ROUTING WITH KNOWN POSITIONS in .NET framework

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direction of the destination. Referring to Figure 8.2, we can see that node c, with angle csd, is smallest among all of the neighbors of s. Thus, the goal is to minimize the change in direction from the source to the destination. The DREAM [17] and LAR [18] projects, simultaneously proposed, use an idea similar to compass routing. However, these two approaches are best suited in networks where nodes are mobile. (Despite their application in mobile environments, we provide an overview for completeness.) The node that holds a message m with destination d calculates an angular range where the message must be forwarded. The angular range is calculated using (i) the circle centered at d with radius equal to the maximum movement of d since the last update and (ii) the tangents from the current location to the aforementioned circle. All nodes within this angular range are sent a copy of the message. Clearly, the success of both methods relies on some knowledge of the global network, as well as duplication of messages. Such methods fall outside of the domain of position-based routing. Each of MFR, NFP, and Compass Routing is myopic. They are localized algorithms that require knowledge only of the immediate neighborhood. Unfortunately, their global behavior is such that none of these approaches can claim to be loop-free. Still, consider that their forwarding decisions attempt to optimize some local criteria, the effect of which is to approximate the shortest Euclidean path between the source and destination. The shortest path may be approximated using another approach that referred to as greedy forwarding. Greedy forwarding is a localized forwarding scheme whose express goal is to traverse the Euclidean shortest path. It is this approach on which most research and development, where there is a known and underlying Euclidean coordinate system, has focused.
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Greedy Forwarding. Greedy forwarding was rst proposed in reference 19 as a routing protocol for wired networks. Referred to as Cartesian routing, the next hop was chosen to be the neighbor that is closest to the destination. Because this work predated GPS and other localization services, knowledge of the global topology was required. The same idea has been reapplied in wireless network settings as the foundation of innumerable routing schemes and algorithms. It is known to behave especially well in dense wireless networks such as those envisioned in many sensor networks. Greedy forwarding works as follows. Say node s has the neighborhood N = n1 , ..., nk of size k where each ni is a potential next hop in a traversal that passes through s. Any message that arrives at s has embedded within it the destination d. The greedy approach says that the successor to s will be the neighbor ni that minimizes the Euclidean distance to d. In Figure 8.2 we can see that node s will select g, the node that most further reduces the distance to the destination among its neighbors. It can be shown that greedy forwarding is loop-free (using the simple fact that every hop reduces the distance to the destination). The delivery rate of greedy forwarding is known to be quite high in dense networks, but diminishes quickly as the density falls [20]. The problem is that a greedy path may terminate in a routing hole, or void, as shown in the next section.
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POSITION-BASED ROUTING FOR SENSOR NETWORKS: APPROACHES AND OBSTACLES
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Figure 8.3. Neighbors of stuck nodes may or may not make progress. (a) Convex case. (b) Concave case.
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8.3.2 Routing Holes Greedy forwarding may be loop-free, but delivery is not guaranteed. A consequence of greedy forwarding is that a route may terminate at local minima, where nodes have no neighbors that further reduce the distance to the destination. We refer our reader to Figure 8.3, which depicts the types of local minima that may occur: The smaller dotted circle represents the communication range of node S, and the larger circle centered at D is used to show that all neighbors of S are further from D than from S itself. Consider that a message destined for node D reaches a minima at node S. There are two cases to consider. The rst, as shown in Figure 8.3a, occurs where neighbors of S make no progress toward D according to De nition 8.3.1. This is the obvious case. Less obvious is the case where neighbors of S may actually make progress toward the destination, yet increase the distance from the current location. This example is demonstrated in Figure 8.3b, where S clearly lies within the circle centered at D, while the neighbors of S, x, and A lie outside of the same circle. These local minima are commonly referred to as voids, holes, or stuck regions. Their occurrence largely determines the performance of greedy forwarding, whose performance varies with network density and distribution. A robust sensor network routing protocol must perform well despite the occurrence of local minima. We proceed in our discussion with proposed solutions to the routing hole problem. 8.3.3 Algorithms for Recovery from Routing Holes Greedy forwarding is known to perform well in suf ciently dense networks [10], yet there are no delivery guarantees. Many sensor network applications are loss-sensitive and have little to no tolerance for undelivered information. Thus greedy forwarding schemes aiming to guarantee delivery demand that routing voids be circumvented or
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