Geometric Routing Research Articles

Aligned virtual coordinates for greedy geometric routing in WSNs

The performance of geographic routing protocols is impacted by physical voids and localisation errors. Traversing voids is carried out by a complimentary algorithm, which requires high overhead and results in lower quality paths. Furthermore, localisation errors lead to inefficient routes or even misrouting of packets. Accordingly, Virtual Coordinate Systems (VCS) were proposed to be an alternative solution that is resilient to localisation errors and naturally traverses physical voids. However, we show that VCS is vulnerable to different forms of anomalies and actually perform worse than physical coordinates. The goal of this paper is to increase the success or Greedy Forwarding (GF) in VCS, to avoid using the expensive complementary algorithm. We identify some of the reasons that cause anomalies in VCS and propose an Aligned Virtual Coordinate System (AVCS) to address them. AVCS aligns the coordinates of nodes by taking into account the coordinates of their neighbours. With AVCS, greedy routing success is significantly improved, approaching perfect delivery for many scenarios. With our approach, and for the first time, we show that greedy routing on VCS out performs that on geographic coordinate systems even in the absence of localisation errors. We compare AVCS against some of the most popular geometric routing protocols both on geographic and VCS and show that AVCS significantly improves performance over the best known solutions.

A Distributed Graph Algorithm for Geometric Routing in Ad Hoc Wireless Networks

This paper presented a fully distributed algorithm to compute a planar subgraph of the underlying wireless connectivity graph. This work considered the idealized unit disk graph model in which nodes are assumed to be connected if, and only if, nodes are within their transmission range. The main contribution of this work is a fully distributed algorithm to extract the connected, planar graph for routing in the wireless networks. The communication cost of the proposed algorithm is O(d log d) bits, where d is the degree of a node. In addition, this paper also presented a geometric routing algorithm and established its lower bound. The algorithm is fully distributed and nodes know only the position of other nodes and can communicate with neighboring nodes in their transmission range.

Ab-initio calculation on Co substitution into NiSi

Vertical interconnect technology called 3D stacking has been a major focus of the next generation of IC industries. 3D stacked devices in the vertical dimension give several important advantages over conventional two-dimensional scaling. The most eminent advantage is its performance improvement. Vertical device stacking enhances a performance such as inter-die bandwidth improvements, RC delay mitigation and geometrical routing and placement advantages. At present memory stacking options are of great interest to many industries and research institutes. However, these options are more focused on a form factor reduction rather than the high performance improvements. In order to improve a stacked device performance significantly vertical interconnect technology with wafer level stacking needs to be much more progressed with reduction in inter-wafer pitch and increases in the number of stacked layers. Even though 3D wafer level stacking technology offers many opportunities both in the short term and long term, the full performance benefits of 3D wafer level stacking require technological developments beyond simply the wafer stacking technology itself.

MAP: Medial axis based geometric routing in sensor networks

One of the challenging tasks in the deployment of dense wireless networks (like sensor networks) is in devising a routing scheme for node to node communication. Important consideration includes scalability, routing complexity, quality of communication paths and the load sharing of the routes. In this paper, we show that a compact and expressive abstraction of network connectivity by the medial axis enables efficient and localized routing. We propose MAP, a Medial Axis based naming and routing Protocol that does not require geographical locations, makes routing decisions locally, and achieves good load balancing. In its preprocessing phase, MAP constructs the medial axis of the sensor field, defined as the set of nodes with at least two closest boundary nodes. The medial axis of the network captures both the complex geometry and non-trivial topology of the sensor field. It can be represented succinctly by a graph whose size is in the order of the complexity of the geometric features (e.g., the number of holes). Each node is then given a name related to its position with respect to the medial axis. The routing scheme is derived through local decisions based on the names of the source and destination nodes and guarantees delivery with reasonable and natural routes. We show by both theoretical analysis and simulations that our medial axis based geometric routing scheme is scalable, produces short routes, achieves excellent load balancing, and is very robust to variations in the network model.

Efficient Delaunay‐based localized routing for wireless sensor networks

AbstractConsider a wireless sensor network consisting of n wireless sensors randomly distributed in a two‐dimensional plane. In this paper, we show that with high probability we can locally find a path for any pair of sensors such that the length of the path is no more than a constant factor of the minimum. By assuming each sensor knows its position, our new routing method decides where to forward the message purely based on the position of current node, its neighbours, and the positions of the source and the target. Our method is based on a novel structure called localized Delaunay triangulation and a geometric routing method that guarantees that the distance travelled by the packets is no more than a small constant factor of the minimum when the Delaunay triangulation of sensor nodes are known. Our experiments show that the delivery rates of existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies, and our localized routing protocol based on Delaunay triangulation works well in practice. We also conducted extensive simulations of another localized routing protocol, face routing. The path found by this protocol is also reasonably good compared with previous one although it cannot guarantee a constant approximation on the length of the path travelled theoretically. Copyright © 2006 John Wiley & Sons, Ltd.

