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Dynamic Parameterized Problems on Unit Disk Graphs

Authors Shinwoo An, Kyungjin Cho , Leo Jang, Byeonghyeon Jung, Yudam Lee, Eunjin Oh , Donghun Shin, Hyeonjun Shin , Chanho Song

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Author Details

Shinwoo An
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea
Kyungjin Cho
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea
Leo Jang
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea
Byeonghyeon Jung
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea
Yudam Lee
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea
Eunjin Oh
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea
Donghun Shin
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea
Hyeonjun Shin
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea
Chanho Song
  • Department of Computer Science and Engineering, POSTECH, Pohang, Republic of Korea

Funding

This work was partly supported by Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (No.RS-2024-00440239, Sublinear Scalable Algorithms for Large-Scale Data Analysis) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.RS-2024-00358505).
  • Cho, Kyungjin: Supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.RS-2024-00410835).

Cite As Get BibTex

Shinwoo An, Kyungjin Cho, Leo Jang, Byeonghyeon Jung, Yudam Lee, Eunjin Oh, Donghun Shin, Hyeonjun Shin, and Chanho Song. Dynamic Parameterized Problems on Unit Disk Graphs. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.6

Abstract

In this paper, we study fundamental parameterized problems such as k-Path/Cycle, Vertex Cover, Triangle Hitting Set, Feedback Vertex Set, and Cycle Packing for dynamic unit disk graphs. Given a vertex set V changing dynamically under vertex insertions and deletions, our goal is to maintain data structures so that the aforementioned parameterized problems on the unit disk graph induced by V can be solved efficiently. Although dynamic parameterized problems on general graphs have been studied extensively, no previous work focuses on unit disk graphs. In this paper, we present the first data structures for fundamental parameterized problems on dynamic unit disk graphs. More specifically, our data structure supports 2^O(√k) update time and O(k) query time for k-Path/Cycle. For the other problems, our data structures support O(log n) update time and 2^O(√k) query time, where k denotes the output size.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Unit disk graphs
  • dynamic parameterized algorithms
  • kernelization

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