
Improved Lower Bound for Competitive Graph Exploration
We give an improved lower bound of 10/3 on the competitive ratio for the...
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The Graph Exploration Problem with Advice
Moving an autonomous agent through an unknown environment is one of the ...
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Fast and Reliable Dispersal of CrashProne Agents on Graphs
We study the ability of mobile agents performing simple local computatio...
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The Space Complexity of Sum Labelling
A graph is called a sum graph if its vertices can be labelled by distinc...
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Maximal Exploration of Trees with EnergyConstrained Agents
We consider the problem of exploring an unknown tree with a team of k in...
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Anytime Coalition Structure Generation with Worst Case Guarantees
Coalition formation is a key topic in multiagent systems. One would pref...
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Fast BreadthFirst Search in Still Less Space
It is shown that a breadthfirst search in a directed or undirected grap...
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Tight bounds for undirected graph exploration with pebbles and multiple agents
We study the problem of deterministically exploring an undirected and initially unknown graph with n vertices either by a single agent equipped with a set of pebbles, or by a set of collaborating agents. The vertices of the graph are unlabeled and cannot be distinguished by the agents, but the edges incident to a vertex have locally distinct labels. The graph is explored when all vertices have been visited by at least one agent. In this setting, it is known that for a single agent without pebbles Θ( n) bits of memory are necessary and sufficient to explore any graph with at most n vertices. We are interested in how the memory requirement decreases as the agent may mark vertices by dropping and retrieving distinguishable pebbles, or when multiple agents jointly explore the graph. We give tight results for both questions showing that for a single agent with constant memory Θ( n) pebbles are necessary and sufficient for exploration. We further prove that the same bound holds for the number of collaborating agents needed for exploration. For the upper bound, we devise an algorithm for a single agent with constant memory that explores any nvertex graph using O( n) pebbles, even when n is unknown. The algorithm terminates after polynomial time and returns to the starting vertex. Since an additional agent is at least as powerful as a pebble, this implies that O( n) agents with constant memory can explore any nvertex graph. For the lower bound, we show that the number of agents needed for exploring any graph of size n is already Ω( n) when we allow each agent to have at most O( n ^1ε) bits of memory for any ε>0. This also implies that a single agent with sublogarithmic memory needs Θ( n) pebbles to explore any nvertex graph.
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