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Volume

OASIcs, Volume 137

25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

ATMOS 2025, September 18-19, 2025, Warsaw, Poland

Editors: Jonas Sauer and Marie Schmidt

Document

DOI: 10.4230/LIPIcs.CPM.2026.20

Longest Common Extension of a Dynamic String in Parallel Constant Time

Authors: Daniel Alexander Albert

Published in: LIPIcs, Volume 369, 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)

Abstract

A longest common extension (LCE) query on a string computes the length of the longest common suffix or prefix at two given positions. A dynamic LCE algorithm maintains a data structure that allows efficient LCE queries on a string that can change via character insertions and deletions. A dynamic parallel constant-time algorithm is presented that can maintain LCE queries on a common CRCW PRAM with 𝒪(n^ε) work, for any ε > 0. The algorithm maintains a string synchronizing sets hierarchy, which it uses to answer substring equality queries, which it in turn uses to answer LCE queries. To achieve constant runtime, the algorithm allows parts of its information to become outdated by up to log n log^* n updates. It answers queries by combining this slightly outdated information with a list of the recent changes. Two applications of this dynamic LCE algorithm are shown. Firstly, a dynamic parallel constant-time algorithm can maintain membership in a Dyck language D_k, k > 0 with 𝒪(n^ε) work for any ε > 0. Secondly, a dynamic parallel constant-time algorithm can maintain squares with 𝒪(n^ε) work for any ε > 0.

Cite as

Daniel Alexander Albert. Longest Common Extension of a Dynamic String in Parallel Constant Time. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{albert:LIPIcs.CPM.2026.20,
  author =	{Albert, Daniel Alexander},
  title =	{{Longest Common Extension of a Dynamic String in Parallel Constant Time}},
  booktitle =	{37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026)},
  pages =	{20:1--20:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-420-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{369},
  editor =	{Bille, Philip and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2026.20},
  URN =		{urn:nbn:de:0030-drops-259467},
  doi =		{10.4230/LIPIcs.CPM.2026.20},
  annote =	{Keywords: Dynamic Strings, Work, Parallel Constant Time, Longest Common Extension, Longest Common Prefix}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.54

Approximating Pareto Sum via Bounded Monotone Min-Plus Convolution

Authors: Geri Gokaj, Marvin Künnemann, Sabine Storandt, and Carina Truschel

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

The Pareto sum of two-dimensional point sets P and Q in ℝ² is defined as the skyline of the points in their Minkowski sum. The problem of efficiently computing the Pareto sum arises frequently in bi-criteria optimization algorithms. Prior work establishes that computing the Pareto sum of sets P and Q of size n suffers from conditional lower bounds that rule out strongly subquadratic O(n^{2-ε})-time algorithms, even when the output size is Θ(n). Naturally, we ask: How efficiently can we approximate Pareto sums, both in theory and practice? Can we beat the near-quadratic-time state of the art for exact algorithms? On the theoretical side, we formulate a notion of additively approximate Pareto sets and show that computing an approximate Pareto set is fine-grained equivalent to Bounded Monotone Min-Plus Convolution. Leveraging a remarkable Õ(n^{1.5})-time algorithm for the latter problem (Chi, Duan, Xie, Zhang; STOC '22), we thus obtain a strongly subquadratic (and conditionally optimal) approximation algorithm for computing Pareto sums. On the practical side, we engineer different algorithmic approaches for approximating Pareto sets on realistic instances. Our implementations enable a granular trade-off between approximation quality and running time/output size compared to the state of the art for exact algorithms established in (Funke, Hespe, Sanders, Storandt, Truschel; Algorithmica '25). Perhaps surprisingly, the (theoretical) connection to Bounded Monotone Min-Plus Convolution remains beneficial even for our implementations: in particular, we implement a simplified, yet still subquadratic version of an algorithm due to Chi, Duan, Xie and Zhang, which on some sufficiently large instances outperforms the competing quadratic-time approaches.

