SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Self-stabilizing systems in spite of distributed control
Communications of the ACM
Chord: A scalable peer-to-peer lookup service for internet applications
Proceedings of the 2001 conference on Applications, technologies, architectures, and protocols for computer communications
Geometric spanner for routing in mobile networks
MobiHoc '01 Proceedings of the 2nd ACM international symposium on Mobile ad hoc networking & computing
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
DIALM-POMC '03 Proceedings of the 2003 joint workshop on Foundations of mobile computing
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Tiara: A Self-stabilizing Deterministic Skip List
SSS '08 Proceedings of the 10th International Symposium on Stabilization, Safety, and Security of Distributed Systems
A distributed polylogarithmic time algorithm for self-stabilizing skip graphs
Proceedings of the 28th ACM symposium on Principles of distributed computing
A Self-stabilizing and Local Delaunay Graph Construction
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Re-Chord: a self-stabilizing chord overlay network
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Building self-stabilizing overlay networks with the transitive closure framework
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
Corona: a stabilizing deterministic message-passing skip list
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
Self-stabilizing De Bruijn networks
SSS'11 Proceedings of the 13th international conference on Stabilization, safety, and security of distributed systems
Communication-efficient construction of the plane localized delaunay graph
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Time complexity of distributed topological self-stabilization: the case of graph linearization
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Fast localized delaunay triangulation
OPODIS'04 Proceedings of the 8th international conference on Principles of Distributed Systems
Localized Delaunay triangulation with application in ad hoc wireless networks
IEEE Transactions on Parallel and Distributed Systems
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This article studies the construction of self-stabilizing topologies for distributed systems. While recent research has focused on chain topologies where nodes need to be linearized with respect to their identifiers, we explore a natural and relevant 2-dimensional generalization. In particular, we present a local self-stabilizing algorithm DStab which is based on the concept of ''local Delaunay graphs'' and which forwards temporary edges in greedy fashion reminiscent of compass routing. DStab constructs a Delaunay graph from any initial connected topology and in a distributed manner in time O(n^3) in the worst-case; if the initial network contains the Delaunay graph, the convergence time is only O(n) rounds. DStab also ensures that individual node joins and leaves affect a small part of the network only. Such self-stabilizing Delaunay networks have interesting applications and our construction gives insights into the necessary geometric reasoning that is required for higher-dimensional linearization problems.