17 Search Results for "Meijer, Erik"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.24
Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support

Authors: Reilly Browne and Hsien-Chih Chang

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

Abstract
Given an unweighted graph G, the minimum r-dominating set problem asks for a subset of vertices S of the smallest cardinality, such that every vertex in G is within radius r to some vertex in S. While the r-dominating set problem on planar graph admits PTAS from Baker’s shifting/layering technique when r is a constant, the problem becomes significantly harder when r can depend on n. In fact, under Exponential-Time Hypothesis, Fox-Epstein ηl [SODA 2019] observed that no efficient PTAS can exist for the unbounded r-dominating set problem on planar graphs. One may consider even harder weighted-variant known as the vertex-weighted metric r-dominating set, where edges are associated with lengths, and every vertex is associated with a positive-valued weight, and the goal is to compute an r-dominating set with minimum total weight. As a result, people resorted to bicriteria algorithms by allowing the returned solution to use radius-(1+ε)r balls instead, in addition to the total weight being a 1+ε approximation to the optimal value. We establish the first single-criteria polynomial-time O(1)-approximation algorithm for the vertex-weighted metric r-dominating set problem on planar graphs when r is part of the input, and can be arbitrarily large compared to n. Our new (single-criteria) O(1)-approximation algorithm uses the quasi-uniformity sampling technique of Chan et al. [SODA 2012] by bounding the shallow cell complexity of the (unbounded) radius-r ball system to be linear in n. To this end we have two technical innovations: 1) The discrete ball system on planar graphs are neither pseudodisks nor have well-defined boundaries for standard union-complexity arguments. We construct a support graph for arbitrary distance ball systems as contractions of Voronoi cells; the sparseness comes as a byproduct. 2) We present an assignment of each depth-(≥3) cell to a unique 3-tuple of ball centers. This allows us to use standard Clarkson-Shor techniques to reduce the counting to cells of depth exactly 3, which we prove to be size O(n) by a novel geometric argument based on our support being a Voronoi contraction.
Cite as

Reilly Browne and Hsien-Chih Chang. Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 24:1-24:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{browne_et_al:LIPIcs.SoCG.2026.24,
  author =	{Browne, Reilly and Chang, Hsien-Chih},
  title =	{{Single-Criteria Metric r-Dominating Set Problem via Minor-Preserving Support}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{24:1--24:17},
  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.2026.24},
  URN =		{urn:nbn:de:0030-drops-258300},
  doi =		{10.4230/LIPIcs.SoCG.2026.24},
  annote =	{Keywords: Minimum dominating set, planar graphs, shallow cell complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.16
Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds

Authors: Håvard Bakke Bjerkevik, Joseph Dorfer, Linda Kleist, Torsten Ueckerdt, and Birgit Vogtenhuber

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

Abstract
We consider the problem of reconfiguring non-crossing spanning trees on point sets. For a set P of n points in general position in the plane, the flip graph ℱ(P) has a vertex for each non-crossing spanning tree on P and an edge between any two spanning trees that can be transformed into each other by the exchange of a single edge (coined a flip). This flip graph has been intensively studied, lately with an emphasis on determining its diameter diam(ℱ(P)) for sets P of n points in convex position. For this case, the current best bounds are 14/9⋅n - O(1) ≤ diam(ℱ(P)) < 15/9⋅n - 3, obtained in a recent breakthrough work [Bjerkevik, Kleist, Ueckerdt, and Vogtenhuber; SODA 2025]. The crucial tool for both the upper and lower bound are so-called conflict graphs, which the authors stated might be the key ingredient for determining the diameter (up to lower-order terms). In this paper, we pick up the concept of conflict graphs from the above-mentioned work and show that this tool is even more versatile than previously hoped. As our first main result, we use conflict graphs to show that computing the flip distance between two non-crossing spanning trees is NP-hard, even for point sets in convex position. Interestingly, the result still holds for more constrained flip operations, concretely, compatible flips (where the removed and the added edge do not cross) and rotations (where the removed and the added edge share an endpoint). Additionally, we present new insights on the diameter of the flip graph, by this directly extending the line of research from [BKUV SODA25]. Their lower bound is based on a constant-size pair of trees, one of which is of a type we refer to as stacked. We show that if one of the trees is stacked, then the lower bound is indeed optimal up to a constant term, that is, there exists a flip sequence of length at most 14/9⋅(n-1) to any other tree. Lastly, we improve the lower bound on the diameter of the flip graph ℱ(P) for n points in convex position to 11/7⋅n-o(n).
Cite as

