul, Kelin Luo, Matthias Mnich, and Heiko Röglin. Approximate Minimum Tree Cover in All Symmetric Monotone Norms Simultaneously. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 57:1-57:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kaul_et_al:LIPIcs.STACS.2025.57,
  author =	{Kaul, Matthias and Luo, Kelin and Mnich, Matthias and R\"{o}glin, Heiko},
  title =	{{Approximate Minimum Tree Cover in All Symmetric Monotone Norms Simultaneously}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{57:1--57:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.57},
  URN =		{urn:nbn:de:0030-drops-228821},
  doi =		{10.4230/LIPIcs.STACS.2025.57},
  annote =	{Keywords: Clustering, spanning trees, all-norm approximation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.50
Connected k-Center and k-Diameter Clustering

Authors: Lukas Drexler, Jan Eube, Kelin Luo, Heiko Röglin, Melanie Schmidt, and Julian Wargalla

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

Abstract
Motivated by an application from geodesy, we study the connected k-center problem and the connected k-diameter problem. These problems arise from the classical k-center and k-diameter problems by adding a side constraint. For the side constraint, we are given an undirected connectivity graph G on the input points, and a clustering is now only feasible if every cluster induces a connected subgraph in G. Usually in clustering problems one assumes that the clusters are pairwise disjoint. We study this case but additionally also the case that clusters are allowed to be non-disjoint. This can help to satisfy the connectivity constraints. Our main result is an O(1)-approximation algorithm for the disjoint connected k-center and k-diameter problem for Euclidean spaces of low dimension (constant d) and for metrics with constant doubling dimension. For general metrics, we get an O(log²k)-approximation. Our algorithms work by computing a non-disjoint connected clustering first and transforming it into a disjoint connected clustering. We complement these upper bounds by several upper and lower bounds for variations and special cases of the model.
Cite as

Lukas Drexler, Jan Eube, Kelin Luo, Heiko Röglin, Melanie Schmidt, and Julian Wargalla. Connected k-Center and k-Diameter Clustering. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{drexler_et_al:LIPIcs.ICALP.2023.50,
  author =	{Drexler, Lukas and Eube, Jan and Luo, Kelin and R\"{o}glin, Heiko and Schmidt, Melanie and Wargalla, Julian},
  title =	{{Connected k-Center and k-Diameter Clustering}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{50:1--50:20},
  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.2023.50},
  URN =		{urn:nbn:de:0030-drops-181024},
  doi =		{10.4230/LIPIcs.ICALP.2023.50},
  annote =	{Keywords: Approximation algorithms, Clustering, Connectivity constraints}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.10
The Price of Hierarchical Clustering

Authors: Anna Arutyunova and Heiko Röglin

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
Hierarchical Clustering is a popular tool for understanding the hereditary properties of a data set. Such a clustering is actually a sequence of clusterings that starts with the trivial clustering in which every data point forms its own cluster and then successively merges two existing clusters until all points are in the same cluster. A hierarchical clustering achieves an approximation factor of α if the costs of each k-clustering in the hierarchy are at most α times the costs of an optimal k-clustering. We study as cost functions the maximum (discrete) radius of any cluster (k-center problem) and the maximum diameter of any cluster (k-diameter problem). In general, the optimal clusterings do not form a hierarchy and hence an approximation factor of 1 cannot be achieved. We call the smallest approximation factor that can be achieved for any instance the price of hierarchy. For the k-diameter problem we improve the upper bound on the price of hierarchy to 3+2√2≈ 5.83. Moreover we significantly improve the lower bounds for k-center and k-diameter, proving a price of hierarchy of exactly 4 and 3+2√2, respectively.
Cite as

Anna Arutyunova and Heiko Röglin. The Price of Hierarchical Clustering. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{arutyunova_et_al:LIPIcs.ESA.2022.10,
  author =	{Arutyunova, Anna and R\"{o}glin, Heiko},
  title =	{{The Price of Hierarchical Clustering}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.10},
  URN =		{urn:nbn:de:0030-drops-169487},
  doi =		{10.4230/LIPIcs.ESA.2022.10},
  annote =	{Keywords: Hierarchical Clustering, approximation Algorithms, k-center Problem}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2022.7
Minimum-Error Triangulations for Sea Surface Reconstruction

Authors: Anna Arutyunova, Anne Driemel, Jan-Henrik Haunert, Herman Haverkort, Jürgen Kusche, Elmar Langetepe, Philip Mayer, Petra Mutzel, and Heiko Röglin

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
We apply state-of-the-art computational geometry methods to the problem of reconstructing a time-varying sea surface from tide gauge records. Our work builds on a recent article by Nitzke et al. (Computers & Geosciences, 157:104920, 2021) who have suggested to learn a triangulation D of a given set of tide gauge stations. The objective is to minimize the misfit of the piecewise linear surface induced by D to a reference surface that has been acquired with satellite altimetry. The authors restricted their search to k-order Delaunay (k-OD) triangulations and used an integer linear program in order to solve the resulting optimization problem. In geometric terms, the input to our problem consists of two sets of points in ℝ² with elevations: a set 𝒮 that is to be triangulated, and a set ℛ of reference points. Intuitively, we define the error of a triangulation as the average vertical distance of a point in ℛ to the triangulated surface that is obtained by interpolating elevations of 𝒮 linearly in each triangle. Our goal is to find the triangulation of 𝒮 that has minimum error with respect to ℛ. In our work, we prove that the minimum-error triangulation problem is NP-hard and cannot be approximated within any multiplicative factor in polynomial time unless P = NP. At the same time we show that the problem instances that occur in our application (considering sea level data from several hundreds of tide gauge stations worldwide) can be solved relatively fast using dynamic programming when restricted to k-OD triangulations for k ≤ 7. In particular, instances for which the number of connected components of the so-called k-OD fixed-edge graph is small can be solved within few seconds.
Cite as

Anna Arutyunova, Anne Driemel, Jan-Henrik Haunert, Herman Haverkort, Jürgen Kusche, Elmar Langetepe, Philip Mayer, Petra Mutzel, and Heiko Röglin. Minimum-Error Triangulations for Sea Surface Reconstruction. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{arutyunova_et_al:LIPIcs.SoCG.2022.7,
  author =	{Arutyunova, Anna and Driemel, Anne and Haunert, Jan-Henrik and Haverkort, Herman and Kusche, J\"{u}rgen and Langetepe, Elmar and Mayer, Philip and Mutzel, Petra and R\"{o}glin, Heiko},
  title =	{{Minimum-Error Triangulations for Sea Surface Reconstruction}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.7},
  URN =		{urn:nbn:de:0030-drops-160155},
  doi =		{10.4230/LIPIcs.SoCG.2022.7},
  annote =	{Keywords: Minimum-Error Triangulation, k-Order Delaunay Triangulations, Data dependent Triangulations, Sea Surface Reconstruction, fixed-Edge Graph}
}
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