Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
Fault-Tolerant Gathering Algorithms for Autonomous Mobile Robots
SIAM Journal on Computing
Impossibility of gathering by a set of autonomous mobile robots
Theoretical Computer Science
Gathering two stateless mobile robots using very inaccurate compasses in finite time
Proceedings of the 1st international conference on Robot communication and coordination
Gathering Problem of Two Asynchronous Mobile Robots with Semi-dynamic Compasses
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
Using eventually consistent compasses to gather memory-less mobile robots with limited visibility
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Dynamic compass models and gathering algorithms for autonomous mobile robots
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Gathering asynchronous mobile robots with inaccurate compasses
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Fault-tolerant and self-stabilizing mobile robots gathering
DISC'06 Proceedings of the 20th international conference on Distributed Computing
Gathering autonomous mobile robots with dynamic compasses: an optimal result
DISC'07 Proceedings of the 21st international conference on Distributed Computing
Collisionless gathering of robots with an extent
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
A tight runtime bound for synchronous gathering of autonomous robots with limited visibility
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
A new approach for analyzing convergence algorithms for mobile robots
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Gathering of six robots on anonymous symmetric rings
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Self-stabilizing gathering with strong multiplicity detection
Theoretical Computer Science
Mobile robots gathering algorithm with local weak multiplicity in rings
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Gathering of robots on anonymous grids without multiplicity detection
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
On the self-stabilization of mobile oblivious robots in uniform rings
SSS'12 Proceedings of the 14th international conference on Stabilization, Safety, and Security of Distributed Systems
How to gather asynchronous oblivious robots on anonymous rings
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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Let us consider the gathering problem of n anonymous and oblivious mobile robots, which requires that all robots meet in finite time at a non-predefined point. While the gathering problem cannot be solved deterministically without any additional capability to robots, randomized approach easily allows it to be solvable. However, only the randomized solution taking expected round complexity exponential of n is currently known. Motivated by this fact, we investigate the feasibility of polynomial-expected-round randomized gathering in this paper. Our first contribution is to give a negative result about the round complexity of randomized gathering. It is proved that any algorithm without no additional assumption has ${\it \Omega}(\mathrm{exp}(n))$ expected-round lower bound. This lower bound yields a question: What additional assumptions are necessary to achieve gathering in polynomial expected rounds? We address this question from the aspect of multiplicity detection. This paper newly introduces two weaker variants of multiplicity detection capability, called local-strong and local-weak multiplicity, and investigates whether those capabilities permit polynomial-expected-round gathering or not. Our second contribution is to reveal the power of local (strong/weak) multiplicity by showing that local-strong multiplicity detection allows O (n )-expected round gathering but local-weak multiplicity detection takes an exponential-time lower bound. These results imply that those two kinds of multiplicity-detection capabilities have inherently large difference about their computational powers.