Cost-sensitive analysis of communication protocols
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Exploring unknown environments
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
The power of a pebble: exploring and mapping directed graphs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Multicasting in heterogeneous networks
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Exploring unknown environments with obstacles
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Pattern formation and optimization in army ant raids
Artificial Life
The freeze-tag problem: how to wake up a swarm of robots
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Efficiently searching a graph by a smell-oriented vertex process
Annals of Mathematics and Artificial Intelligence
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Analysis of Heuristics for the Freeze-Tag Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Two Dimensional Rendezvous Search
Operations Research
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
ACM Transactions on Algorithms (TALG)
Theoretical Computer Science
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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In the Freeze-Tag Problem, the objective is to awaken a set of "asleep" robots, starting with only one "awake" robot. A robot awakens a sleeping robot by moving to the sleeping robot's position. When a robot awakens, it is available to assist in awakening other slumbering robots. The objective is to compute an optimal awakening schedule/ such that all robots are awake by time t*, for the smallest possible value of t*. Because of its resemblance to the children's game of freeze-tag, this problem has been called Freeze-Tag Problem (FTP).A particularly intriguing aspect of the FTP is that any algorithm that is not purposely unproductive yields an O(log n)-approximation, while no o(log n)-approximation algorithms are known for general metric spaces.This paper presents an O(1)-approximation algorithm for the FTP in unweighted graphs, in which there is one asleep robot at each node. We show that this version of the FTP is NP-hard.We generalize our methods to the case in which there are multiple robots at each node and edges are unweighted; we obtain a θ(∗log n)-approximation in this case. In the case of weighted edges, our methods yield an O((L/d)log n)-approximation algorithm, where L is the length of the longest edge and d is the diameter of the graph.