Address Lookup and Classification

1
Address Lookup and Classification
EE384Y May 12, 2003

• Pankaj Gupta
• Principal Architect,
• Cypress Semiconductor
• pankaj_at_cs.stanford.edu,
• pankaj_at_cypress.com
• http//klamath.stanford.edu/pankaj

2
Generic Router Architecture (Review from EE384x)
Header Processing
Lookup IP Address
Update Header
Queue Packet
1M prefixes Off-chip DRAM
1M packets Off-chip DRAM
3
Lookups Must be Fast (Review)
40B packets (Mpkt/s)
Line
Year
1.94
622Mb/s
1997
7.81
2.5Gb/s
1999
31.25
10Gb/s
2001
125
40Gb/s
2003
4
Memory Technology (2003-04)
Note Price, speed and power are manufacturer and
market dependent.
5
Lookup Mechanism is Protocol Dependent
6
Outline

• Routing Lookups
• Overview
• Exact matching
• Direct lookup
• Associative lookup
• Hashing
• Trees and tries
• Longest prefix matching
• Why LPM?
• Tries and compressed tries
• Binary search on prefix intervals
• References
• Packet Classification

7
Exact Matches in ATM/MPLS
Direct Memory Lookup
(Outgoing Port, new VCI/label)
VCI/MPLS-label
Memory
Address
Data

• VCI/Label space is 24 bits
• - Maximum 16M addresses. With 64b data, this is
  1Gb of memory.
• VCI/Label space is private to one link
• Therefore, table size can be negotiated
• Alternately, use a level of indirection

8
Exact Matches in Ethernet Switches

• Layer-2 addresses are usually 48-bits long,
• The address is global, not just local to the
  link,
• The range/size of the address is not negotiable
  (like it is with ATM/MPLS)
• 248 gt 1012, therefore cannot hold all addresses
  in table and use direct lookup.

9
Exact Matches in Ethernet Switches (Associative
Lookup)

• Associative memory (aka Content Addressable
  Memory, CAM) compares all entries in parallel
  against incoming data.

Associative Memory (CAM)
Network address
Location
Address
Data
48bits
Match
10
Exact Matches in Ethernet SwitchesHashing
Memory
Memory
Network Address
Hashing Function
Pointer
16, say
List/Bucket
Address
Data
Data
Address
48
List of network addresses in this bucket

• Use a pseudo-random hash function (relatively
  insensitive to actual function)
• Bucket linearly searched (or could be binary
  search, etc.)
• Leads to unpredictable number of memory
  references

11
Exact Matches Using HashingNumber of memory
references
12
Exact Matches in Ethernet SwitchesPerfect Hashing
Network Address
Hashing Function
Port
16, say
Data
Address
Memory
48
There always exists a perfect hash
function. Goal With a perfect hash function,
memory lookup always takes O(1) memory
references. Problem - Finding perfect hash
functions (particularly minimal perfect
hashings) is very complex. - Updates?
13
Exact Matches in Ethernet SwitchesHashing

• Advantages
• Simple
• Expected lookup time is small
• Disadvantages
• Inefficient use of memory
• Non-deterministic lookup time
• ? Attractive for software-based switches, but
  being increasingly dumped by hardware platforms

14
Exact Matches in Ethernet Switches Trees and
Tries
Binary Search Tree
Binary Search Trie
lt
gt
0
1
lt
gt
lt
gt
0
1
0
1
111
010
Lookup time bounded and independent of table
size, storage is O(NW)
Lookup time dependent on table size, but
independent of address length, storage is O(N)
15
Exact Matches in Ethernet Switches Multiway tries
16-ary Search Trie
0000, ptr
1111, ptr
Ptr0 means no children
0000, 0
1111, ptr
1111, ptr
0000, 0
000011110000
111111111111
Q Why cant we just make it a 248-ary trie?
16
Exact Matches in Ethernet Switches Multiway tries
As degree increases, more and more pointers are
0
Table produced from 215 randomly generated 48-bit
addresses
17
Exact Matches in Ethernet Switches Trees and
Tries

• Advantages
• Fixed lookup time
• Simple to implement and update
• Disadvantages
• Inefficient use of memory and/or requires large
  number of memory references

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Outline

• Routing Lookups
• Overview
• Exact matching
• Direct lookup
• Associative lookup
• Hashing
• Trees and tries
• Longest prefix matching
• Why LPM?
• Tries and compressed tries
• Binary search on prefix intervals
• References
• Packet Classification