Cite as

Geri Gokaj, Marvin Künnemann, Sabine Storandt, and Carina Truschel. Approximating Pareto Sum via Bounded Monotone Min-Plus Convolution. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 54:1-54:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gokaj_et_al:LIPIcs.SoCG.2026.54,
  author =	{Gokaj, Geri and K\"{u}nnemann, Marvin and Storandt, Sabine and Truschel, Carina},
  title =	{{Approximating Pareto Sum via Bounded Monotone Min-Plus Convolution}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{54:1--54:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.54},
  URN =		{urn:nbn:de:0030-drops-258602},
  doi =		{10.4230/LIPIcs.SoCG.2026.54},
  annote =	{Keywords: computational geometry, fine-grained complexity, algorithm engineering}
}

Document

DOI: 10.4230/LIPIcs.SoCG.2026.44

Tilt Automata: Gathering Particles with Uniform External Control

Authors: Sándor P. Fekete, Jonas Friemel, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract

Motivated by targeted drug delivery, we investigate the gathering of particles in the full tilt model of externally controlled motion planning: A set of particles is located at the tiles of a polyomino with all particles reacting uniformly to an external force by moving as far as possible in one of the four axis-parallel directions until they hit the boundary. The goal is to choose a sequence of directions that moves all particles to a common position. Our results include a polynomial-time algorithm for gathering in a completely filled polyomino as well as hardness reductions for approximating shortest gathering sequences and for determining whether the particles in a partially filled polyomino can be gathered. We pay special attention to the impact of restricted geometry, particularly polyominoes without holes. As a corollary, we make progress on an open question from [Balanza-Martinez et al., SODA 2020] by showing that deciding whether a given position can be occupied remains NP-hard in polyominoes without holes. Our results build on a connection we establish between tilt models and the theory of synchronizing automata.

Cite as

Sándor P. Fekete, Jonas Friemel, Peter Kramer, Jan-Marc Reinhardt, Christian Rieck, and Christian Scheffer. Tilt Automata: Gathering Particles with Uniform External Control. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fekete_et_al:LIPIcs.SoCG.2026.44,
  author =	{Fekete, S\'{a}ndor P. and Friemel, Jonas and Kramer, Peter and Reinhardt, Jan-Marc and Rieck, Christian and Scheffer, Christian},
  title =	{{Tilt Automata: Gathering Particles with Uniform External Control}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{44:1--44:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.44},
  URN =		{urn:nbn:de:0030-drops-258508},
  doi =		{10.4230/LIPIcs.SoCG.2026.44},
  annote =	{Keywords: Uniform control, gathering, full tilt, polyominoes, synchronizing automata}
}

Document

DOI: 10.4230/LIPIcs.IPEC.2025.4

On the Complexity of Secluded Path Problems

Authors: Tesshu Hanaka and Daisuke Tsuru

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

Abstract

This paper investigates the complexity of finding secluded paths in graphs. We focus on the Short Secluded Path problem and a natural new variant we introduce, Shortest Secluded Path. Formally, given an undirected graph G = (V, E), two vertices s,t ∈ V, and two integers k,l, the Short Secluded Path problem asks whether there exists an s-t path of length at most k with at most l neighbors. This problem is known to be computationally hard: it is W[1]-hard when parameterized by the path length k or by cliquewidth, and para-NP-complete when parameterized by the number l of neighbors. The fixed-parameter tractability is known for k+l or treewidth. In this paper, we expand the parameterized complexity landscape by designing (1) an XP algorithm parameterized by cliquewidth and (2) fixed-parameter algorithms parameterized by neighborhood diversity and twin cover number, respectively. As a byproduct, our results also provide parameterized algorithms for the classic s-t k-Path problem. Furthermore, we introduce the Shortest Secluded Path problem, which seeks a shortest s-t path with the minimum number of neighbors. In contrast to the hardness of the original problem, we reveal that this variant is solvable in polynomial time on unweighted graphs. We complete this by showing that for edge-weighted graphs, the problem becomes W[1]-hard yet remains in XP when parameterized by the shortest path distance between s and t.

Cite as

Tesshu Hanaka and Daisuke Tsuru. On the Complexity of Secluded Path Problems. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hanaka_et_al:LIPIcs.IPEC.2025.4,
  author =	{Hanaka, Tesshu and Tsuru, Daisuke},
  title =	{{On the Complexity of Secluded Path Problems}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{4:1--4:16},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-251361},
  doi =		{10.4230/LIPIcs.IPEC.2025.4},
  annote =	{Keywords: Secluded path, Parameterized complexity, Polynomial-time algorithm}
}

Document

Research

DOI: 10.4230/TGDK.3.3.4

Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web

Authors: Florian Ruosch, Cristina Sarasua, and Abraham Bernstein

Published in: TGDK, Volume 3, Issue 3 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 3

