Black Hole Search in Dynamic Tori
We investigate the black hole search problem using a set of mobile agents in a dynamic torus. A black hole is defined as a dangerous stationary node that has the capability to destroy any number of incoming agents without leaving any trace of its existence. A torus of size n× m (3 ≤ n ≤ m) is a collection of n row rings and m column rings, and the dynamicity is such that each ring is considered to be 1-interval connected, i.e., in other words at most one edge can be missing from each ring at any round. The parameters which define the efficiency of any black hole search algorithm are: the number of agents and the number of rounds (or time) for termination. We consider two initial configurations of mobile agents: first, the agents are co-located, second, the agents are scattered. In each case, we establish lower and upper bounds on the number of agents and on the amount of time required to solve the black hole search problem.
Black Hole Search
Time Varying Graphs
Dynamic Torus
Distributed Algorithms
Mobile Agents
Theory of computation~Distributed algorithms
6:1-6:16
Regular Paper
https://arxiv.org/abs/2402.04746
This work was done while Partha Sarathi Mandal was in the position of Visiting Professor at Luiss University, Rome, Italy.
Adri
Bhattacharya
Adri Bhattacharya
Indian Institute of Technology Guwahati, Assam, India
https://orcid.org/0000-0003-1517-8779
Supported by CSIR, Govt. of India, Grant Number: 09/731(0178)/2020-EMR-I.
Giuseppe F.
Italiano
Giuseppe F. Italiano
Luiss University, Rome, Italy
https://orcid.org/0000-0002-9492-9894
Partha Sarathi
Mandal
Partha Sarathi Mandal
Indian Institute of Technology Guwahati, Assam, India
https://orcid.org/0000-0002-8632-5767
10.4230/LIPIcs.SAND.2024.6
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Adri Bhattacharya, Giuseppe F. Italiano, and Partha Sarathi Mandal
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