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Longest Prefix Matching IPv4 Addresses

• 32-bit addresses
• Dotted quad notation e.g. 12.33.32.1
• Can be represented as integers on the IP number
  line 0, 232-1 a.b.c.d denotes the integer
  (a224b216c28d)

IP Number Line
0.0.0.0
255.255.255.255
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Class-based Addressing
A
B
C
D
E
128.0.0.0
192.0.0.0
0.0.0.0
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Lookups with Class-based Addresses
netid
port
23
Port 1
Class A
192.33.32.1
Class B
186.21
Port 2
Class C
Exact match
192.33.32
Port 3
22
Problems with Class-based Addressing

• Fixed netid-hostid boundaries too inflexible
• Caused rapid depletion of address space
• Exponential growth in size of routing tables

23
Early Exponential Growth in Routing Table Sizes
Number of BGP routes advertised
24
Classless Addressing (and CIDR)

• Eliminated class boundaries
• Introduced the notion of a variable length prefix
  between 0 and 32 bits long
• Prefixes represented by P/l e.g., 122/8,
  212.128/13, 34.43.32/22, 10.32.32.2/32 etc.
• An l-bit prefix represents an aggregation of
  232-l IP addresses

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CIDRHierarchical Route Aggregation
Router
Backbone
R3
R1
R4
R2
R2
ISP, P
ISP, Q
192.2.0/22
200.11.0/22
Site, S
Site, T
192.2.1/24
192.2.2/24
192.2.1/24
192.2.2/24
192.2.0/22
200.11.0/22
IP Number Line
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Post-CIDR Routing Table sizes
Optional Exercise What would this graph look
like without CIDR? (Pick any one random AS, and
plot the two curves side-by-side)
Number of active BGP prefixes

• Source http//bgp.potaroo.net

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Routing Lookups with CIDR
Optional Exercise Find the nesting
distribution for routes in your randomly-picked
AS
192.2.2/24
192.2.2/24, R3
192.2.0/22
200.11.0/22
192.2.0/22, R2
200.11.0/22, R4
200.11.0.33
192.2.0.1
LPM Find the most specific route, or the longest
matching prefix among all the prefixes matching
the destination address of an incoming packet
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Longest Prefix Match is Harder than Exact Match

• The destination address of an arriving packet
  does not carry with it the information to
  determine the length of the longest matching
  prefix
• Hence, one needs to search among the space of all
  prefix lengths as well as the space of all
  prefixes of a given length

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LPM in IPv4Use 32 exact match algorithms for LPM!
Exact match against prefixes of length 1
Exact match against prefixes of length 2
Port
Priority Encode and pick
Exact match against prefixes of length 32
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Metrics for Lookup Algorithms

• Speed ( number of memory accesses)
• Storage requirements ( amount of memory)
• Low update time (support 5K updates/s)
• Scalability
• With length of prefix IPv4 unicast (32b),
  Ethernet (48b), IPv4 multicast (64b), IPv6
  unicast (128b)
• With size of routing table (sweetspot for
  todays designs 1 million)
• Flexibility in implementation
• Low preprocessing time

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Radix Trie (Recap)
Trie node
A
next-hop-ptr (if prefix)
1
B
right-ptr
left-ptr
1
C
D
0
P2
1
1
F
E
P1
0
G
P3
1
H
P4
32
Radix Trie

• W-bit prefixes O(W) lookup, O(NW) storage and
  O(W) update complexity

• Advantages
• Simplicity
• Extensible to wider fields

• Disadvantages
• Worst case lookup slow
• Wastage of storage space in chains

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Leaf-pushed Binary Trie
Trie node
A
left-ptr or next-hop
right-ptr or next-hop
1
B
1
C
D
0
P1
P2
1
E
P2
0
G
P4
P3
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PATRICIA
A
Patricia tree internal node
2
0
bit-position
1
B
C
right-ptr
left-ptr
P1
3
1
E
0
D
5
P2
1
0
F
G
P3
P4
Lookup 10111
Bitpos 12345
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PATRICIA

• W-bit prefixes O(W2) lookup, O(N) storage and
  O(W) update complexity

• Advantages
• Decreased storage
• Extensible to wider fields

• Disadvantages
• Worst case lookup slow
• Backtracking makes implementation complex

