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Figure 8.7. Localized constructions of planar subgraph. (a) Gabriel graph construction. (b) Relative neighborhood graph construction.
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Face- and perimeter-routing techniques choose to route greedily whenever possible. The recovery phase is initiated only when a message gets stuck at some node. Upon receipt of message m destined for node t, node s inspects the message to reveal it either in greedy or recovery mode. The corresponding algorithms, executed at each node, are listed in Algorithms 1 and 2.
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ALGORITHM 1. Greedy Mode
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let s be the current node let w be the neighbor closest to t if (w, t) < (s, t) then forward m to w else {no such w exists; m is stuck at s} mark packet as recovery with location of s forward to neighbor that is left of t s, end if
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ALGORITHM 2. Face/Recovery Mode
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let u be the node from which m was received let v be the current node let w be the neighbor closest to t if (w, t) < (s, t) then mark packet as greedy forward to w else forward to neighbor that is left of u v, end if
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POSITION-BASED ROUTING FOR SENSOR NETWORKS: APPROACHES AND OBSTACLES
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Algorithms 1 and 2 assume that a stuck node has rst constructed the portion of the planar subgraph that occurs within its view, as above. If in greedy mode a packet is forwarded according to Algorithm 1, where a sensor forwards to the neighbor closest to the destination. If no such neighbor exists, then the sensor node forwards according to Algorithm 2. Once stuck, the message m is marked recovery and is forwarded to the neighbor that appears rst in a counterclockwise direction. While in recovery mode, each sensor that receives the message rst checks for a neighbor closer to the destination than the point at which the message was marked recovery. Returning to Figure 8.3a, we can see s is a stuck node. In the case of the left-hand rule, sx is left of sd. The recovery path sxy terminates upon nding z since z is closer to d than s, where recovery began. One special case occurs where an edge uv intersects sd during recovery. The solution is left as an exercise. These algorithms are especially suited to sensor networking environments: They guarantee delivery, are localized in their operation, and are stateless in the sense that they require no information outside of the location of their neighbors. However, we see in the next section that subplanar methods are not without their drawbacks.
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Drawbacks and Challenges of Planar Methods. Planar subgraph methods, while promising, face three major challenges before their deployment may be considered feasible. First, planarization assumes locations are accurate, an assumption that may be untrue. Second, the localized nature of the planarization process means that one sensor node may be blind to environmental obstacles that are visible to neighboring sensors. Finally, the unit disk model on which these algorithms are constructed is a poor representation of the real world. We use this section to touch on each of these challenges. Routing protocols that operate over pre-established coordinate systems are generally designed under the assumption that location information is accurate. This assumption is challenged by real-world limitations. GPS, for example, offers high-resolution localization, but is subject to line-of-sight constraints rendering it ill-suited to underground, underwater, and undercoverage applications, to name a few. Furthermore, the added expense incurred by supporting GPS in all nodes is restrictive. Many proposals exist to resolve this issue by supporting some small location-aware infrastructure [27 30], from which all other nodes may learn their locations; yet even these fall prey to poor resolution and estimation errors. There are cases where localization and estimation errors have little adverse effect. For example, in reference 31 greedy routing was evaluated in simulated networks with localization errors. The results show that the performance of greedy routing is largely unaffected by inaccuracies up to 40% of the radio range. Conversely, there are contexts in which localization errors can be destructive to correct protocol operation. One such example is demonstrated in reference 32, which models and evaluates location error on face-routing techniques; here we nd that errors of as little as 20% of the communication range caused high packet drop rates,
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