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The authors consider the map construction problem in a simple, connected graph by a set of mobile computation entities or agents that start from scattered locations throughout the graph. The problem is further complicated by dangerous elements, nodes and links, in the graph that eliminate agents traversing or arriving at them. The agents working in the graph communicate using a limited amount of storage at each node and work asynchronously. They present a deterministic algorithm that solves the exploration and map construction problems. The end result is also a rooted spanning tree and the election of a leader.
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