Data structures and network algorithms
Data structures and network algorithms
Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
On approximating arbitrary metrices by tree metrics
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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Approximating a Finite Metric by a Small Number of Tree Metrics
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Analysis of Heuristics for the Freeze-Tag Problem
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Improved approximation algorithms for the freeze-tag problem
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Fault-tolerant gathering algorithms for autonomous mobile robots
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Traveling salesmen in the presence of competition
Theoretical Computer Science - Algorithmic combinatorial game theory
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
Convergence of autonomous mobile robots with inaccurate sensors and movements
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Distributed coordination algorithms for mobile robot swarms: new directions and challenges
IWDC'05 Proceedings of the 7th international conference on Distributed Computing
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
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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An optimization problem that naturally arises in the study of "swarm robotics" is to wake up a set of "asleep" robots, starting with only one "awake" robot. One robot can only awaken another when they are in the same location. As soon as a robot is awake, it assists in waking up other robots. The goal is to compute an optimal awakening schedule such that all robots are awake by time t*, for the smallest possible value of t*.We consider both scenarios on graphs and in geometric environments. In the graph setting, robots sleep at vertices and there is a length function on the edges. An awake robot can travel from vertex to vertex along edges, and the length of an edge determines the time it takes to travel from one vertex to the other.While this problem bears some resemblance to problems from various areas in combinatorial optimization such as routing, broadcasting, scheduling and covering, its algorithmic characteristics are surprisingly different. We prove that the problem is NP-hard, even for the special case of star graphs. We also establish hardness of approximation, showing that it is NP-hard to obtain an approximation factor better than 5/3, even for graphs of bounded degree.These lower bounds are complemented with several algorithmic results. We present a simple on-line algorithm that is O(logΔ)-competitive for graphs with maximum degree Δ. Other results include algorithms that require substantially more sophistication and development of new techniques:(1) The natural greedy strategy on star graphs has a worst-case performance of 7/3, which is tight.(2) There exists a PTAS for star graphs.(3) For the problem on ultrametrics, there is a polynomial-time approximation algorithm with performance ratio 2O(√log log n).(4) There is a PTAS, running in nearly linear time, for geometrically embedded instances (e.g., Euclidean distances in any fixed dimension).