Håvard Bakke Bjerkevik, Joseph Dorfer, Linda Kleist, Torsten Ueckerdt, and Birgit Vogtenhuber. Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bjerkevik_et_al:LIPIcs.SoCG.2026.16,
  author =	{Bjerkevik, H\r{a}vard Bakke and Dorfer, Joseph and Kleist, Linda and Ueckerdt, Torsten and Vogtenhuber, Birgit},
  title =	{{Flip Distance of Non-Crossing Spanning Trees: NP-Hardness and Improved Bounds}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{16:1--16:18},
  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.2026.16},
  URN =		{urn:nbn:de:0030-drops-258225},
  doi =		{10.4230/LIPIcs.SoCG.2026.16},
  annote =	{Keywords: Non-crossing, spanning tree, plane graph, flip graph, reconfiguration, diameter, complexity, NP-hard, edge exchange, compatible flip, rotation, happy edge property}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.18
A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light

Authors: Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We extend the existing HOL Light Library for Modal Systems (HOLMS) to support a modular implementation of modal reasoning within the HOL Light proof assistant. We deeply embed axiomatic calculi and relational semantics for seven normal modal logics (K, T, B, K4, S4, S5, GL) and formalise modal adequacy theorems for these systems. We then leverage those formalisations to implement a mechanism for automated reasoning via proof-search in the associated labelled sequent calculi, which we shallowly embed in HOL Light’s goal-stack mechanism. This way, we equip the general-purpose proof assistant with (semi)decision procedures for these logics that, in case of failure to construct a proof for the input formula, return a certified countermodel within the appropriate class for the logic under consideration. On the methodological side, we propose a precise measure of the modularity of our approach by systematically adopting Christopher Strachey’s distinction between ad hoc and parametric polymorphism throughout the library.
Cite as

Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi. A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 18:1-18:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bilotta_et_al:LIPIcs.CSL.2026.18,
  author =	{Bilotta, Antonella and Maggesi, Marco and Perini Brogi, Cosimo},
  title =	{{A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{18:1--18:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.18},
  URN =		{urn:nbn:de:0030-drops-254427},
  doi =		{10.4230/LIPIcs.CSL.2026.18},
  annote =	{Keywords: Modal logic, HOL Light, Labelled sequent calculi, Logical verification, Interactive theorem proving, Automated proof-search}
}
Document
Poster Abstract
DOI: 10.4230/LIPIcs.GD.2025.47
Reconfigurations of Plane Caterpillars and Paths (Poster Abstract)

Authors: Todor Antić, Guillermo Gamboa Quintero, and Jelena Glišić

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
Let S be a point set in the plane, and let 𝒫(S) and 𝒞(S) be the sets of all plane spanning paths and caterpillars on S. We study reconfiguration operations on 𝒫(S) and 𝒞(S). In particular, we prove that all of the commonly studied reconfigurations on plane spanning trees still yield connected reconfiguration graphs for caterpillars when S is in convex position. If S is in general position, we show that the rotation, compatible flip and flip graphs of 𝒞(S) are connected while the slide graph is sometimes disconnected, but always has a component of size 1/4(3ⁿ-1). We then study sizes of connected components in reconfiguration graphs of plane spanning paths. In this direction, we show that no component of size at most 7 can exist in the flip graph on 𝒫(S).
Cite as

