A Novel Family of Geometric Planar Graphs for Wireless Ad Hoc Networks

International audienceWe propose a radically new family of geometric graphs, i.e., Hypocomb, Reduced Hypocomb and Local Hypocomb. The first two are extracted from a complete graph; the last is extracted from a Unit Disk Graph (UDG). We analytically study their properties including connectivity, planarity and degree bound. All these graphs are connected (provided the original graph is connected) planar. Hypocomb has unbounded degree while Reduced Hypocomb and Local Hypocomb have maximum degree 6 and 8, respectively. To our knowledge, Local Hypocomb is the first strictly-localized, degree-bounded planar graph computed using merely 1-hop neighbor position information. We present a construction algorithm for these graphs and analyze its time complexity. Hypocomb family graphs are promising for wireless ad hoc networking. We report our numerical results on their average degree and their impact on FACE routing. We discuss their potential applications and some open problems

A Novel Family of Geometric Planar Graphs for Wireless Ad Hoc Networks

International audienceWe propose a radically new family of geometric graphs, i.e., Hypocomb, Reduced Hypocomb and Local Hypocomb. The first two are extracted from a complete graph; the last is extracted from a Unit Disk Graph (UDG). We analytically study their properties including connectivity, planarity and degree bound. All these graphs are connected (provided the original graph is connected) planar. Hypocomb has unbounded degree while Reduced Hypocomb and Local Hypocomb have maximum degree 6 and 8, respectively. To our knowledge, Local Hypocomb is the first strictly-localized, degree-bounded planar graph computed using merely 1-hop neighbor position information. We present a construction algorithm for these graphs and analyze its time complexity. Hypocomb family graphs are promising for wireless ad hoc networking. We report our numerical results on their average degree and their impact on FACE routing. We discuss their potential applications and some open problems

Improving Routing Efficiency through Intermediate Target Based Geographic Routing

The greedy strategy of geographical routing may cause the local minimum problem when there is a hole in the routing area. It depends on other strategies such as perimeter routing to find a detour path, which can be long and result in inefficiency of the routing protocol. In this paper, we propose a new approach called Intermediate Target based Geographic Routing (ITGR) to solve the long detour path problem. The basic idea is to use previous experience to determine the destination areas that are shaded by the holes. The novelty of the approach is that a single forwarding path can be used to determine a shaded area that may cover many destination nodes. We design an efficient method for the source to find out whether a destination node belongs to a shaded area. The source then selects an intermediate node as the tentative target and greedily forwards packets to it, which in turn forwards the packet to the final destination by greedy routing. ITGR can combine multiple shaded areas to improve the efficiency of representation and routing. We perform simulations and demonstrate that ITGR significantly reduces the routing path length, compared with existing geographic routing protocols

Planarisation de graphes dans les réseaux ad-hoc

We propose a radically new family of geometric graphs, i.e., Hypocomb, Reduced Hypocomb and Local Hypocomb. The first two are extracted from a complete graph; the last is extracted from a Unit Disk Graph (UDG). We analytically study their properties including connectivity, planarity and degree bound. All these graphs are connected (provided the original graph is connected) planar. Hypocomb has unbounded degree while Reduced Hypocomb and Local Hypocomb have maximum degree 6 and 8, respectively. To our knowledge, Local Hypocomb is the first strictly-localized, degree-bounded planar graph computed using merely 1-hop neighbor position information. We present a construction algorithm for these graphs and analyze its time complexity. Hypocomb family graphs are promising for wireless ad hoc networking. We report our numerical results on their average degree and their impact on FACE routing. We discuss their potential applications and pinpoint some interesting open problems for future research

Connected Spatial Networks over Random Points and a Route-Length Statistic

We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate a particular statistic $R$ measuring shortness of routes in a network. We illustrate, via Monte Carlo in part, the trade-off between normalized network length and $R$ in a one-parameter family of proximity graphs. How close this family comes to the optimal trade-off over all possible networks remains an intriguing open question. The paper is a write-up of a talk developed by the first author during 2007--2009.Comment: Published in at http://dx.doi.org/10.1214/10-STS335 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

An Analysis of Planarity in Face-Routing

In this report we investigate the limits of routing according to left- or right-hand rule (LHR). Using LHR, a node upon receipt of a message will forward to the neighbour that sits next in counter-clockwise order in the network graph. When used to recover from greedy routing failures, LHR guarantees success if implemented over planar graphs. This is often referred to as face or geographic routing. In the current body of knowledge it is known that if planarity is violated then LHR is guaranteed only to eventually return to the point of origin. Our work seeks to understand why a non-planar environment stops LHR from making delivery guarantees. Our investigation begins with an analysis to enumerate all node con gurations that cause intersections. A trace over each con guration reveals that LHR is able to recover from all but a single case, the `umbrella' con guration so named for its appearance. We use this information to propose the Prohibitive Link Detection Protocol (PDLP) that can guarantee delivery over non-planar graphs using standard face-routing techniques. As the name implies, the protocol detects and circumvents the `bad' links that hamper LHR. The goal of this work is to maintain routing guarantees while disturbing the network graph as little as possible. In doing so, a new starting point emerges from which to build rich distributed protocols in the spirit of protocols such as CLDP and GDSTR

A clustered back-bone for routing in ad-hoc networks

In the recent years, a lot of research work has been undertaken in the area of ad-hoc networks due to the increasing potential of putting them to commercial use in various types of mobile computing devices. Topology control in ad-hoc networks is a widely researched topic; with a number of algorithms being proposed for the construction of a power-efficient topology that optimizes the battery usage of the mobile nodes. This research proposes a novel technique of partitioning the ad-hoc network into virtually-disjoint clusters. The ultimate aim of forming a routing graph over which power-efficient routing can be implemented in a simple and effective manner is realized by partitioning the network into disjoint clusters and thereafter joining them through gateways to form a connected, planar back-bone which is also a t-spanner of the original Unit Disk Graph (UDG). Some of the previously proposed algorithms require the nodes to construct local variations of the Delaunay Triangulation and undertake several complicated steps for ensuring the planarity of the back-bone graph. The construction of the Delaunay Triangulation is very complex and time-consuming. This work achieves the objective of constructing a routing graph which is a planar spanner, without requiring the expensive construction of the Delaunay Triangulation, thus saving the node power, an important resource in the ad-hoc network. Moreover, the algorithm guarantees that the total number of messages required to be sent by each node is O(n). This makes the topology easily reconfigurable in case of node motion