Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits

doi:10.1007/978-3-032-11127-2_5

Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits

2026-01-01

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DOI：10.1007/978-3-032-11127-2_5

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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(k log n) rounds w.h.p., and to its incompressible form in O(log n) rounds w.h.p. given prior knowledge of the incompressible nodes, or in O(k log n) 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(k log n+log(2) n) rounds w.h.p. On the negative side, we show that one cannot hope for O(log(2) n)-round transformations for all shapes of Theta(log n) turning points.

Keywords:

growth process

shrinking process

collision avoidance

programmable matter

Efficient Distributed Algorithms for Shape Reduction via Reconfigurable Circuits

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