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The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have...
A general and direct method for computing the Betti numbers of a finite simplicial complex in S d is given. This method is complete for d 3, where versions of this method run in time O(nα(n)) and O(n), n the number of simplices. An implementation of the algorithm is applied to alpha shapes, which is a novel geometric modeling tool.
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