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Firefighter Problem with Minimum Budget: Hardness and Approximation Algorithm for Unit Disk Graphs

Year: 2022

Type: preprint

Abstract: Unit disk graphs are the set of graphs which represent the intersection of disk graphs and interval graphs. These graphs are of great importance due to their structural similarity with wireless communication networks. Firefighter problem on unit disk graph is interesting as it models the virus spreading in an wireless network and asks for a solution to stop it. In this paper, we consider the MIN-BUDGET firefighter problem where the goal is to determine the minimum number of firefighters required and the nodes to place them at each time instant to save a given set of vertices of a given graph and a fire breakout node. We show that, the MIN-BUDGET firefighter problem in a unit disk graph is NP-Hard. We also present a constant factor approximation algorithm.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2203.15509

Authors: Chatterjee, Diptendu, Bhattacharyya, Rishiraj

Institutions: Indian Statistical Institute, National Institute of Science Education and Research

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4221149080

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