TY - GEN

T1 - Distance-2-Dispersion with Termination by a Strong Team

AU - Gorain, Barun

AU - Kaur, Tanvir

AU - Mondal, Kaushik

N1 - Publisher Copyright:
© 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2024/1/1

Y1 - 2024/1/1

N2 - Distance-2-Dispersion (D-2-D) problem aims to disperse k mobile robots starting from an arbitrary initial configuration on an anonymous port-labeled graph G with n nodes such that no two robots occupy adjacent nodes in the final configuration, though multiple robots may occupy a single node if there is no other empty node whose all adjacent nodes are also empty. In the existing literature, this problem is solved starting from a rooted configuration for k(≥ 1 ) robots using O(mΔ) synchronous rounds with a total of O(log n) memory per robot, where m is the number of edges and Δ is the maximum degree of the graph. In this work, we start with k> n mobile robots and improve the run time to O(m) starting from a rooted configuration using the same amount of memory per robot. Further, we achieve D-2-D for an arbitrary initial configuration in O(pm) rounds using O(log n) memory per robot, where p is the number of nodes containing robots in the initial configuration. Both the algorithms terminate without any global knowledge of m, n, Δ, k, p. As we start with k> n robots, the nodes occupied by robots in the final configuration form a maximal independent set of the graph.

AB - Distance-2-Dispersion (D-2-D) problem aims to disperse k mobile robots starting from an arbitrary initial configuration on an anonymous port-labeled graph G with n nodes such that no two robots occupy adjacent nodes in the final configuration, though multiple robots may occupy a single node if there is no other empty node whose all adjacent nodes are also empty. In the existing literature, this problem is solved starting from a rooted configuration for k(≥ 1 ) robots using O(mΔ) synchronous rounds with a total of O(log n) memory per robot, where m is the number of edges and Δ is the maximum degree of the graph. In this work, we start with k> n mobile robots and improve the run time to O(m) starting from a rooted configuration using the same amount of memory per robot. Further, we achieve D-2-D for an arbitrary initial configuration in O(pm) rounds using O(log n) memory per robot, where p is the number of nodes containing robots in the initial configuration. Both the algorithms terminate without any global knowledge of m, n, Δ, k, p. As we start with k> n robots, the nodes occupied by robots in the final configuration form a maximal independent set of the graph.

KW - Deterministic algorithm

KW - Dispersion

KW - Distance-2-Dispersion

KW - Distributed algorithm

KW - Mobile robots

UR - http://www.scopus.com/inward/record.url?scp=85184117475&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-52213-0_4

DO - 10.1007/978-3-031-52213-0_4

M3 - Conference contribution

AN - SCOPUS:85184117475

SN - 9783031522123

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 44

EP - 58

BT - Algorithms and Discrete Applied Mathematics - 10th International Conference, CALDAM 2024, Proceedings

A2 - Kalyanasundaram, Subrahmanyam

A2 - Maheshwari, Anil

PB - Springer Science and Business Media Deutschland GmbH

T2 - 10th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2024

Y2 - 15 February 2024 through 17 February 2024

ER -