A SubLinear Time Distributed Algorithm for Minimum-Weight Spanning Trees
SIAM Journal on Computing
Fast distributed construction of small k-dominating sets and applications
Journal of Algorithms
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Graph exploration by a finite automaton
Theoretical Computer Science - Mathematical foundations of computer science 2004
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
Journal of Graph Theory
Ping Pong in Dangerous Graphs: Optimal Black Hole Search with Pure Tokens
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
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
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 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
Synchronous black hole search in directed graphs
Theoretical Computer Science
Improving the optimal bounds for black hole search in rings
SIROCCO'11 Proceedings of the 18th 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
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In a network environments supporting mobile entities (called robots or agents), a black hole is harmful site that destroys any incoming entity without leaving any visible trace. The black-hole search problem is the task of a team of k 1 mobile entities, starting from the same safe location and executing the same algorithm, to determine within finite time the location of the black hole. In this paper we consider the black hole search problem in asynchronous ring networks of n nodes, and focus on the time complexity. It is known that any algorithm for black-hole search in a ring requires at least 2(n-2) time in the worst case. The best algorithm achieves this bound with a team of n - 1 agents with an average time cost 2(n - 2), equal to the worst case. In this paper we first show how the same number of agents using 2 extra time units from optimal in the worst case, can solve the problem in only 7/4n- O(1) time on the average. We then prove that the optimal average case complexity 3/2n - O(1) can be achieved without increasing the worst case using 2(n- 1) agents Finally we design an algorithm that achieves asymptotically optimal both worst case and average case time complexity employing an optimal team of k = 2 agents, thus improving on the earlier results that required O(n) agents.