## 3 Motivation
### Manifestation of the Challenges  
Both aggregation and skyline have practical issues when applied to dynamic web service discovery. Null values are perhaps the most debilitating, because they introduce increased incomparability. The summation on which aggregation depends is ill-defined in the presence of null values. The biggest \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Telescope**} & \multirow{2}{*}{**Context/QoS attributes**} & \multicolumn{3}{c}{**Days**} \\  & & **1** & **2** & **3** & **4** \\ \hline \multirow{8}{*}{T1} & functional & Y & Y & Y & Y \\  & availability (\%) & 20 & 40 & 50 & 60 \\  & user preference/contrast & 8 & 9 & 8 & 5 \\  & time/dayLight & 8 & 9 & & 5 \\  & user preference/composition & 8 & & & 5 \\  & latency (ms) & 6 & 2 & & 3 \\  & weather/visibility (\%) & 70 & 90 & 90 & 80 \\  & location/viewing angle & 8 & 8 & 4 & 5 \\ \hline \multirow{8}{*}{T2} & functional & Y & Y & Y & Y \\  & availability & 85 & 93 & 65 & 89 \\  & user preference/contrast & 8 & 9 & 4 & 5 \\  & time/daylight & 8 & 9 & 5 & 5 \\  & composition & 8 & 9 & 9 & 5 \\  & latency & 9 & 8 & & 9 \\  & weather/visibility & 90 & 80 & 80 & 90 \\  & location/viewing angle & 8 & 6 & & 8 \\ \hline \multirow{8}{*}{T3} & functional & Y & Y & Y & Y \\  & availability & 30 & 60 & 30 & 60 \\  & user preference/contrast & 8 & 9 & 4 & 1 \\  & time/daylight & 8 & 9 & & 1 \\  & composition & 8 & & & 3 \\  & latency & 5 & 7 & 4 & 1 \\  & weather/visibility & 70 & & 70 & 50 \\  & location/viewing angle & 8 & 9 & 9 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: An example set of telescope web services with multiple dynamic QoS attributes, as measured on four consecutive days. Y, yes. drawback of skyline is that it often is insufficiently selective, especially as the dimensionality increases; introducing more incomparability via null values only serves to exacerbate this problem. A conceivable approach is to replace null values with zeros or estimates, but zeroing values can be unnecessarily harsh, especially when the null arises from network issues with an external data source. Temporary fluctuations and unreliable measurements can significantly affect the skyline. A service that is consistently part of the skyline because of a maximal value on one attribute could be dropped at run-time. The context should affect the relevancy of dynamic attributes. For instance, availability is usually extremely important for quality-driven service selection. However, the importance of this attribute can be tempered if the user decides to wait for a higher quality service that is temporarily unavailable, rather than settle for a lower-quality service that is immediately available. Ideally, one could apply both well-established selection approaches--aggregation and skyline--to dynamic web service selection; however, the challenges detailed above obfuscate QoS comparisons between services. The definition of skyline (or, more precisely, of dominance) requires a well-defined, ordinal relationship (_i.e._, the comparison operators \(<\) and \(>\) must be well defined for the attribute values of any two services). Null values invalidate this, because they are incomparable to non-null values. Snapshot values distort this, because they cause the ordinal relationship among services to fluctuate wildly. Thus, we need to restore the relationship somehow when null and fluctuating values arise. For aggregation, the problem is even trickier, because the scoring function relies on attributes that are real valued, not just ordinal. Thus, it is important that, for example, the difference between three and one is larger than the difference between three and two, since this will affect the aggregate score. Naturally, any technique that supports the case of aggregation can be used to re-establish the concept of dominance, because the ordinal operators \(<\) and \(>\) can be applied to any real-valued attribute.