Todor Antić, Guillermo Gamboa Quintero, and Jelena Glišić. Reconfigurations of Plane Caterpillars and Paths (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 47:1-47:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{antic_et_al:LIPIcs.GD.2025.47,
  author =	{Anti\'{c}, Todor and Gamboa Quintero, Guillermo and Gli\v{s}i\'{c}, Jelena},
  title =	{{Reconfigurations of Plane Caterpillars and Paths}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{47:1--47:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.47},
  URN =		{urn:nbn:de:0030-drops-250337},
  doi =		{10.4230/LIPIcs.GD.2025.47},
  annote =	{Keywords: reconfiguration graph, caterpillar, path, geometric graph}
}
Document
Poster Abstract
DOI: 10.4230/LIPIcs.GD.2025.51
Graph Tiles (Poster Abstract)

Authors: Oswin Aichholzer, Robert Ganian, Phillip Keldenich, Maarten Löffler, Gert Meijer, Alexandra Weinberger, and Carola Wenk

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
We define a graph tile to be a unit square (or more generally, a polygon) on which a piece of a graph has been drawn/embedded; in particular, it may have vertices in its interior, edges connecting those vertices, or half-edges that extend to the boundary of the tile. In a graph tiling problem, we are given as input a set of graph tiles, with multiplicities, and the output is an arrangement of those tiles forming a graph of larger area. We focus on a simple tile set: unit square tiles with a central vertex and either a half-edge or no half-edge on each side. Up to symmetry this gives us six different types. We characterize which multiplicities are compatible for sets of at most three different tiles.
Cite as

Oswin Aichholzer, Robert Ganian, Phillip Keldenich, Maarten Löffler, Gert Meijer, Alexandra Weinberger, and Carola Wenk. Graph Tiles (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 51:1-51:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aichholzer_et_al:LIPIcs.GD.2025.51,
  author =	{Aichholzer, Oswin and Ganian, Robert and Keldenich, Phillip and L\"{o}ffler, Maarten and Meijer, Gert and Weinberger, Alexandra and Wenk, Carola},
  title =	{{Graph Tiles}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{51:1--51:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.51},
  URN =		{urn:nbn:de:0030-drops-250371},
  doi =		{10.4230/LIPIcs.GD.2025.51},
  annote =	{Keywords: graph tiles}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.57
Improved Hardness-Of-Approximation for Token-Swapping

Authors: Sam Hiken and Nicole Wein

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

Abstract
We study the token swapping problem, in which we are given a graph with an initial assignment of one distinct token to each vertex, and a final desired assignment (again with one token per vertex). The goal is to find the minimum length sequence of swaps of adjacent tokens required to get from the initial to the final assignment. The token swapping problem is known to be NP-complete. It is also known to have a polynomial-time 4-approximation algorithm. From the hardness-of-approximation side, it is known to be NP-hard to approximate with a ratio better than 1001/1000. Our main result is an improvement of the approximation ratio of the lower bound: We show that it is NP-hard to approximate with ratio better than 14/13. We then turn our attention to the 0/1-weighted version, in which every token has a weight of either 0 or 1, and the cost of a swap is the sum of the weights of the two participating tokens. Unlike standard token swapping, no constant-factor approximation is known for this version, and we provide an explanation. We prove that 0/1-weighted token swapping is NP-hard to approximate with ratio better than (1-ε) ln(n) for any constant ε > 0. Lastly, we prove two barrier results for the standard (unweighted) token swapping problem. We show that one cannot beat the current best known approximation ratio of 4 using a large class of algorithms which includes all known algorithms, nor can one beat it using a common analysis framework.
Cite as

