A heuristic with worst-case analysis for minimax routing of two travelling salesmen on a tree
Discrete Applied Mathematics
(p-1)/(p+1)-approximate algorithms for p-traveling salemen problems on a tree with minmax objective
Discrete Applied Mathematics
Performing Work Efficiently in the Presence of Faults
SIAM Journal on Computing
A Framework to Protect Mobile Agents by Using Reference States
ICDCS '00 Proceedings of the The 20th International Conference on Distributed Computing Systems ( ICDCS 2000)
Randomization helps to perform independent tasks reliably
Random Structures & Algorithms
A faster 2-approximation algorithm for the minmax p-traveling salesmen problem on a tree
Discrete Applied Mathematics
Networks
Do-All Computing in Distributed Systems
Do-All Computing in Distributed Systems
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
The power of team exploration: two robots can learn unlabeled directed graphs
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Searching for black-hole faults in a network using multiple agents
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Distributed security algorithms by mobile agents
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
Black hole search in asynchronous rings using tokens
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Searching for a black hole in tree networks
OPODIS'04 Proceedings of the 8th international conference on Principles of Distributed Systems
Mapping an unfriendly subway system
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
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
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We consider a fixed, undirected, known network and a number of ''mobile agents'' which can traverse the network in synchronised steps. Some nodes in the network may be faulty and the agents are to find the faults and repair them. The agents could be software agents, if the underlying network represents a computer network, or robots, if the underlying network represents some potentially hazardous physical terrain. Assuming that the first agent encountering a faulty node can immediately repair it, it is easy to see that the number of steps necessary and sufficient to complete this task is @Q(n/k+D), where n is the number of nodes in the network, D is the diameter of the network, and k is the number of agents. We consider the case where one agent can repair only one faulty node. After repairing the fault, the agent dies. We show that a simple deterministic algorithm for this problem terminates within O(n/k+Dlogf/loglogf) steps, where f=min{n/k,n/D}, assuming that the number of faulty nodes is at most k/2. We also demonstrate the worst-case asymptotic optimality of this algorithm by showing a network such that for any deterministic algorithm, there is a placement of k/2 faults forcing the algorithm to work for @W(n/k+Dlogf/loglogf) steps.