Fast and Reliable Dispersal of Crash-Prone Agents on Graphs
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We study the ability of mobile agents performing simple local computations to completely cover an unknown graph environment while implicitly constructing a distributed spanning tree. Whenever an agent moves, it may crash and disappear from the environment. The agents activate autonomously at exponential waiting times of mean 1 and enter the graph over time at a source vertex s. They are able to settle at vertices of the graph and mark a neighbour. The agents are identical and make decisions driven by the same local rule of behaviour. The local rule is only based on the presence of neighbouring agents, and whether a neighbour marks the agent's current location. An implicit spanning tree is gradually constructed by having certain agents settle and act as its vertices, marking their parent. Each vertex in the environment has limited physical space and may contain at most a settled and an unsettled agent. Our goal is to show that even under conditions of asynchronicity, frequent crashing, and limited physical space, the simple mobile agents successfully cover the environment and construct a distributed spanning tree in linear time. Specifically, we show that, assuming at most ct/4 crashes happen before time t for all times t, the agents can complete the tree asymptotically almost surely in 8((1-c)^-1+o(1))n time where n is the number of vertices. The analysis relates our algorithm to the “totally asymmetric simple exclusion process” in statistical mechanics.
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