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
The power of a pebble: exploring and mapping directed graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Online computation and competitive analysis
Online computation and competitive analysis
Exploring unknown undirected graphs
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Piecemeal graph exploration by a mobile robot
Information and Computation
Optimal Graph Exploration without Good Maps
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
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
Power-Aware collective tree exploration
ARCS'06 Proceedings of the 19th international conference on Architecture of Computing Systems
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Space lower bounds for graph exploration via reduced automata
SIROCCO'05 Proceedings of the 12th international conference on Structural Information and Communication Complexity
Operations Research Letters
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Online graph exploration: new results on old and new algorithms
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Online graph exploration: New results on old and new algorithms
Theoretical Computer Science
Fast collaborative graph exploration
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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We consider a tree which has to be completely explored by a group of k robots, initially placed at the root. The robots are mobile and can communicate using radio devices, but the communication range is bounded. They decide based on local, partial knowledge, and exchange information gathered during the exploration. There is no central authority which knows the graph and could control the movements of the robots – they have to organize themselves and jointly explore the tree. The problem is that at every point of time the remaining unknown part of the tree may appear to be the worst case setting for the current deployment of robots. We present a deterministic distributed algorithm to explore T and we use a parameter of a tree called density. We compare the performance of our algorithm with the optimal algorithm having a-priori knowledge of the same tree. We show that the above ratio is influenced only by the density and the height of the tree. Since the competitive ratio does not depend on the number of robots, our algorithm truly emphasizes the phenomena of self-organization. The more robots are provided, the faster the exploration of the terrain is completed.