Univ. of Tehran Adv. topics in Computer Network
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Advanced topicsAdvanced topics inin
Computer Computer NetworksNetworks
University of TehranDept. of EE and Computer Engineering
By:Dr. Nasser Yazdani
Lecture 8: Trie-based lookup
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Trie Based Methods Trie or radix tree is a data
structure in which each data element is represented by the path to the leaf and no. of internal nodes are the no. of alphabet.
Two branching.Black node in theleaves representnext hops
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Trie Based Methods (cont)Trie has been the base of many methods.There are two main problems with trie: The blank nodes do not correspond to
any data element in the lookup table. The number of branching is small, 2.Both of these add to the height of trie,
waste memory and prolong the search time.
The Max search time is proportional to string length or O(32) for IPv4 and O(128) for IPv6.
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Trie Based Methods (cont)Trie based schemes try to reduce the
memory usage and shorten the trie height and expedite the search time.
In the worst case, the memory usage can be O(NL) where N is number of prefixes and L is their length.
Compressed Trie:The idea is to eliminate blank node as much as possible.Patricia trie compress the path from root to the leaf.
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Trie Based Methods (cont)
An Example:
The information of skippedbits can be kept in links
Max memory usages is O(2N)The worst case search is again O(NL).
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Trie Based Methods (cont) Dynamic Prefix Trie (DP-Trie)
Introduced by IBM research center in Zurich.the idea is to
I) Eliminate the blank nodes completelyII) Push common prefixes upper.III) To Make the height proportional to the # of prefixes than prefix lengths.IV) Compare more bits as much as
possible.They introduce a specific data structure each
node having the following fields.
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Trie Based Methods (cont)1. Index: differentiating bit
position.2. LeftKey and RightKey:
Prefixes with leftKey[Index]=0RightKey[Index]=1.
The trie is build dynamically. Example: {1000100, 1001, 10, 1111, 11}
First the trie is empty. Then, 1000100 isinserted. A node is allocated.
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Trie Based Methods (cont)
6 in the first implies the differentiating bit is 6th.In the second node, 1001 is inserted. The differentiating bit is3th. 10 inserted. Index is 1. New node is allocated.
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Trie Based Methods (cont)
And the final trie with those elements is:
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Trie Based Methods (cont)
Problems: Two way branching. Too much overhead for each node.
What is next?
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Trie Based Methods (cont) Controlled Prefix Expansion
the idea is to compare more bits at the same time. (reduce the height of trie)Reduce prefixes with N distinct lengths to equivalent prefixes of M (M<N) lengths.
Expansion: Expand Prefix P of length L into two Prefixes P0 and P1 of lengths L+1.
Reduction: delete any repeated prefix.Indeed, this method compress few level
together and use extra memory to reduce trie height.
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Trie Based Methods (cont)
Example: The same data setExpand length 1 -> 2. Then,00, 01, 10, 11P5, P5, P1, P4
Final lengths are 2, 5 and 7.
Reduce the search timefrom 7 to 3.
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Trie Based Methods (cont) Problem: Extra memory usage. Solution: Optimize the memory
usage.Pick stride s for root and recursively solve the covering problem for the subtrees rooted at Trie level s+1 using k-1 level
The dynamic programmingmethod can be used to buildthe data structure bottomup with all values of K.
Insertion?
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Trie Based Methods (cont) Level Compress Trie LC-trie
the idea is the same as the previous one, to compare more bits at the same time.Few levels are compress together.
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Trie Based Methods (cont)
LC-trie reduces the height of trie in the expense of memory usage.
In order to have better memory utilization, it uses Greedy algorithm and compress the part which is more populated.
In each level, we have tokeep all possible combinationlike 000, 001, 010, etc.
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Trie Based Methods (cont) Problems With expansion methods.
1. Insertion may need to reconstruct the trie.2. Not scaleable to IPv6.
Problems with LC-trie:1. It uses greedy algorithm and optimize
memory locally, the final memory utilization may not be good.
2. Higher trie height and skip count compression leads to slower search times.
The Controlled Prefix Expansion method uses the same technique but, try to globally optimize memory usage.