A Routing Algorithm for Ad Hoc Networks Based on Delaunay Triangulation

Delaunay triangulation has been widely used in many fields such as computational fluid dynamics, statistics, meteorology, solid state physics, computational geometry and so on. With the development of Ad Hoc networks, some researchers proposed geometric routing protocols to guarantee the delivery of the packet between any pair of nodes in the network, and the underlying network topology is also constructed by the ways of Delaunay triangulation. In this paper, a novel online routing algorithm GLNFR (greedy and local neighbor face routing) for finding communication paths between the mobile nodes is proposed. The localized manner is used to form the local Delaunay triangulation as the underlying topology of a wireless network on which the GLNFR routing algorithm could guarantee the delivery of the packets. It has better scalability and adaptability for the change of networks. Experiment on NS (network simulator) has been conducted. The results show that the delivery success rate of packets and routing protocol overhead under such novel routing protocols performs better than others proposed

On a conjecture related to geometric routing

We conjecture that any planar 3-connected graph can be embedded in the plane in such a way that for any nodes s and t, there is a path from s to t such that the Euclidean distance to t decreases monotonically along the path. A consequence of this conjecture would be that in any ad hoc network containing such a graph as a spanning subgraph, two-dimensional virtual coordinates for the nodes can be found for which the method of purely greedy geographic routing is guaranteed to work. We discuss this conjecture and its equivalent forms show that its hypothesis is as weak as possible, and show a result delimiting the applicability of our approach: any 3-connected K 3 , 3 -free graph has a planar 3-connected spanning subgraph. We also present two alternative versions of greedy routing on virtual coordinates that provably work. Using Steinitz's theorem we show that any 3-connected planar graph can be embedded in three dimensions so that greedy routing works, albeit with a modified notion of distance; we present experimental evidence that this scheme can be implemented effectively in practice. We also present a simple but provably robust version of greedy routing that works for any graph with a 3-connected planar spanning subgraph.

A comparative study of two Boolean formulations of FPGA detailed routing constraints

We present empirical analyses of two Boolean satisfiability (SAT) formulations of FPGA (field programmable gate array) detailed routing constraints. Boolean SAT-based routing transforms a routing problem into a Boolean SAT instance by rendering geometric routing constraints as an atomic Boolean function. The generated Boolean function is satisfiable if and only if the corresponding routing is possible. Two different Boolean SAT-based routing models are analyzed: the track-based and the route-based routing constraint model. The track-based routing model transforms a routing task into a net-to-track assignment problem, whereas the route-based routing model reduces it into a routability-checking problem with explicitly enumerated set of detailed routes for nets. In both models, routing constraints are represented as CNF Boolean satisfiability clauses. Through comparative experiments, we demonstrate that the route-based formulation yields an easier-to-evaluate and more scalable routability Boolean function than the track-based method. This is empirical evidence that a smart/efficient Boolean formulation can achieve significant performance improvement in real-world applications.

The Application of Remote Sensor Technology To Assist the Recovery of Rare and Endangered Species

We describe a wireless sensor network designed for the long-term study of rare and endangered species of plants. We wish to monitor plants and their environment via high-resolution cameras and temperature, humidity, rainfall, wind, and solar radiation sensors. Our units must be “invisible” (camouflaged), very low energy, and must allow distributed local computation. Data rates are 1 to 100 bytes/second per node, but networks can be large — an early prototype had 60 nodes. Failures are expensive and we must exploit redundancy whenever possible. Nodes are stationary but for energy reasons may decline to participate in transmissions. We have designed two wireless routing protocols that satisfy these constraints. Multipath On-demand Routing (MOR) computes multiple optimal routes to avoid depleting the energy at any given node. Geometric Routing scales to large networks, relying on Geographic Routing when possible and on selected global information otherwise. We have simulated and are implementing both protocols.

Automatic router for the pin grid array package

A pin grid array (PGA) package router is described. Given a chip cavity with a number of I/O pads around its boundary and an equivalent number of pins distributed on the substrate, the objective of the router is to complete the planar interconnection of pad-to-pin nets on one or more layers. This router consists of three phases: layer assignment, topological routing and geometrical routing. Examples tested on a windows-based environment show that our router is efficient and can complete the routing task with less substrate layers. Compared to manual routing, this router has a user-friendly graphic interface and can be applied practically to industrial strength VLSI packaging.