Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Self-stabilizing systems in spite of distributed control
Communications of the ACM
Arbitrary pattern formation by asynchronous, anonymous, oblivious robots
Theoretical Computer Science
Solving the robots gathering problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Characterizing geometric patterns formable by oblivious anonymous mobile robots
Theoretical Computer Science
Leader election problem versus pattern formation problem
DISC'10 Proceedings of the 24th international conference on Distributed computing
Pattern formation through optimum matching by oblivious CORDA robots
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
The Gathering Problem for Two Oblivious Robots with Unreliable Compasses
SIAM Journal on Computing
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We present an oblivious pattern formation algorithm for anonymous mobile robots in the asynchronous model. The robots obeying the algorithm, starting from any initial configuration I, always form a given pattern F, if I and F do not contain multiplicities and ρ(I) divides ρ(F), where ρ(·) denotes the geometric symmetricity. Our algorithm substantially outdoes an algorithm by Dieudonné et al. proposed in DISC 2010, which is dedicated to ρ(I)=1. Our algorithm is best possible (as long as I and F do not contain multiplicities), since there is no algorithm that always forms F from I when ρ(F) is not divisible by ρ(I). All known pattern formation algorithms are constructed from scratch. We instead use a bipartite matching algorithm (between the robots and the points in F) we proposed in OPODIS 2011 as a core subroutine, to make the description of algorithm concise and easy to understand.