Efficient and accurate protocols for distributed delaunay triangulation under churn

Abstract

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.

A Radius Geocast Routing Protocol

“…Our protocols run on a distributed DT of a set of nodes in Euclidean space. A suite of protocols to construct and maintain a distributed DT for a dynamic set of nodes in d-dimensional space (d ≥ 2) is presented in our prior work [10].…”

“…Definition of a distributed DT and a discussion of its properties are presented in section 3. We present a suite of protocols to construct and maintain a distributed DT for a dynamic set of nodes in d-dimensional space (d ≥ 2) in [10].…”

In-Network Analytics for Ubiquitous Sensing

“…To achieve this, we employ selective learning; each node learns an estimate for its local area, or sector, based on its samples and communication with its neighbors. (The division of the region and assignment of nodes can be done with known techniques [2,3,4,5] and is outside the scope of this paper.) We thus define an optimization problem where each node's estimate has to minimize some convex error function related to collected samples, while requiring that the union of these estimates is continuous over the entire region.…”

GoDel: Delaunay overlays in P2P networks via Gossip

“…Recently, a few distributed algorithms targeted at P2P environments have been proposed. In [6] and [2] a protocol is proposed where each peer first exploits a greedy routing phase to find its neighbours in the overlay and then exchanges information with them to stabilize the overlay. The stabilization phase generally entails exchanging a large number of messages, however in the presence of a high churn rate, the consistency of the network is not guaranteed.…”

“…These kinds of applications cover many fields such as, spatial data storing and retrieval [1], spatial clustering of peers [2] and P2P Distributed Virtual Environments (DVE) [3]. In a P2P DVE each peer is associated with an "avatar" whose geographical coordinates in the virtual world are exploited to map the peer onto a 2D space.…”