Sam Hiken and Nicole Wein. Improved Hardness-Of-Approximation for Token-Swapping. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 57:1-57:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hiken_et_al:LIPIcs.ESA.2025.57,
  author =	{Hiken, Sam and Wein, Nicole},
  title =	{{Improved Hardness-Of-Approximation for Token-Swapping}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{57:1--57:16},
  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.2025.57},
  URN =		{urn:nbn:de:0030-drops-245251},
  doi =		{10.4230/LIPIcs.ESA.2025.57},
  annote =	{Keywords: algorithms, token-swapping, hardness-of-approximation, lower-bounds}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.28
Sliding Squares in Parallel

Authors: Hugo A. Akitaya, Sándor P. Fekete, Peter Kramer, Saba Molaei, Christian Rieck, Frederick Stock, and Tobias Wallner

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

Abstract
We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given n square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of sliding moves to transform it into a desired goal configuration, maintaining connectivity of the configuration at all times. Recent work has aimed at minimizing the total number of moves, resulting in fully sequential schedules that can perform reconfiguration in 𝒪(n²) moves, or 𝒪(nP) for arrangements of bounding box perimeter size P. We provide first results in the sliding square model that exploit parallel motion, performing reconfiguration in worst-case optimal makespan of 𝒪(P). We also provide tight bounds on the complexity of the problem by showing that even deciding the possibility of reconfiguration within makespan 1 is NP-complete in the unlabeled case. In the labeled variant, we note that deciding the same for makespan 2 is NP-complete, while makespan 1 is straightforward.
Cite as

Hugo A. Akitaya, Sándor P. Fekete, Peter Kramer, Saba Molaei, Christian Rieck, Frederick Stock, and Tobias Wallner. Sliding Squares in Parallel. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 28:1-28:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{a.akitaya_et_al:LIPIcs.ESA.2025.28,
  author =	{A. Akitaya, Hugo and Fekete, S\'{a}ndor P. and Kramer, Peter and Molaei, Saba and Rieck, Christian and Stock, Frederick and Wallner, Tobias},
  title =	{{Sliding Squares in Parallel}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{28:1--28:17},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-244961},
  doi =		{10.4230/LIPIcs.ESA.2025.28},
  annote =	{Keywords: Sliding squares, parallel motion, reconfigurability, motion planning, multi-agent path finding, makespan, swarm robotics, computational geometry}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.2
Covering Simple Orthogonal Polygons with Rectangles

Authors: Aniket Basu Roy

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study the problem of Covering Orthogonal Polygons with Rectangles, focusing on three variants: covering the interior, the boundary, and the corners. While previous work provided constant-factor approximation algorithms for these problems, significant improvements had not been achieved for over two decades. The main contribution of this work is the development of a Polynomial Time Approximation Scheme (PTAS) for both the Boundary Cover and Corner Cover problems on simple polygons, using a local search algorithm. Our work advances the state of the art, improving upon the previous best-known 4-approximation for the Boundary Cover and 2-approximation for the Corner Cover problems. The technical core of our work lies in proving the existence of planar support graphs for certain geometric hypergraphs defined by the polygon and its containment-maximal rectangles. This structural insight enables the application of the local search framework to achieve the PTAS results. We also demonstrate the limitations of this approach by constructing instances where local search fails for the Interior Cover and certain dual problems, such as the Maximum Antirectangle and Hitting Set problems. Additionally, the methods yield a PTAS for a special case of the Discrete Independent Set problem for rectangles. These results not only settle longstanding open questions but also introduce new techniques that may be of independent interest within computational geometry.
Cite as

Aniket Basu Roy. Covering Simple Orthogonal Polygons with Rectangles. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{basuroy:LIPIcs.APPROX/RANDOM.2025.2,
  author =	{Basu Roy, Aniket},
  title =	{{Covering Simple Orthogonal Polygons with Rectangles}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.2},
  URN =		{urn:nbn:de:0030-drops-243686},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.2},
  annote =	{Keywords: Polygon Covering, Approximation Algorithms, Orthogonal Polygons, Rectangles, Local Search, Planar Supports}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.39
Sweeping a Domain with Line-Of-Sight Between Covisible Agents

