1. Packet Classification Using Coarse-Grained Tuple Spaces
Haoyu Song, Jon Turner and Sarang Dharmapurikar

2. Overview Two-dimensional packet classification problem
in list of 2d filters, find first match for given address pair
(1011,0111): [<101*,10*>, <10*,011*>, <1*,01*>]
Limitations of current solutions
fast algorithmic methods require excessive space (≥50x)
TCAM has high cost per bit, significant power usage
Combining cross-product and tuple-space search
hybrid strategy with range of time-space tradeoff options
Improving 1d lookups
combining tree bitmap and Bloom filters
Possible extensions

3. Cross-Product Method Procedure
do 1d lookup on all fields
combine results into lookup key in cross-product table
direct lookup table or hash table
Fast, but space grows as nk for n filters, k fields
filter set
F0: <1010*, 01*> F1: < 101*,0111*>
cross product table
key filter
S0D F S0D F S1D none S1D F1
10100, 01110
S0D1

4. 2D Tuple Space Search Group by prefix length Rectangle search32
Source IP Prefix Length
Destination IP Prefix Length
Group by prefix length
hash table per group
up to 33 x 33= 1,089 groups
in practice occupied tuples
Rectangle search
markers to guide search
at most 33 probes, often less
hard to update
Pruned tuple space search
1d search on src/dest fields
find prefix lengths that match src/dest fields of packet
search intersecting tuples
if ≤k matching prefixes, at most k2 probes

5. Coarse-Grained Tuple Space
Select coarse-grained partition of tuple space
Build cross-product table per sub-space
Search procedure
1d lookups for LPM
probe each subspace
terminate early if possible
Pruning
identify candidate sub-spaces during 1d lookup
probe selected sub-spaces
Space/time tradeoff 32
Source IP Prefix Length
Destination IP Prefix Length

6. Performance of Basic Algorithm
Equal size divisions of 2d tuple space
Ratio of cross-products to filter set size
2x2 partition brings space usage to 2x minimum
maximum of four probes required
compared to for simple tuple space search
Pruning of limited use for filter sets of size <104

7. Performance of Best Configurations2x 3x 4x

8. Alternate Partitioning Approaches32
Source IP Prefix Length
Destination IP Prefix Length
Arbitrary sub-spaces are possible
potential for fewer regions with good space efficiency
Preliminary results mixed
may be useful for smaller filter sets
More evaluation needed
Note: filters of form <prefix,*> and <*,prefix> stored in 1d data structures

9. Fast 1d Lookups Tree Bitmap Hashing + Bloom Filters Multibit trie
110
1011 1
1 0 1
Bloom Filters
0,1
110,111, 000,001
10100,10101, 10110,10111 1 3 5
off-chip hash tables 1
Multibit trie
Co-located children
Bitmaps for
prefix nodes
subtree presence
4 bit stride implies 8 memory accesses
Expand prefixes to “standard” lengths
Off-chip hash table per length
On-chip Bloom filters to avoid unproductive probes
Large space requirements for good worst-case performance

10. Fast and Compact 1d Lookups
Bloom filters 2 4
subtree hash tables 1 1
Insert tree bitmap subtree roots into off-chip hash tables and on-chip Bloom filters
Lookup prefix of subtree roots in Bloom filters
if match on length k and all shorter lengths, probe off-chip table for length k
Reduction in on-chip memory for Bloom filters
shape-shifting trie yields further space reduction

11. 1d Lookup Performance 200K IPv4 prefixes 5 bit stride for tree bitmap
8 bit on-chip “root table”
4 Bloom filters
1 BF entry for every 2 prefixes
1 off-chip probes (4 incl. FP)
2 Bloom filters
1 BF entry for every 6 prefixes
2 off-chip probes (4 incl. FP)

12. Practical Configuration
Configure 1d lookups for 1 off-chip probe each (excluding false positives)
about 5 bits per prefix for Bloom filters with low FP rate
Record <prefix,*> and <*,prefix> filters in 1d lookup data structures
also proposed in recent paper by Kounavis, et. al.
Divide remaining filters among four subspaces
approximately 2 off-chip hash table entries per filter
at most four probes
With single QDR SRAM at 200 MHz, 32 bit word size can do 200 million probes per second
about 33 million packets/second
40 byte packets at 10 Gb/s

13. Possible Extensions More extensive evaluation
scaling to larger filter sets – K filters
integrated evaluation of 1d and 2d lookups
systematic evaluation of alternate partitioning strategies
Alternate representations of filter sub-spaces
any filter set data structure is candidate
using decision trees, can skip 1d lookups
Generalization to more dimensions
handling fields with ranges (for port numbers)
coarse-grained grouping of tuple-spaces defined on “nesting level”
can we beat TCAM?