Searching for a Black Hole in Synchronous Tree Networks¶
Combinatorics, Probability and Computing
Mobile Search for a Black Hole in an Anonymous Ring
Algorithmica
Fast periodic graph exploration with constant memory
Journal of Computer and System Sciences
Graph Decomposition for Improving Memoryless Periodic Exploration
MFCS '09 Proceedings of the 34th International Symposium on Mathematical Foundations of Computer Science 2009
Locating a Black Hole without the Knowledge of Incoming Link
Algorithmic Aspects of Wireless Sensor Networks
Synchronization Helps Robots to Detect Black Holes in Directed Graphs
OPODIS '09 Proceedings of the 13th International Conference on Principles of Distributed Systems
Locating and repairing faults in a network with mobile agents
Theoretical Computer Science
Time optimal algorithms for black hole search in rings
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Black hole search in directed graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Asynchronous exploration of an unknown anonymous dangerous graph with o(1) pebbles
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Fault-Tolerant exploration of an unknown dangerous graph by scattered agents
SSS'12 Proceedings of the 14th international conference on Stabilization, Safety, and Security of Distributed Systems
Exploring an unknown dangerous graph using tokens
Theoretical Computer Science
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The paper considers a team of robots which has to explore a graph G, where some nodes can be harmful. Robots are initially located at the so-called home base node. The dangerous nodes are the so-called black hole nodes, and once a robot enters in one of them, it is destroyed. The goal is to find a strategy in order to explore G in such a way that minimum number of robots is wasted. The exploration ends if there is at least one surviving robot which knows all the edges leading to the black holes. As many variations of the problem have been considered so far, the solution and its measure heavily depend on the initial knowledge and the capabilities of the robots. In this paper, we assume that G is a directed graph, the robots are associated with unique identifiers, they know the number of nodes n of G (or at least an upper bound on n), and they know the number of edges @D leading to the black holes. Each node is associated with a whiteboard where robots can read and write information in a mutual exclusive way. A recently posed question [J. Czyzowicz, S. Dobrev, R. Kralovic, S. Miklik, D. Pardubska, Black hole search in directed graphs, in: Proc. of 16th International Colloquium on Structural Information and Communication Complexity, SIROCCO, LNCS, vol. 5869, 2009, pp. 182-194.] is whether some number of robots, expressed as a function of parameter @D only, is sufficient to detect black holes in directed graphs of arbitrarily large order n. We give a positive answer to this question for the synchronous case, i.e., when the robots share a common clock, showing that O(@D@?2^@D) robots are sufficient to solve the problem. This bound is nearly tight, since it is known that at least 2^@D robots are required for some instances. Quite surprisingly, we also show that unlike in the case of undirected graphs, for the directed version of the problem, synchronization can sometimes make a difference: for @D=2, in the synchronous case 4 robots are always sufficient, whereas in the asynchronous case at least 5 robots are sometimes required.