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Gabriel graphs are subgraphs of Delaunay graphs that are used in many domains such as sensor networks and computer graphics. Although very useful in their original form, their definition is bounded to applications involving Euclidean spaces only, but their principles seem to be applicable to a wider range of applications. In this article, we generalize this… (More)
—When programming a spatial computing medium such as a cellular automaton, the hop count distance to some set of sources (particles) is an often used information. In particular, we consider the case where the sources themselves are moving. Due to the locality of communication, only an estimation of the distance can be made at each time step, and each… (More)
The current trend in electronics is to integrate more and more transistors on a chip and produce massive hardware resources. As a consequence, traditional computing models, which mainly compute in the temporal domain, do not work well anymore since it becomes increasingly difficult to orchestrate these massive-scale hardware resources in a centralized way.… (More)
In this paper, we consider Global Graph Transformations where all occurrences of a set of predefined local rules are applied altogether synchronously so that each part of the original graph gives rise to a part of the result graph, without any reference to the original one. The particularity here is that our framework is deterministic. This is achieved by… (More)
—In the cellular automata domain, the discrete convex hull computation rules proposed until now only deal with a connected set of seeds in infinite space, or with distant set of seeds in finite space. Taking a spatial computing point of view, we present a cellular automata rule that constructs the discrete convex hull of arbitrary set of seeds in infinite… (More)
Firing Squad Synchronization Problems are well known to be solvable by voluminous transition tables describing signals traveling and colliding. In this paper, we show that it is possible to solve it by expressing directly the fact that we want a recursive division of the space into two parts of equal size, and a notification when no further division is… (More)
We present a solution to the Firing Squad Synchronization Problem that works both in Von Neumann and Moore neighborhood and whatever is the dimension of the space. That solution is based on fields that provide a clean modular decomposition of such cellular automata problem.