Improved Deterministic Leader Election in Diameter-Two Networks

Document Type

Conference Article

Publication Title

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

Abstract

In this paper, we investigate the leader election problem in diameter-two networks. Recently, Chatterjee et al. [DC 2020] studied the leader election in diameter-two networks. They presented a -round deterministic implicit leader election algorithm which incurs optimal messages, but a drawback of their algorithm is that it requires knowledge of n. An important question– whether it is possible to remove the assumption on the knowledge of n was left open in their paper. Another interesting open question raised in their paper is whether explicit leader election can be solved in messages deterministically. In this paper, we give an affirmative answer to them. Further, we solve the broadcast problem, another fundamental problem in distributed computing, deterministically in diameter-two networks with messages and rounds without the knowledge of n. In fact, we address all the open questions raised by Chatterjee et al. for the deterministic leader election problem in diameter-two networks. In particular, our results are: 1.We present a deterministic explicit leader election algorithm which takes rounds and messages, where n in the number of nodes and is the maximum degree of the network. The algorithm works without the knowledge of n. The message bound is tight due to the matching lower bound, showed Chatterjee et al. [DC 2020].2.We show that broadcast can be solved deterministically in rounds using messages. More precisely, a broadcast tree can be computed with the same complexities and the depth of the tree is. This also doesn’t require the knowledge of n. To the best of our knowledge, this is the first deterministic result for the explicit leader election in the diameter-two networks, that too without the knowledge of n.

First Page

323

Last Page

335

DOI

10.1007/978-3-031-30448-4_23

Publication Date

1-1-2023

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