Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits

Almalki, N ORCID: 0000-0001-9403-1702, Gupta, S ORCID: 0000-0003-4671-9822, Michail, O ORCID: 0000-0002-6234-3960 and Padalkin, A ORCID: 0000-0002-4601-9597 (2026) Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits In: International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS).

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Abstract

In this paper, we study the problem of efficiently reducing geometric shapes into other such shapes in a distributed setting through size-changing operations. We develop distributed algorithms using the reconfigurable circuit model to enable fast node-to-node communication. We study the connectivity graph model. Let n denote the number of agents and k the number of turning points in the initial shape. We show that any tree-shaped configuration can be reduced to a single agent using only shrinking operations in O(klogn) rounds w.h.p., and to its incompressible form in O(logn) rounds w.h.p. given prior knowledge of the incompressible nodes, or in O(klogn) rounds otherwise. When both shrinking and growth operations are available, we give an algorithm that transforms any tree to a topologically equivalent one in O(klogn+log²n) rounds w.h.p. On the negative side, we show that one cannot hope for o(log²n)-round transformations for all shapes of Θ(logn) turning points.

Item Type:	Conference Item (Unspecified)
Uncontrolled Keywords:	46 Information and Computing Sciences
Divisions:	Faculty of Science & Engineering
Depositing User:	Symplectic Admin
Date Deposited:	11 Sep 2025 08:50
Last Modified:	22 Jan 2026 07:22
DOI:	10.1007/978-3-032-11127-2_5
Related Websites:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3194354
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