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
A faster 2-approximation algorithm for the minmax p-traveling salesmen problem on a tree
Discrete Applied Mathematics
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
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Smart robot teams exploring sparse trees
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Collecting information by power-aware mobile agents
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Fast collaborative graph exploration
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
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An n-node tree has to be explored by a group of k mobile robots deployed initially at the root. Robots traverse the edges of the tree until all nodes are visited. We would like to minimize maximal distance traveled by each robot (e.g. to preserve the battery power). First, we assume that a tree is known in advance. For this NP-hard problem we present a 2-approximation. Moreover, we present an optimal algorithm for a case where k is constant. From the 2-approximation algorithm we develop a fast 8-competitive online algorithm, which does not require a previous knowledge of the tree and collects information during the exploration. Furthermore, our online algorithm is distributed and uses only a local communication. We show a lower bound of 1.5 for the competitive ratio of any deterministic online algorithm.