Authors: Kien C. Huynh, Joseph S. B. Mitchell, and Valentin Polishchuk

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We consider sweeping a polygonal domain using variable-length segments whose endpoints can be considered to be mobile agents moving with bounded speeds; a point in the domain is swept when it belongs to one of the segments. The objective is to sweep the domain as quickly as possible. We show that the problem is NP-hard even in simple polygons and even for a single segment (two agents), and give constant-factor approximation algorithms, both for simple polygons and polygons with holes. Our approximations are obtained by introducing a new type of "window partition" of the polygon, which may find other applications. For domains with holes, our results are based on a non-trivial topological argument proving a surprising fact: a connected subset of the domain, whose points are swept but not directly touched by the agents, may contain at most one hole.
Cite as

Kien C. Huynh, Joseph S. B. Mitchell, and Valentin Polishchuk. Sweeping a Domain with Line-Of-Sight Between Covisible Agents. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 39:1-39:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{huynh_et_al:LIPIcs.WADS.2025.39,
  author =	{Huynh, Kien C. and Mitchell, Joseph S. B. and Polishchuk, Valentin},
  title =	{{Sweeping a Domain with Line-Of-Sight Between Covisible Agents}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{39:1--39:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.39},
  URN =		{urn:nbn:de:0030-drops-242706},
  doi =		{10.4230/LIPIcs.WADS.2025.39},
  annote =	{Keywords: Polygon sweeping, collaborating agents, motion coordination, makespan optimization}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.10
EGGs Are Adhesive!

Authors: Roberto Biondo, Davide Castelnovo, and Fabio Gadducci

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
The use of rewriting-based visual formalisms is on the rise. In the formal methods community, this is due also to the introduction of adhesive categories, where most properties of classical approaches to graph transformation, such as those on parallelism and confluence, can be rephrased and proved in a general and uniform way. E-graphs (EGGs) are a formalism for program optimisation via an efficient implementation of equality saturation. In short, EGGs can be defined as (acyclic) term graphs with an additional notion of equivalence on nodes that is closed under the operators of the signature. Instead of replacing the components of a program, the optimisation step is performed by adding new components and linking them to the existing ones via an equivalence relation, until an optimal program is reached. This work describes EGGs via adhesive categories. Besides the benefits in itself of a formal presentation, which renders precise the properties of the data structure, the description of the addition of equivalent program components using standard graph transformation tools offers the advantages of the adhesive framework in modelling, for example, concurrent updates.
Cite as

Roberto Biondo, Davide Castelnovo, and Fabio Gadducci. EGGs Are Adhesive!. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{biondo_et_al:LIPIcs.CALCO.2025.10,
  author =	{Biondo, Roberto and Castelnovo, Davide and Gadducci, Fabio},
  title =	{{EGGs Are Adhesive!}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.10},
  URN =		{urn:nbn:de:0030-drops-235690},
  doi =		{10.4230/LIPIcs.CALCO.2025.10},
  annote =	{Keywords: Hypergraphs, terms graphs, e-graphs, adhesive categories}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.30
In-Memory Object Graph Stores

Authors: Aditya Thimmaiah, Zijian Yi, Joseph Kenis, Christopher J Rossbach, and Milos Gligoric

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract
We present a design and implementation of an in-memory object graph store, dubbed εStore. Our key innovation is a storage model - epsilon store - that equates an object on the heap to a node in a graph store. Thus any object on the heap (without changes) can be a part of one, or multiple, graph stores, and vice versa, any node in a graph store can be accessed like any other object on the heap. Specifically, each node in a graph is an object (i.e., instance of a class), and its properties and its edges are the primitive and reference fields declared in its class, respectively. Necessary classes, which are instantiated to represent nodes, are created dynamically by εStore. εStore uses a subset of the Cypher query language to query the graph store. By design, the result of any query is a table (ResultSet) of references to objects on the heap, which users can manipulate the same way as any other object on the heap in their programs. Moreover, a developer can include (transitively) an arbitrary object to become a part of a graph store. Finally, εStore introduces compile-time rewriting of Cypher queries into imperative code to improve the runtime performance. εStore can be used for a number of tasks including implementing methods for complex in-memory structures, writing complex assertions, or a stripped down version of a graph database that can conveniently be used during testing. We implement εStore in Java and show its application using the aforementioned tasks.
Cite as