Abstract

In Argument Mining, predicting argumentative relations between texts (or spans) remains one of the most challenging aspects, even more so in the cross-document setting. This paper makes three key contributions to advance research in this domain. We first extend an existing dataset, the Sci-Arg corpus, by annotating it with explicit inter-document argumentative relations, thereby allowing arguments to be distributed over several documents forming an Argument Web; these new annotations are published using Semantic Web technologies (RDF, OWL). Second, we explore and evaluate three automated approaches for predicting these inter-document argumentative relations, establishing critical baselines on the new dataset. We find that a simple classifier based on discourse indicators with access to context outperforms neural methods. Third, we conduct a comparative analysis of these approaches for both intra- and inter-document settings, identifying statistically significant differences in results that indicate the necessity of distinguishing between these two scenarios. Our findings highlight significant challenges in this complex domain and open crucial avenues for future research on the Argument Web of Science, particularly for those interested in leveraging Semantic Web technologies and knowledge graphs to understand scholarly discourse. With this, we provide the first stepping stones in the form of a benchmark dataset, three baseline methods, and an initial analysis for a systematic exploration of this field relevant to the Web of Data and Science.

Cite as

Florian Ruosch, Cristina Sarasua, and Abraham Bernstein. Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 3, pp. 4:1-4:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{ruosch_et_al:TGDK.3.3.4,
  author =	{Ruosch, Florian and Sarasua, Cristina and Bernstein, Abraham},
  title =	{{Mining Inter-Document Argument Structures in Scientific Papers for an Argument Web}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{4:1--4:33},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{3},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.3.4},
  URN =		{urn:nbn:de:0030-drops-252159},
  doi =		{10.4230/TGDK.3.3.4},
  annote =	{Keywords: Argument Mining, Large Language Models, Knowledge Graphs, Link Prediction}
}

Document

Invited Paper

DOI: 10.4230/OASIcs.RW.2024/2025.6

Explaining Reasoning Results for Description Logic Ontologies (Invited Paper)

Authors: Patrick Koopmann

Published in: OASIcs, Volume 138, Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025)

Abstract

The Web Ontology Language (OWL), grounded in description logics, enables reasoning systems to infer implicit knowledge in a transparent manner. However, the expressivity of description logics and the complexity of large ontologies often results in reasoning outcomes that are hard to understand without additional tool support. Explanations of these outcomes are essential for users to understand ontology content, communicate its structure and behavior effectively, and debug undesired or missing inferences. This chapter provides an overview of the central explanation techniques that have been developed for explaining reasoning with description logic ontologies. Here, we consider both explanations for positive entailments (explaining why something can be deduced), as well as negative entailments (why something cannot be deduced). More specifically, we discuss justifications, proofs and interpolation as a means to explain positive entailments, and abduction for explaining negative entailments, where we also have a closer look at practical algorithms as well as practical and theoretical challenges.

Cite as

Patrick Koopmann. Explaining Reasoning Results for Description Logic Ontologies (Invited Paper). In Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 & RW 2025). Open Access Series in Informatics (OASIcs), Volume 138, pp. 6:1-6:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koopmann:OASIcs.RW.2024/2025.6,
  author =	{Koopmann, Patrick},
  title =	{{Explaining Reasoning Results for Description Logic Ontologies}},
  booktitle =	{Joint Proceedings of the 20th and 21st Reasoning Web Summer Schools (RW 2024 \& RW 2025)},
  pages =	{6:1--6:29},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-405-5},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{138},
  editor =	{Artale, Alessandro and Bienvenu, Meghyn and Garc{\'\i}a, Yazm{\'\i}n Ib\'{a}\~{n}ez and Murlak, Filip},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.RW.2024/2025.6},
  URN =		{urn:nbn:de:0030-drops-250514},
  doi =		{10.4230/OASIcs.RW.2024/2025.6},
  annote =	{Keywords: Explanations, Justifications, Proofs, Craig Interpolation, Contrastive Explanations}
}

