Complexity of Searching for a Black Hole
Fundamenta Informaticae
Mobile Search for a Black Hole in an Anonymous Ring
Algorithmica
Hardness and approximation results for Black Hole Search in arbitrary networks
Theoretical Computer Science
Black Hole Search with Tokens in Interconnected Networks
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Synchronous black hole search in directed graphs
Theoretical Computer Science
Tight bounds for scattered black hole search in a ring
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Improving the optimal bounds for black hole search in rings
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Black hole search with finite automata scattered in a synchronous torus
DISC'11 Proceedings of the 25th international conference on Distributed computing
Searching for Black Holes in Subways
Theory of Computing Systems - Special Issue: Fun with Algorithms
Black hole search in directed graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Rendezvous of mobile agents in unknown graphs with faulty links
DISC'07 Proceedings of the 21st international conference on Distributed Computing
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We consider the a team of asynchronous agents that must explore an unknown graph in presence of a black hole, a node which destroys all incoming agents without leaving any observable trace. Communication is achieved using pebbles that an agent can pick up, carry, and drop. It is known that, when the graph is unknown, Δ+1 agents are necessary, and solutions exist with those many agents, using a total of O(logΔ) pebbles, where Δ is the max node degree. On the other hand, it is also known that if the agents have a map of the graph, the problem can be solved with O(1) pebbles in total, without increasing the size of the team. In this paper we address the question of whether it is possible to locate the black hole using O(1) pebbles even if the graph is unknown, and, if so, with how many agents. We first prove that with O(1) pebbles, Δ+1 agents are not sufficient. We next prove that, regardless of the team size, 2 pebbles are not sufficient. We then show that these bounds are tight presenting a protocol that allows to locate a black hole in an unknown anonymous graph with only 3 pebbles and Δ+2 agents.