Search Results

Documents authored by Spalding-Jamieson, Jack


Document
Separating Two Points with Obstacles in the Plane: Improved Upper and Lower Bounds

Authors: Jack Spalding-Jamieson and Anurag Murty Naredla

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


Abstract
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for a minimum-weight subset of the obstacles separating the two points. A few computational models for this problem have been previously studied. We give a unified approach to this problem in all models via a reduction to a particular shortest-path problem, and obtain improved running times in essentially all cases. In addition, we also give fine-grained lower bounds for many cases.

Cite as

Jack Spalding-Jamieson and Anurag Murty Naredla. Separating Two Points with Obstacles in the Plane: Improved Upper and Lower Bounds. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 90:1-90:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


Copy BibTex To Clipboard

@InProceedings{spaldingjamieson_et_al:LIPIcs.ESA.2025.90,
  author =	{Spalding-Jamieson, Jack and Naredla, Anurag Murty},
  title =	{{Separating Two Points with Obstacles in the Plane: Improved Upper and Lower Bounds}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{90:1--90:18},
  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.2025.90},
  URN =		{urn:nbn:de:0030-drops-245598},
  doi =		{10.4230/LIPIcs.ESA.2025.90},
  annote =	{Keywords: obstacle separation, point separation, geometric intersection graph, Z₂-homology, fine-grained lower bounds}
}
Document
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)


Copy BibTex To Clipboard

@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
Morphing Planar Graph Drawings via Orthogonal Box Drawings

Authors: Therese Biedl, Anna Lubiw, and Jack Spalding-Jamieson

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)


Abstract
We give an algorithm to morph planar graph drawings that achieves small grid size at the expense of allowing a constant number of bends on each edge. The input is an n-vertex planar graph and two planar straight-line drawings of the graph on an O(n) × O(n) grid. The planarity-preserving morph is composed of O(n) linear morphs between successive pairs of drawings, each on an O(n) × O(n) grid with a constant number of bends per edge. The algorithm to compute the morph runs in O(n²) time on a word RAM model with standard arithmetic operations - in particular no square roots or cube roots are required. The first step of the algorithm is to morph each input drawing to a planar orthogonal box drawing where vertices are represented by boxes and each edge is drawn as a horizontal or vertical segment. The second step is to morph between planar orthogonal box drawings. This is done by extending known techniques for morphing planar orthogonal drawings with point vertices.

Cite as

Therese Biedl, Anna Lubiw, and Jack Spalding-Jamieson. Morphing Planar Graph Drawings via Orthogonal Box Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{biedl_et_al:LIPIcs.GD.2024.40,
  author =	{Biedl, Therese and Lubiw, Anna and Spalding-Jamieson, Jack},
  title =	{{Morphing Planar Graph Drawings via Orthogonal Box Drawings}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{40:1--40:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.40},
  URN =		{urn:nbn:de:0030-drops-213242},
  doi =		{10.4230/LIPIcs.GD.2024.40},
  annote =	{Keywords: morphing, graph morphing, linear morph, planar graph drawing, orthogonal box drawing, orthogonal drawing, algorithm}
}
Document
CG Challenge
Conflict-Based Local Search for Minimum Partition into Plane Subgraphs (CG Challenge)

Authors: Jack Spalding-Jamieson, Brandon Zhang, and Da Wei Zheng

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


Abstract
This paper examines the approach taken by team gitastrophe in the CG:SHOP 2022 challenge. The challenge was to partition the edges of a geometric graph, with vertices represented by points in the plane and edges as straight lines, into the minimum number of planar subgraphs. We used a simple variation of a conflict optimizer strategy used by team Shadoks in the previous year’s CG:SHOP to rank second in the challenge.

Cite as

Jack Spalding-Jamieson, Brandon Zhang, and Da Wei Zheng. Conflict-Based Local Search for Minimum Partition into Plane Subgraphs (CG Challenge). In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 72:1-72:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{spaldingjamieson_et_al:LIPIcs.SoCG.2022.72,
  author =	{Spalding-Jamieson, Jack and Zhang, Brandon and Zheng, Da Wei},
  title =	{{Conflict-Based Local Search for Minimum Partition into Plane Subgraphs}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{72:1--72:6},
  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.2022.72},
  URN =		{urn:nbn:de:0030-drops-160807},
  doi =		{10.4230/LIPIcs.SoCG.2022.72},
  annote =	{Keywords: local search, planar graph, graph colouring, geometric graph, conflict optimizer}
}
Document
CG Challenge
Coordinated Motion Planning Through Randomized k-Opt (CG Challenge)

Authors: Paul Liu, Jack Spalding-Jamieson, Brandon Zhang, and Da Wei Zheng

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)


Abstract
This paper examines the approach taken by team gitastrophe in the CG:SHOP 2021 challenge. The challenge was to find a sequence of simultaneous moves of square robots between two given configurations that minimized either total distance travelled or makespan (total time). Our winning approach has two main components: an initialization phase that finds a good initial solution, and a k-opt local search phase which optimizes this solution. This led to a first place finish in the distance category and a third place finish in the makespan category.

Cite as

Paul Liu, Jack Spalding-Jamieson, Brandon Zhang, and Da Wei Zheng. Coordinated Motion Planning Through Randomized k-Opt (CG Challenge). In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 64:1-64:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{liu_et_al:LIPIcs.SoCG.2021.64,
  author =	{Liu, Paul and Spalding-Jamieson, Jack and Zhang, Brandon and Zheng, Da Wei},
  title =	{{Coordinated Motion Planning Through Randomized k-Opt}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{64:1--64:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.64},
  URN =		{urn:nbn:de:0030-drops-138635},
  doi =		{10.4230/LIPIcs.SoCG.2021.64},
  annote =	{Keywords: motion planning, randomized local search, path finding}
}
Document
CG Challenge
Computing Low-Cost Convex Partitions for Planar Point Sets with Randomized Local Search and Constraint Programming (CG Challenge)

Authors: Da Wei Zheng, Jack Spalding-Jamieson, and Brandon Zhang

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)


Abstract
The Minimum Convex Partition problem (MCP) is a problem in which a point-set is used as the vertices for a planar subdivision, whose number of edges is to be minimized. In this planar subdivision, the outer face is the convex hull of the point-set, and the interior faces are convex. In this paper, we discuss and implement the approach to this problem using randomized local search, and different initialization techniques based on maximizing collinearity. We also solve small instances optimally using a SAT formulation. We explored this as part of the 2020 Computational Geometry Challenge, where we placed first as Team UBC.

Cite as

Da Wei Zheng, Jack Spalding-Jamieson, and Brandon Zhang. Computing Low-Cost Convex Partitions for Planar Point Sets with Randomized Local Search and Constraint Programming (CG Challenge). In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 83:1-83:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{zheng_et_al:LIPIcs.SoCG.2020.83,
  author =	{Zheng, Da Wei and Spalding-Jamieson, Jack and Zhang, Brandon},
  title =	{{Computing Low-Cost Convex Partitions for Planar Point Sets with Randomized Local Search and Constraint Programming}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{83:1--83:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.83},
  URN =		{urn:nbn:de:0030-drops-122412},
  doi =		{10.4230/LIPIcs.SoCG.2020.83},
  annote =	{Keywords: convex partition, randomized local search, planar point sets}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail