1. Scalable High Speed IP Routing Lookups Scalable High Speed IP Routing Lookups Authors: M. Waldvogel, G. Varghese, J. Turner, B. Plattner Presenter: Zhqi Qiu

2.  Outline Routing and the BMP (Best Matching Prefix) problem Basic scheme: binary search of hash tables Refinements: asymmetric trees, mutated binary search and ropes Implementation: building the tree Performance and comparison study

3.  Introduction Increases in Internet traffic demands: link speed, router data throughput, packet forward rate Packet forwarding rate becomes bottleneck Address lookup: main step in packet forwarding Need efficient Best Prefix Match algorithm

4.  More about BMP Classless Inter-Domain Routing (CIDR) - cope with routing table growth Aggregation results in address prefix list in routing tables Packets forwarded according to Best Matching Prefix Goal: use hashing to find BMP

5.  Outline Routing and the BMP (Best Matching Prefix) problem Basic scheme: binary search of hash tables Refinements: asymmetric trees and ropes Implementation: building the tree Performance and comparison study

6.  Basic Scheme Hash table organized by prefix length Markers needed

7.  Marker Management Reducing marker storage: markers only needed in levels visited by binary search when looking for P E. g. : In table of 8 levels: a prefix with length of 7 [111] needs markers in level 4 and 6 a prefix with length of 3 [11] needs markers in level 2

8.  False Markers What if table entries are: P1=1, P2=00, P3=110 in the previous example? Solution: to avoid backtracking, record current best matching prefix of marker M in M.bmp

9.  Basic Algorithm Initialize range R = array L Initialize BMP to be null string While R not empty I = middle level in range R D’ = D(L[i].length) M = Search(D’, L[i].hash) If M is nil Then set R = upper R Elseif M is a prefix & not a marker Then BMP = M.bmp; break Else { BMP = M.bmp; R = lower R} Endif Endwhile

10.  Outline Routing and the BMP (Best Matching Prefix) problem Basic scheme: binary search of hash tables Refinements: asymmetric trees and ropes Implementation: building the tree Performance and comparison study

11.  Algorithm Refinements To optimize, need to exploit deeper structure in routing table Simplest improvement: Search only non-empty tries

12.  Asymmetric Binary Search Try to search the most promising trie first Example: Maximize table entries while keeping tree balance

13.  Mutating Binary Search The number of distinct prefix lengths rarely exceeds 12 Every match with some marker X means that we need only search among the set of prefixes for which X is a prefix

15.  Potential Disadvantages Pre-computing optimal trees increases insertion time Storage of binary trees for each prefix enormous Storage problem solved with “rope” data structure Rope maximum length: log 2 W pointers

16.  Rope: Encoded Trees Only need to store the sequence of levels which binary search on a given subtrie will follow on repeated failures to find a match e.g.: Rope 1 contains 16, 8, 4, 2, 1 Rope algorithm: a prefix not a marker: end of rope a prefix and a marker: X.bmp = X

18.  Rope Search Initialize Rope R = default search sequence Initialize BMP = null string While R not empty i = first pointer of R D’ = D(L[i].length) M = Search(D’, L[i].hash) If M is success Then BMP = M.bmp; R = M.rope Endif Endwhile

19.  Building Rope Search Pass 1: builds a conventional trie Pass 2: all prefixes inserted into hash tables, starting with shortest prefix Batch insertions and deletions into the table as these operations are expensive.

20.  Outline Routing and the BMP (Best Matching Prefix) problem Basic scheme: binary search of hash tables Refinements: asymmetric trees and ropes Implementation: building the tree Performance and comparison study

21.  Existing Approaches Modification of exact matching:log 2 2N Trie based: BDS radix trie O(W 2 ) Hardware: parallelism, CAM expensive Protocol based: IP/tag switching, still need some IP lookups Caching: CAM (Content Addressable Memory)

22.  Complexity Comparison

23.  Performance Comparison

24.  Conclusion Intellectual contribution: markers and pre-computation ensure log time in worst-case Solution scalable and can be implemented in software efficiently Future work: choice of balancing function and faster insertion algorithms