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Path-compressed Tree
A
1, ?, 2
0
1
C
B
P1
10,P2,4
0
D
1010,P3,5
1
E
P4
Path-compressed tree node structure
next-hop (if prefix present)
variable-length bitstring
bit-position
left-ptr
right-ptr
37
Path-compressed Tree

• W-bit prefixes O(W) lookup, O(N) storage and
  O(W) update complexity

• Advantages
• Decreased storage

• Disadvantages
• Worst case lookup slow

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Multi-bit Tries
Binary trie
W
Depth W Degree 2 Stride 1 bit
39
Prefix Expansion with Multi-bit Tries
If stride k bits, prefix lengths that are not a
multiple of k need to be expanded
E.g., k 2
Maximum number of expanded prefixes corresponding
to one non-expanded prefix 2k-1
40
Four-ary Trie (k2)
A four-ary trie node
next-hop-ptr (if prefix)
A
ptr00
ptr01
ptr10
ptr11
11
10
B
C
P2
11
10
F
D
E
10
P3
P12
P11
11
10
H
G
P42
P41
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Prefix Expansion Increases Storage Consumption

• Replication of next-hop ptr
• Greater number of unused (null) pointers in a node

Time W/k Storage NW/k 2k-1
Optional Exercise The increase in number of null
pointers in LPM is a worse problem than in exact
match. Why?
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Generalization Different Strides at Each Trie
Level

• 16-8-8 split
• 4-10-10-8 split
• 24-8 split
• 21-3-8 split

Optional Exercise Why does this not work well
for IPv6?
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Choice of Strides Controlled Prefix Expansion
Sri98

• Given a forwarding table and a desired number of
  memory accesses in the worst case (i.e., maximum
  tree depth, D)

A dynamic programming algorithm to compute the
optimal sequence of strides that minimizes the
storage requirements runs in O(W2D) time
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Binary Search on Prefix Intervals Lampson98
45
0111
Alphabetic Tree
gt
?
0011
1101
?
?
gt
gt
I3
I6
1100
0001
gt
?
?
gt
I1
I2
I4
I5
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Another Alphabetic Tree
0001
0011
I1
1/2
0111
I2
1/4
1100
I3
1/8
1101
I4
1/16
I5
I6
1/32
1/32
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Multiway Search on Intervals

• W-bit N prefixes O(logN) lookup,
• O(N) storage

• Advantages
• Storage is linear
• Can be balanced
• Lookup time independent of W

• Disadvantages
• But, lookup time is dependent on N
• Incremental updates complex
• Each node is big in size requires higher memory
  bandwidth

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Routing Lookups References

• lulea98 A. Brodnik, S. Carlsson, M. Degermark,
  S. Pink. Small Forwarding Tables for Fast
  Routing Lookups, Sigcomm 1997, pp 3-14. Example
  of techniques for decreasing storage consumption
• gupta98 P. Gupta, S. Lin, N.McKeown. Routing
  lookups in hardware at memory access speeds,
  Infocom 1998, pp 1241-1248, vol. 3. Example of
  hardware-optimized trie with increased storage
  consumption
• P. Gupta, B. Prabhakar, S. Boyd. Near-optimal
  routing lookups with bounded worst case
  performance, Proc. Infocom, March 2000 Example
  of deliberately skewing alphabetic trees
• P. Gupta, Algorithms for routing lookups and
  packet classification, PhD Thesis, Ch 1 and 2,
  Dec 2000, available at http//yuba.stanford.edu/
  pankaj/phd.html Background and introduction to
  LPM

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Routing lookups References (contd)

• lampson98 B. Lampson, V. Srinivasan, G.
  Varghese. IP lookups using multiway and
  multicolumn search, Infocom 1998, pp 1248-56,
  vol. 3.
• LC-trie S. Nilsson, G. Karlsson. Fast address
  lookup for Internet routers, IFIP Intl Conf on
  Broadband Communications, Stuttgart, Germany,
  April 1-3, 1998.
• sri98 V. Srinivasan, G.Varghese. Fast IP
  lookups using controlled prefix expansion,
  Sigmetrics, June 1998.
• wald98 M. Waldvogel, G. Varghese, J. Turner, B.
  Plattner. Scalable high speed IP routing
  lookups, Sigcomm 1997, pp 25-36.