FIB lookup time under different n

(a) Real-world dataset (b) Synthetic dataset

Figure 10: FIB lookup time for four methods comparison under different n

In Figure 10 (a), we evaluate the FIB lookup time of Trie, Ternary Trie, Patricia Trie and DePT under different n that means that each name needs to put its first n components into filtering phase. In our FIB, name prefix are set to have at least four components and the first component are “ndn”. Therefore, we compare n by 2, 3 and 4.

Among Trie, Ternary Trie and Patricia Trie, Trie has better lookup efficiency than Patricia Trie, and Ternary Trie is at a disadvantage not only on lookup efficiency but also on lookup fairness. In particular, stepped curve of Patricia Trie become relatively more than Trie and Ternary Trie. The reason why does these steps occur is that there is not only one group of common prefix in real-world datast and these common prefix have different length. This situation is likely to occur in NDN router in the future.

In terms of DePT, three curves show lookup time when n equals to 2, 3 and 4.

We found that if n equals to 3, then the vertical extent of curve is bigger than others. It means that when n equals to 3, the fairness of lookup time is the best. Besides, the

curves show that lookup time is the best also. Therefore, DePT has the best lookup efficiency and fairness when n is initialized to 3.

In Figure 10 (b), the number of common prefix is 50% of total name prefix (p = 50), and the number of components in common prefix we set is 3. It represents that there are more than half of total name prefix have the same prefix in their first 3 components. After incremental update, n in additional DePT will be set to 4.

5.2.4. FIB lookup time under different p

(a) 0% (b) 30%

(c) 60% (d) 90%

Figure 11: FIB lookup time for four methods comparison among 0%, 30%, 60% and 90% of common prefix

In Figure 11, there are Trie, Ternary Trie, Patricia Trie and DePT four methods comparisons of FIB lookup time under 0%, 30%, 60% and 90% (p = 0, 30, 60, 90) common prefix. Besides, the standard k we set for incremental update is 50. In (a), there are totally different name prefix in their first three components. Ternary has a worst-case for lookup efficiency and lookup fairness, on the contrary, DePT is the most efficient and fair method. However, DePT method is based on Patricia Trie, the maximum difference between these two methods and others is that their curves have vibration. The reason why the vibration exists is that matching process in Patricia Trie may not has only one character, it will be a long section of name. Therefore, curves are not as smooth as Trie and Ternary Trie. Besides, zero percentage of common prefix in FIB is the best case for our method DePT, the situation which excessive name prefix accumulate in one sub-trie will hardly occur.

In (b) and (c), the curve of Trie and Ternary Trie is more vertical than zero percentage. The reason is that as number of common prefix increase and variant prefix decrease, name prefix lookup needs relatively less time. Besides, there is an increasingly segment of smooth part in curves and it represents that a section of name prefix has nearly lookup time. In (b), we can find that Trie is faster than Patricia Trie in the beginning of curve, and the vibration amplitude is much bigger than zero percentage in (a), and tendency of DePT curve is similar to Patricia Trie curve.

However in (c), curve of Patricia Trie shows that a part of lookup time is worse than Trie, and the gap in curve is bigger and obvious than zero percentage in (a), and tendency of DePT curve is not similar to Patricia curve due to incremental update in

building DePT when p is more than 50 so it will not affected by increasing number of common prefix.

In (d), p is equal to 90 and it shows that names are almost following a common prefix in FIB and it may be a local NDN router. In terms of Trie and Ternary Trie, they both have a relatively vertical part in curve. It represents that almost name lookups are gather in the same part of Trie. Similarly, curve of Patricia Trie has a relatively larger gap than (b) and (c). Although vertical extent of Patricia Trie curve is better than Trie, most of the lookup time obviously is worse than Trie. Best of all, DePT has the best lookup efficiency and lookup fairness because it has an incremental update when number of name prefix in one sub-trie achieves the default standard. After incremental update, the number of name prefix in every sub-trie in DePT keeps in nearly equal so that it has better fairness of lookup.

!

Figure 12: Average FIB lookup time for four methods comparison in different p

Figure 12 shows the average FIB lookup time of different dataset that percentage of common prefix range from 0% to 100% (p = 0 ~ 100). Obviously, Ternary Trie is

the worst one of these four methods due to its redundant comparison of alphabetical order. Unlike methods like Patricia Trie and DePT, average lookup time of Trie and Ternary Trie decrease as the ratio increaces. It indicates that more common prefix in FIB, lookup efficiency in Patricia Trie become worse instead. The fact is that if Patricia Trie has a lot of common prefix, decomposition of string in Patricia Trie is more than general Trie and Ternary Trie. Therefore, name lookup needs relatively more time. In particular, DePT line shows that almost every percentage point has about the same search time. The reason is that incremental update mechanism has been activated when number of common prefix in someone sub-trie exceeds 50% (p = 50) of total name prefix in FIB.