@inproceedings{6e3e0d68be41490e9d1461b98c17fb01,
title = "Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits",
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.",
keywords = "collision avoidance, growth process, programmable matter, shrinking process",
author = "Nada Almalki and Siddharth Gupta and Othon Michail and Andreas Padalkin",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.; 27th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS2025 ; Conference date: 09-10-2025 Through 11-10-2025",
year = "2026",
month = jan,
day = "1",
doi = "10.1007/978-3-032-11127-2\_5",
language = "English",
isbn = "9783032111265",
series = "Lecture Notes in Computer Science",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "40--55",
editor = "Silvia Bonomi and Mandal, \{Partha Sarathi\} and Peter Robinson and Gokarna Sharma and Sebastien Tixeuil",
booktitle = "Stabilization, Safety, and Security of Distributed Systems - 27th International Symposium, SSS 2025, Proceedings",
address = "Germany",
}