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The correlation coef cient, (i,j) , between each representative node ni and nj affects the distortion positively As the distance between nodes increases, distortion decreases Since nodes that are further apart observe less correlated data, the distortion is decreased if these nodes are chosen as the representative nodes Consequently, due to the spatial correlation between sensor observations, significant energy saving can be achieved by choosing representative nodes among the nodes in the event area without degrading the achieved distortion at the sink It is clear that smaller number of nodes transmitting information reduces contention in the wireless medium, resulting in decreased energy consumption Energy consumed from both transmission of packets and collision penalties can be reduced drastically if the spatial correlation is exploited As a result, it is important to nd the minimum number of representative nodes that achieve the distortion constraint given by the sensor application.

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This minimum number can be given as M = arg (min {D(M) < Dmax }) M where Dmax is the maximum distortion allowed by the sensor application It is important to note that the minimum number of representative nodes, M , depends on the locations of the representative nodes It follows from our previous discussions that, for a xed number of representative nodes, the minimum distortion can be achieved by choosing these nodes such that (i) they are located as close to the event source as possible and (ii) they are located as farther apart from each other as possible As an example, as illustrated in Figure 53, choosing representative nodes such that they are spread over the event area results in a decrease in distortion, due to less redundant data sent by these nodes.

public Image getColumnImage(Object element, int columnIndex) { if (columnIndex == 0) return images[((TestResult)element)status]; return null; } Only the first column has an image After casting the passed-in element to TestResult, we return the image corresponding to the test result's status We override the dispose() method, which JFace calls to enable clients to free resources

Note that such a formation also improves the medium access performance during the transmission of the information Since the representative nodes are not located close to each other, the probability of collision in the wireless medium decreases As a result, exploiting spatial correlation not only improves the distortion but also utilizes the wireless channel due to the spatial reuse property of the wireless medium..

public void dispose () { for (int i= 0; i < imageslength; i++) images[i]dispose(); } Finally, to emphasize failed tests in the table we want to render them in red We can add IColorProvider to the label provider to define the color representation Therefore, to render a failed test we add the IColorProvider interface and implement its methods:

Figure 5.3. Spatial re-usage in sensor networks [18].

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In a recent work [18], a correlation-based MAC protocol has been proposed which exploits the spatial correlation between closely located sensor nodes that regulate medium access and prevent redundant transmissions from closely located sensors. Based on the spatial correlation among sensor nodes, the MAC protocol collaboratively regulates medium access so that redundant transmissions from correlation neighbors are suppressed. In addition, necessary mechanisms for the ef cient transmission of the information from the sensor nodes to the sink have also been incorporated into the proposed correlation-based MAC solution. The experimental results in reference 18 reveal that signi cant performance gains and energy savings are obtained by exploiting spatial correlation in sensor networks. 5.4.2 Spatiotemporal Correlation and Reliable Event Communication In order to realize the potential gains of the WSN, it is imperative that desired event features are reliably communicated to the sink. Unlike traditional communication networks, the sensor network paradigm necessitates that the event features are estimated within a certain distortion bound (i.e., required reliability level) at the sink as discussed in Section 5.2. Reliable event detection at the sink is based on collective information provided by source nodes and not on any individual report. Hence, conventional endto-end reliability de nitions and solutions are inapplicable in the WSN regime and would only lead to overutilization of scarce sensor resources. On the other hand, the absence of reliable transport altogether can seriously impair event detection, which is the main objective of WSN deployment. Hence, the WSN paradigm necessitates a collective event-to-sink reliability notion rather than the traditional end-to-end notion [19]. Such event-to-sink reliable transport notion based on collective identi cation of spatially and temporally correlated data ows from the event to the sink is illustrated in Figure 5.4 and depends on the following de nitions:

public class TestReportLabelProvider extends LabelProvider implements ITableLabelProvider, IColorProvider { public Color getForeground (Object element) {

Figure 5.4. Typical sensor network topology with event and sink. The sink is only interested in collective information of sensor nodes within the event radius and not in their individual data.

if (((TestResult)element)isFailure()) return DisplaygetDefault() getSystemColor(SWTCOLOR_RED); return null; } public Color getBackground(Object element) { return null; } Next we implement the content provider, which typically is the most involved piece of a viewer