Document

DOI: 10.4230/LIPIcs.ISAAC.2025.53

A Parameterized Study of Secluded Structures in Directed Graphs

Authors: Jonas Schmidt, Shaily Verma, and Nadym Mallek

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

Abstract

Given an undirected graph G and an integer k, the Secluded Π-Subgraph problem asks you to find a maximum size induced subgraph that satisfies a property Π and has at most k neighbors in the rest of the graph. This problem has been extensively studied; however, there is no prior study of the problem in directed graphs. This question has been mentioned by Jansen et al. [ISAAC'23]. In this paper, we initiate the study of Secluded Subgraph problems in directed graphs by incorporating different notions of neighborhoods: in-neighborhood, out-neighborhood, and their union. Formally, we call these problems {In, Out, Total}-Secluded Π-Subgraph, where given a directed graph G and an integer k, we want to find an induced subgraph satisfying Π of maximum size that has at most k in/out/total-neighbors in the rest of the graph, respectively. We investigate the parameterized complexity of these problems for different properties Π. In particular, we prove the following parameterized results: - We design an FPT algorithm for the Total-Secluded Strongly Connected Subgraph problem when parameterized by k. - We show that the Out-Secluded ℱ-Free Subgraph problem with parameter k is W[1]-hard, where ℱ is a family of directed graphs except any subgraph of a star graph whose edges are directed towards the center. This result also implies that In/Out-Secluded DAG is W[1]-hard, unlike the undirected variants of the two problems, which are FPT. - We design an FPT-algorithm for In/Out/Total-Secluded α-Bounded Subgraph when parameterized by k, where α-bounded graphs are a superclass of tournaments. - For undirected graphs, we improve the best-known FPT algorithm for Secluded Clique by providing a faster FPT algorithm that runs in time 1.6181^k n^𝒪(1).

Cite as

Jonas Schmidt, Shaily Verma, and Nadym Mallek. A Parameterized Study of Secluded Structures in Directed Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 53:1-53:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schmidt_et_al:LIPIcs.ISAAC.2025.53,
  author =	{Schmidt, Jonas and Verma, Shaily and Mallek, Nadym},
  title =	{{A Parameterized Study of Secluded Structures in Directed Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{53:1--53:21},
  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.2025.53},
  URN =		{urn:nbn:de:0030-drops-249616},
  doi =		{10.4230/LIPIcs.ISAAC.2025.53},
  annote =	{Keywords: Secluded Subgraph, Parametrized Complexity, Directed Graphs, Strong Connectivity}
}

Document

DOI: 10.4230/OASIcs.ATMOS.2025.15

Exact and Heuristic Dynamic Taxi Sharing with Transfers Using Shortest-Path Speedup Techniques

Authors: Johannes Breitling and Moritz Laupichler

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract

We introduce a first-of-its-kind efficient, exact algorithm for the dynamic taxi-sharing problem with single-transfer journeys, i.e., a dispatcher that assigns traveler requests to a fleet of shared taxi-like vehicles allowing transfers between vehicles. We extend an existing no-transfer solution by collecting all viable pickup and dropoff vehicles for a request and computing the optimal transfer point for every pair of vehicles. We analyze underlying shortest-path problems and employ state-of-the-art routing algorithms to compute distances on-the-fly, which serves as the basis of dispatching requests with exact and up-to-date travel time information. We utilize constraints on existing routes, pruning techniques for transfer points, and both instruction- and thread-level parallelism to speed up the computation of the best assignment for every traveler. In addition to the exact variant, we propose a tunable heuristic approach that sacrifices solution quality in favor of improved running time. We evaluate our algorithm on a large road network with realistic input sets (up to 150000 requests). We demonstrate the effectiveness of our speedup techniques and the heuristic. We show first results on the benefits of transfers for taxi sharing on dense request sets, proving that our algorithm is well suited for the analysis of taxi sharing with transfers on large input instances.

Cite as

Johannes Breitling and Moritz Laupichler. Exact and Heuristic Dynamic Taxi Sharing with Transfers Using Shortest-Path Speedup Techniques. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 15:1-15:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{breitling_et_al:OASIcs.ATMOS.2025.15,
  author =	{Breitling, Johannes and Laupichler, Moritz},
  title =	{{Exact and Heuristic Dynamic Taxi Sharing with Transfers Using Shortest-Path Speedup Techniques}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{15:1--15:22},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas 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.2025.15},
  URN =		{urn:nbn:de:0030-drops-247718},
  doi =		{10.4230/OASIcs.ATMOS.2025.15},
  annote =	{Keywords: Dynamic taxi sharing, ride pooling, dial-a-ride problem, transfers, route planning}
}

Document

DOI: 10.4230/OASIcs.ATMOS.2025.17

The Line-Based Dial-a-Ride Problem with Transfers

Authors: Jonas Barth, Kendra Reiter, and Marie Schmidt

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract

We introduce the line-based dial-a-ride problem with transfers (liDARPT), a variation of the well-studied dial-a-ride problem (DARP), where vehicles transport requests on-demand but are constrained to operate along a set of lines, and passengers are allowed to transfer between lines on their journey. We develop an event-based solution approach for the liDARPT that relies on the construction of an event-based graph and uses a MILP to find optimal circulations in the event-based graph. To make this solution approach effective, we devise a pre-processing routine to limit the size of the event-based graph. We extensively test our approach on novel benchmark instances, inspired by real-life long-distance bus networks. In our experiments, problem instances with up to 80 requests can be solved to optimality within 15 minutes, and an average of 99.69% of requests are accepted in all instances solved to optimality.