Aditya Thimmaiah, Zijian Yi, Joseph Kenis, Christopher J Rossbach, and Milos Gligoric. In-Memory Object Graph Stores. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 30:1-30:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{thimmaiah_et_al:LIPIcs.ECOOP.2025.30,
  author =	{Thimmaiah, Aditya and Yi, Zijian and Kenis, Joseph and Rossbach, Christopher J and Gligoric, Milos},
  title =	{{In-Memory Object Graph Stores}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{30:1--30:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2025.30},
  URN =		{urn:nbn:de:0030-drops-233225},
  doi =		{10.4230/LIPIcs.ECOOP.2025.30},
  annote =	{Keywords: Object stores, Graph stores, Cypher}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.3
Pydrofoil: Accelerating Sail-Based Instruction Set Simulators

Authors: Carl Friedrich Bolz-Tereick, Luke Panayi, Ferdia McKeogh, Tom Spink, and Martin Berger

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract
We present Pydrofoil, a multi-stage compiler that generates instruction set simulators (ISSs) from processor instruction set architectures (ISAs) expressed in the high-level, verification-oriented ISA specification language Sail. Pydrofoil achieves a > 230× speedup over the C-based ISS generated by Sail on our benchmarks, thanks to the following insights. (i) An ISS is effectively an interpreter loop, and tracing just-in-time (JIT) compilers have proven effective at accelerating those, albeit mostly for dynamically typed languages. (ii) ISS workloads are highly atypical, dominated by intensive bit manipulation operations. Conventional compiler optimisations for general-purpose programming languages have limited impact for speeding up such workloads. We develop suitable domain-specific optimisations. (iii) Neither tracing JIT compilers, nor ahead-of-time (AOT) compilation alone, even with domain-specific optimisations, suffice for the generation of performant ISSs. Pydrofoil therefore implements a hybrid approach, pairing an AOT compiler with a tracing JIT built on the meta-tracing PyPy framework. AOT and JIT use domain-specific optimisations. Our benchmarks demonstrate that combining AOT and JIT compilers provides significantly greater performance gains than using either compiler alone.
Cite as

Carl Friedrich Bolz-Tereick, Luke Panayi, Ferdia McKeogh, Tom Spink, and Martin Berger. Pydrofoil: Accelerating Sail-Based Instruction Set Simulators. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 3:1-3:31, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bolztereick_et_al:LIPIcs.ECOOP.2025.3,
  author =	{Bolz-Tereick, Carl Friedrich and Panayi, Luke and McKeogh, Ferdia and Spink, Tom and Berger, Martin},
  title =	{{Pydrofoil: Accelerating Sail-Based Instruction Set Simulators}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{3:1--3:31},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2025.3},
  URN =		{urn:nbn:de:0030-drops-232962},
  doi =		{10.4230/LIPIcs.ECOOP.2025.3},
  annote =	{Keywords: Instruction set architecture, processor, domain-specific language, just-in-time compilation, meta-tracing}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.20
Polynomial-Time Algorithms for Contiguous Art Gallery and Related Problems

Authors: Ahmad Biniaz, Anil Maheshwari, Magnus Christian Ring Merrild, Joseph S. B. Mitchell, Saeed Odak, Valentin Polishchuk, Eliot W. Robson, Casper Moldrup Rysgaard, Jens Kristian Refsgaard Schou, Thomas Shermer, Jack Spalding-Jamieson, Rolf Svenning, and Da Wei Zheng

