Complexity of Searching for a Black Hole
Fundamenta Informaticae
Searching for a Black Hole in Synchronous Tree Networks¶
Combinatorics, Probability and Computing
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
Map construction and exploration by mobile agents scattered in a dangerous network
IPDPS '09 Proceedings of the 2009 IEEE International Symposium on Parallel&Distributed Processing
Black Hole Search with Tokens in Interconnected Networks
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
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
Searching for black-hole faults in a network using multiple agents
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Black hole search in asynchronous rings using tokens
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Black hole search in directed graphs
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Periodic data retrieval problem in rings containing a malicious host
SIROCCO'10 Proceedings of the 17th 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
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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In this paper we re-examine the well known problem of asynchronous black hole search in a ring. It is well known that at least 2 agents are needed and the total number of agents' moves is at least Ω(n log n); solutions indeed exist that allow a team of two agents to locate the black hole with the asymptotically optimal cost of Θ(n log n) moves. In this paper we first of all determine the exact move complexity of black hole search in an asynchronous ring. In fact, we prove that 3n log3 n-O(n) moves are necessary. We then present a novel algorithm that allows two agents to locate the black hole with at most 3n log3 n + O(n) moves, improving the existing upper bounds, and matching the lower bound up to the constant of proportionality. Finally we show how to modify the protocol so to achieve asymptotically optimal time complexity Θ(n), still with 3n log3 n + O(n) moves; this improves upon all existing time-optimal protocols, which require O(n2) moves. This protocol is the first that is optimal with respect to all three complexity measures: size (number of agents), cost (number of moves) and time; in particular, its cost and size complexities match the lower bounds up to the constant.