Protocol Design for Dynamic Delaunay Triangulation

“…Suppose a node u fails to forward to its neighbor v, while there exists an edge from u to v in the global reverse-path tree. [From (2) and (11).] (13) It is impossible that x and p co-exist on the local DT of u, since they overlap.…”

Section: Theorem 1 Let a Set S Of Nodes Form A Correct Distributed Dmentioning

confidence: 99%

A Radius Geocast Routing Protocol

Lee

Chung

Lam

2008

2008 10th IEEE International Conference on High Performance Computing and Communications

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“…Our proofs of Lemma 3 and Theorem 4 are presented in the appendix. A proof of Theorem 3 is provided in [6]. We omit proof of Theorem 3 herein because it is very similar to that of Theorem 4.…”

Section: Lemma 3 Let S Be a Set Of Nodes And S ′ = S − {U} Let V Bementioning

confidence: 99%

“…Theorem 1, previously presented in [6], [8], identifies a necessary and sufficient condition for a distributed DT to be correct, namely: the candidate set of each node contains all of its global neighbors. We use the above correctness condition as a guide to design our protocols.…”

Section: Theorem 1 (Correctness Condition) Let S Be a Set Of Nodes Amentioning

confidence: 99%

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Efficient and accurate protocols for distributed delaunay triangulation under churn

Lee

Lam

2008

2008 IEEE International Conference on Network Protocols

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Abstract-We design a new suite of protocols for a set of nodes in d-dimension (d > 1) to construct and maintain a distributed Delaunay triangulation (DT) in a dynamic environment. The join, leave, and failure protocols in the suite are proved to be correct for a single join, leave, and failure, respectively. For a system under churn, it is impossible to maintain a correct distributed DT continually. We define an accuracy metric such that accuracy is 100% if and only if the distributed DT is correct. The suite also includes a maintenance protocol designed to recover from incorrect system states and to improve accuracy. In designing the protocols, we make use of two novel observations to substantially improve protocol efficiency. First, in the neighbor discovery process of a node, many replies to the node's queries contain redundant information. Second, the use of a new failure protocol that employs a proactive approach to recovery is better than the reactive approaches used in prior work. Experimental results show that our new suite of protocols maintains high accuracy for systems under churn and each system converges to 100% accuracy after churning stopped. They are much more efficient than protocols in prior work.

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