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

Abstract
We introduce the contiguous art gallery problem which is to guard the boundary of a simple polygon with a minimum number of guards such that each guard covers exactly one contiguous portion of the boundary. Art gallery problems are often NP-hard. In particular, it is NP-hard to minimize the number of guards to see the boundary of a simple polygon, without the contiguity constraint. This paper is a merge of three concurrent works [Ahmad Biniaz et al., 2024; Magnus Christian Ring Merrild et al., 2024; Eliot W. Robson et al., 2024] each showing that (surprisingly) the contiguous art gallery problem is solvable in polynomial time. The common idea of all three approaches is developing a greedy function that maps a point on the boundary to the furthest point on the boundary so that the contiguous interval along the boundary between them could be guarded by one guard. Repeatedly applying this function immediately leads to an OPT+1 approximation. By studying this greedy algorithm, we present three different approaches that achieve an optimal solution. The first and second approach apply this greedy algorithm from different points on the boundary that could be found in advance or on the fly while traversing along the boundary (respectively). The third approach represents this function as a piecewise linear rational function, which can be reduced to an abstract arc cover problem involving infinite families of arcs. We identify other problems that can be represented by similar functions, and solve them via the third approach. From the combinatorial point of view, we show that any n-vertex polygon can be guarded by at most ⌊(n-2)/2⌋ guards. This bound is tight because there are polygons that require this many guards.
Cite as

Ahmad Biniaz, Anil Maheshwari, Magnus Christian Ring Merrild, Joseph S. B. Mitchell, Saeed Odak, Valentin Polishchuk, Eliot W. Robson, Casper Moldrup Rysgaard, Jens Kristian Refsgaard Schou, Thomas Shermer, Jack Spalding-Jamieson, Rolf Svenning, and Da Wei Zheng. Polynomial-Time Algorithms for Contiguous Art Gallery and Related Problems. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 20:1-20:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{biniaz_et_al:LIPIcs.SoCG.2025.20,
  author =	{Biniaz, Ahmad and Maheshwari, Anil and Merrild, Magnus Christian Ring and Mitchell, Joseph S. B. and Odak, Saeed and Polishchuk, Valentin and Robson, Eliot W. and Rysgaard, Casper Moldrup and Schou, Jens Kristian Refsgaard and Shermer, Thomas and Spalding-Jamieson, Jack and Svenning, Rolf and Zheng, Da Wei},
  title =	{{Polynomial-Time Algorithms for Contiguous Art Gallery and Related Problems}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{20:1--20:21},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-231720},
  doi =		{10.4230/LIPIcs.SoCG.2025.20},
  annote =	{Keywords: Art Gallery Problem, Computational Geometry, Combinatorics, Discrete Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.44
A Minor-Testing Approach for Coordinated Motion Planning with Sliding Robots

Authors: Eduard Eiben, Robert Ganian, Iyad Kanj, and M. S. Ramanujan

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

Abstract
We study a variant of the Coordinated Motion Planning problem on undirected graphs, referred to herein as the Coordinated Sliding-Motion Planning (CSMP) problem. In this variant, we are given an undirected graph G, k robots R₁,… ,R_k positioned on distinct vertices of G, p ≤ k distinct destination vertices for robots R₁,… ,R_p, and 𝓁 ∈ ℕ. The problem is to decide if there is a serial schedule of at most 𝓁 moves (i.e., of makespan 𝓁) such that at the end of the schedule each robot with a destination reaches it, where a robot’s move is a free path (unoccupied by any robots) from its current position to an unoccupied vertex. The problem is known to be NP-hard even on full grids. It has been studied in several contexts, including coin movement and reconfiguration problems, with respect to feasibility, complexity, and approximation. Geometric variants of the problem, in which congruent geometric-shape robots (e.g., unit disk/squares) slide or translate in the Euclidean plane, have also been studied extensively. We investigate the parameterized complexity of CSMP with respect to two parameters: the number k of robots and the makespan 𝓁. As our first result, we present a fixed-parameter algorithm for CSMP parameterized by k. For our second result, we present a fixed-parameter algorithm parameterized by 𝓁 for the special case of CSMP in which only a single robot has a destination and the graph is planar. A crucial new ingredient for both of our results is that the solution admits a succinct representation as a small labeled topological minor of the input graph.
Cite as