Cite as

Jonas Barth, Kendra Reiter, and Marie Schmidt. The Line-Based Dial-a-Ride Problem with Transfers. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{barth_et_al:OASIcs.ATMOS.2025.17,
  author =	{Barth, Jonas and Reiter, Kendra and Schmidt, Marie},
  title =	{{The Line-Based Dial-a-Ride Problem with Transfers}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{17:1--17:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas 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.2025.17},
  URN =		{urn:nbn:de:0030-drops-247736},
  doi =		{10.4230/OASIcs.ATMOS.2025.17},
  annote =	{Keywords: dial-a-ride, line-based, transfers, on-demand, ridepooling}
}

Document

DOI: 10.4230/OASIcs.ATMOS.2025.16

A Model for Strategic Ridepooling and Its Integration with Line Planning

Authors: Lena Dittrich, Michael Rihlmann, Sarah Roth, and Anita Schöbel

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract

Ridepooling becomes more and more popular and providing comfortable and easy-to-use transportation (nearly as taxi rides) is known to motivate passengers to use public transport. In this paper we develop a model for strategic planning of ridepooling. Here we decide in which regions ridepooling should be offered and what capacities are needed, neglecting the operational details of dial-a-ride planning. We use this model for integrating ridepooling and line planning, and analyze the integrated model theoretically and numerically. Our experiments show the potential of the approach.

Cite as

Lena Dittrich, Michael Rihlmann, Sarah Roth, and Anita Schöbel. A Model for Strategic Ridepooling and Its Integration with Line Planning. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dittrich_et_al:OASIcs.ATMOS.2025.16,
  author =	{Dittrich, Lena and Rihlmann, Michael and Roth, Sarah and Sch\"{o}bel, Anita},
  title =	{{A Model for Strategic Ridepooling and Its Integration with Line Planning}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{16:1--16:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas 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.2025.16},
  URN =		{urn:nbn:de:0030-drops-247720},
  doi =		{10.4230/OASIcs.ATMOS.2025.16},
  annote =	{Keywords: Multi-modal planning, Line plan, Ridepooling, Integrated models}
}

Document

DOI: 10.4230/OASIcs.ATMOS.2025.18

Energy-Efficient Line Planning by Implementing Express Lines

Authors: Sarah Roth and Anita Schöbel

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract

While a shift from individual transport to public transport reduces greenhouse gas emissions, public transport itself also consumes a non-negligible amount of energy. Acceleration processes have a high part in that, especially in urban transportation networks where stops are not far from each other. Express lines which skip stops hence use less energy than a vehicle on a normal line on the same route. Additionally, they increase the attractiveness of public transport by reducing travel times. In this paper, we introduce the express line planning problem ELP which extends the well-known line planning problem by the additional planning of express lines and which stops they skip. The problem is stated in a bicriteria setting minimizing the passengers travel time and the energy consumption of the public transport system. We investigate the problem’s complexity and develop two different MIP formulations and show their equivalence. The models are tested numerically on medium sized instances.

Cite as

Sarah Roth and Anita Schöbel. Energy-Efficient Line Planning by Implementing Express Lines. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 18:1-18:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{roth_et_al:OASIcs.ATMOS.2025.18,
  author =	{Roth, Sarah and Sch\"{o}bel, Anita},
  title =	{{Energy-Efficient Line Planning by Implementing Express Lines}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{18:1--18:21},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas 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.2025.18},
  URN =		{urn:nbn:de:0030-drops-247746},
  doi =		{10.4230/OASIcs.ATMOS.2025.18},
  annote =	{Keywords: Line Planning, Express Lines, Sustainable Public Transport}
}

Document

DOI: 10.4230/OASIcs.ATMOS.2025.11

Design of Distance Tariffs in Public Transport

Authors: Philine Schiewe, Anita Schöbel, and Reena Urban

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract

Setting the ticket prices is a crucial decision in public transport. Its basis, relevant for all related questions, such as dynamic prices or prices for different passenger groups, is the underlying fare strategy. Popular fare strategies are based on zones or on distances. Transitions from one fare strategy to another occur frequently, e.g., if public transport operators are joined to a larger association, or if structural decisions in a region have taken place. In this paper we report practically relevant issues when a fare structure should be changed to a distance tariff, a problem frequently arising when a ticket system based on mobile devices is introduced. We present mixed-integer linear programs for finding the parameters of a distance tariff, analyze rounding properties, and reflect how the change in revenue for the operator and the number of highly affected passengers can be controlled. Additionally, we evaluate the developed models experimentally.

