Publikation: Improved Bounds for Geodetic Hulls
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2025
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FINOCCHI, Irene, Hrsg., Loukas GEORGIADIS, Hrsg.. Algorithms and Complexity : 14th International Conference, CIAC 2025, Rome, Italy, June 10–12, 2025, Proceedings, Part II. Cham: Springer, 2025, S. 69-86. Lecture Notes in Computer Science (LNCS). 15680. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-031-92934-2. Verfügbar unter: doi: 10.1007/978-3-031-92935-9_5
Zusammenfassung
In this paper we study geodetic convex hulls in graphs and prove new bounds on the size of hull sets and related parameters. A set of vertices in a graph is geodetic convex if no shortest path between vertices in the set leaves the set. The geodetic hull of a vertex set is its smallest convex superset. A hull set is a set of vertices whose geodetic hull is the entire graph. Computing a hull set of minimum size poses an NP-hard problem. We present an exact kernelization algorithm which implies that the problem is FPT in the vertex cover number. Furthermore we provide new bounds on the size of a minimum hull set in relation to other graph parameters. For practical application, we design an improved heuristic as well as an algorithm to obtain strong instance-based lower bounds. We evaluate the efficiency and quality of the heuristic and the lower bound on diverse graphs. Our experiments demonstrate that our methods outperform previous ones by a large margin.
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Geodetic hull, Geodetic iteration number, Hull set
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14th International Conference on Algorithms and Complexity : CIAC 2025, 10. Juni 2025 - 12. Juni 2025, Rome, Italy
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DIATZKO, Gregor, Sabine STORANDT, Tobias TÖPFER, 2025. Improved Bounds for Geodetic Hulls. 14th International Conference on Algorithms and Complexity : CIAC 2025. Rome, Italy, 10. Juni 2025 - 12. Juni 2025. In: FINOCCHI, Irene, Hrsg., Loukas GEORGIADIS, Hrsg.. Algorithms and Complexity : 14th International Conference, CIAC 2025, Rome, Italy, June 10–12, 2025, Proceedings, Part II. Cham: Springer, 2025, S. 69-86. Lecture Notes in Computer Science (LNCS). 15680. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-031-92934-2. Verfügbar unter: doi: 10.1007/978-3-031-92935-9_5BibTex
@inproceedings{Diatzko2025Impro-74288,
title={Improved Bounds for Geodetic Hulls},
year={2025},
doi={10.1007/978-3-031-92935-9_5},
number={15680},
isbn={978-3-031-92934-2},
issn={0302-9743},
address={Cham},
publisher={Springer},
series={Lecture Notes in Computer Science (LNCS)},
booktitle={Algorithms and Complexity : 14th International Conference, CIAC 2025, Rome, Italy, June 10–12, 2025, Proceedings, Part II},
pages={69--86},
editor={Finocchi, Irene and Georgiadis, Loukas},
author={Diatzko, Gregor and Storandt, Sabine and Töpfer, Tobias}
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