Eduard Eiben, Robert Ganian, Iyad Kanj, and M. S. Ramanujan. A Minor-Testing Approach for Coordinated Motion Planning with Sliding Robots. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 44:1-44:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eiben_et_al:LIPIcs.SoCG.2025.44,
  author =	{Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Ramanujan, M. S.},
  title =	{{A Minor-Testing Approach for Coordinated Motion Planning with Sliding Robots}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{44:1--44:15},
  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.2025.44},
  URN =		{urn:nbn:de:0030-drops-231966},
  doi =		{10.4230/LIPIcs.SoCG.2025.44},
  annote =	{Keywords: coordinated motion planning on graphs, parameterized complexity, topological minor testing, planar graphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2018.29
Coordinated Motion Planning: Reconfiguring a Swarm of Labeled Robots with Bounded Stretch

Authors: Erik D. Demaine, Sándor P. Fekete, Phillip Keldenich, Christian Scheffer, and Henk Meijer

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Abstract
We present a number of breakthroughs for coordinated motion planning, in which the objective is to reconfigure a swarm of labeled convex objects by a combination of parallel, continuous, collision-free translations into a given target arrangement. Problems of this type can be traced back to the classic work of Schwartz and Sharir (1983), who gave a method for deciding the existence of a coordinated motion for a set of disks between obstacles; their approach is polynomial in the complexity of the obstacles, but exponential in the number of disks. Despite a broad range of other non-trivial results for multi-object motion planning, previous work has largely focused on sequential schedules, in which one robot moves at a time, with objectives such as the number of moves; attempts to minimize the overall makespan of a coordinated parallel motion schedule (with many robots moving simultaneously) have defied all attempts at establishing the complexity in the absence of obstacles, as well as the existence of efficient approximation methods. We resolve these open problems by developing a framework that provides constant-factor approximation algorithms for minimizing the execution time of a coordinated, parallel motion plan for a swarm of robots in the absence of obstacles, provided their arrangement entails some amount of separability. In fact, our algorithm achieves constant stretch factor: If all robots want to move at most d units from their respective starting positions, then the total duration of the overall schedule (and hence the distance traveled by each robot) is O(d). Various extensions include unlabeled robots and different classes of robots. We also resolve the complexity of finding a reconfiguration plan with minimal execution time by proving that this is NP-hard, even for a grid arrangement without any stationary obstacles. On the other hand, we show that for densely packed disks that cannot be well separated, a stretch factor Omega(N^{1/4}) may be required. On the positive side, we establish a stretch factor of O(N^{1/2}) even in this case. The intricate difficulties of computing precise optimal solutions are demonstrated by the seemingly simple case of just two disks, which is shown to be excruciatingly difficult to solve to optimality.
Cite as

Erik D. Demaine, Sándor P. Fekete, Phillip Keldenich, Christian Scheffer, and Henk Meijer. Coordinated Motion Planning: Reconfiguring a Swarm of Labeled Robots with Bounded Stretch. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{demaine_et_al:LIPIcs.SoCG.2018.29,
  author =	{Demaine, Erik D. and Fekete, S\'{a}ndor P. and Keldenich, Phillip and Scheffer, Christian and Meijer, Henk},
  title =	{{Coordinated Motion Planning: Reconfiguring a Swarm of Labeled Robots with Bounded Stretch}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.29},
  URN =		{urn:nbn:de:0030-drops-87423},
  doi =		{10.4230/LIPIcs.SoCG.2018.29},
  annote =	{Keywords: Robot swarms, coordinated motion planning, parallel motion, makespan, bounded stretch, complexity, approximation}
}
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