Cite as

Philine Schiewe, Anita Schöbel, and Reena Urban. Design of Distance Tariffs in Public Transport. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schiewe_et_al:OASIcs.ATMOS.2025.11,
  author =	{Schiewe, Philine and Sch\"{o}bel, Anita and Urban, Reena},
  title =	{{Design of Distance Tariffs in Public Transport}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{11:1--11:20},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas 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.2025.11},
  URN =		{urn:nbn:de:0030-drops-247670},
  doi =		{10.4230/OASIcs.ATMOS.2025.11},
  annote =	{Keywords: public transport, fare strategy, distance tariff}
}

Document

DOI: 10.4230/OASIcs.ATMOS.2025.14

Using A* for Optimal Train Routing on Moving Block Systems

Authors: Stefan Engels and Robert Wille

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract

Modern control systems based on Moving Block allow for shorter headways and higher capacity on existing railway infrastructure. At the same time, few algorithms for optimal routing on networks equipped with such modern control systems exist. Previous methods rely on Mixed Integer Linear Programming (MILP) and face a trade-off between model size and accuracy, especially considering comparably complex and nonlinear headway constraints as well as train dynamics. With this work, we propose a complementary approach based on A*. Under a reasonable and easy assumption on train driver behavior, we propose a solution encoding and state space that is flexible concerning the choice of search algorithm and the modeling detail. The applicability is showcased on a small benchmark set. The implementation is available open-source as part of the Munich Train Control Toolkit (MTCT) on GitHub at https://github.com/cda-tum/mtct.

Cite as

Stefan Engels and Robert Wille. Using A* for Optimal Train Routing on Moving Block Systems. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{engels_et_al:OASIcs.ATMOS.2025.14,
  author =	{Engels, Stefan and Wille, Robert},
  title =	{{Using A* for Optimal Train Routing on Moving Block Systems}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{14:1--14:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas 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.2025.14},
  URN =		{urn:nbn:de:0030-drops-247701},
  doi =		{10.4230/OASIcs.ATMOS.2025.14},
  annote =	{Keywords: ETCS, Train Routing, Moving Block, A*, Munich Train Control Toolkit}
}

Document

DOI: 10.4230/OASIcs.ATMOS.2025.12

Separator-Based Alternative Paths in Customizable Contraction Hierarchies

Authors: Scott Bacherle, Thomas Bläsius, and Michael Zündorf

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract

We propose an algorithm for computing alternatives to the shortest path in a road network, based on the speed-up technique CCH (customizable contraction hierarchy). Computing alternative paths is a well-studied problem, motivated by the fact that route-planning applications benefit from presenting different high-quality options the user can choose from. Another crucial feature of modern routing applications is the inclusion of live traffic, which requires speed-up techniques that allow efficient metric updates. Besides CCH, the other speed-up technique supporting metric updates is CRP (customizable route planning). Of the two, CCH is the more modern solution with the advantages of providing faster queries and being substantially simpler to implement efficiently. However, so far, CCH has been lacking a way of computing alternative paths. While for CRP, the commonly used plateau method for computing alternatives can be applied, this is not so straightforward for CCH. With this paper, we make CCH a viable option for alternative paths, by proposing a new separator-based approach to computing alternative paths that works hand-in-hand with the CCH data structure. With our experiments, we demonstrate that CCH can indeed be used to compute alternative paths efficiently. With this, we provide an alternative to CRP that is simpler and has lower query times.

Cite as

Scott Bacherle, Thomas Bläsius, and Michael Zündorf. Separator-Based Alternative Paths in Customizable Contraction Hierarchies. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bacherle_et_al:OASIcs.ATMOS.2025.12,
  author =	{Bacherle, Scott and Bl\"{a}sius, Thomas and Z\"{u}ndorf, Michael},
  title =	{{Separator-Based Alternative Paths in Customizable Contraction Hierarchies}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{12:1--12:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas 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.2025.12},
  URN =		{urn:nbn:de:0030-drops-247685},
  doi =		{10.4230/OASIcs.ATMOS.2025.12},
  annote =	{Keywords: Alternative routes, realistic road networks, customizable contraction hierarchies, route planning, shortest paths}
}

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