The algebraic degree of geometric optimization problems
Discrete & Computational Geometry
Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Circle formation for oblivious anonymous mobile robots with no common sense of orientation
Proceedings of the second ACM international workshop on Principles of mobile computing
Fault-tolerant gathering algorithms for autonomous mobile robots
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems
SIAM Journal on Computing
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
Local strategies for maintaining a chain of relay stations between an explorer and a base station
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Optimal strategies for maintaining a chain of relays between an explorer and a base camp
Theoretical Computer Science
Randomized Gathering of Mobile Robots with Local-Multiplicity Detection
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A local O(n2) gathering algorithm
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Gathering asynchronous mobile robots with inaccurate compasses
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
A continuous, local strategy for constructing a short chain of mobile robots
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Gathering autonomous mobile robots with dynamic compasses: an optimal result
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Energy-efficient strategies for building short chains of mobile robots locally
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Local, self-organizing strategies for robotic formation problems
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
Optimal and competitive runtime bounds for continuous, local gathering of mobile robots
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
Gathering of robots on anonymous grids without multiplicity detection
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
How to gather asynchronous oblivious robots on anonymous rings
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Energy-efficient strategies for building short chains of mobile robots locally
Theoretical Computer Science
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The problem of gathering n autonomous robots in the Euclidean plane at one (not predefined) point is well-studied under various restrictions on the capabilities of the robots and in several time models. However, only very few runtime bounds are known. We consider the scenario of local algorithms in which the robots can only observe their environment within a fixed viewing range and have to base their decision where to move in the next step solely on the relative positions of the robots within their viewing range. Such local algorithms have to guarantee that the (initially connected) unit disk graph defined by the viewing range of the robots stays connected at all times. In this paper, we focus on the synchronous setting in which all robots are activated concurrently. Ando et al. [2] presented an algorithm where a robot essentially moves to the center of the smallest enclosing circle of the robots in its viewing range and showed that this strategy performs gathering of the robots in finite time. However, no bounds on the number of rounds needed by the algorithm are known. We present a lower bound of ©(n2) for the number of rounds as well as a matching upper bound of O(n2) and thereby obtain a tight runtime analysis of the algorithm of Θ(n).