Asynchronous Filling by Luminous Robots
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In this work we investigate this problem in the asynchronous model by luminous robots. In this model a light is attached to the robots, which serves as externally visible bits stored in that light encoded by a color. First, we present an algorithm solving the asynchronous Filling problem with robots having 1 hop visibility range, O(logΔ) bits of persistent storage, and Δ+3 colors, where Δ is the maximum degree of the graph. Then we show, how the number of colors can be reduced to O(1) at the cost of the running time. After this we show, how the running time can be improved by robots with visibility range of 2 hops, O(logΔ) bits of persistent memory, and Δ + 3 colors. We show, that in the fully synchronous case, the running time of this algorithm is O(n). We show how to extend our asynchronous solution to the k-Door case, k≥ 2, by using Δ + k + 3 colors. Finally, we present simulation results.
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