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Optimal XOR Hashing for a Linearly Distributed Address Lookup in Computer Networks. Christopher Martinez, Wei-Ming Lin, Parimal Patel The University of Texas at San Antonio October 28, 2005. Outline. Motivation Hashing Background Linear Distribution Optimal Hashing Simulation Conclusion.

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optimal xor hashing for a linearly distributed address lookup in computer networks

Optimal XOR Hashing for a Linearly Distributed Address Lookup in Computer Networks

Christopher Martinez, Wei-Ming Lin, Parimal Patel

The University of Texas at San Antonio

October 28, 2005

outline
Outline
  • Motivation
  • Hashing Background
  • Linear Distribution
  • Optimal Hashing
  • Simulation
  • Conclusion
motivation
Motivation
  • All network applications require some searching
    • Switches, routers and intrusion detection systems require the searching of IP address or subnet IDs
  • Searching should be based on distribution of the records in the database
  • For computer networks, searching needs to be real-time
motivation cont
Motivation (cont.)
  • A capture of network traffic shows the non-uniform distribution of IP type C addresses
  • Since IP address entering the network are non-uniform then searching should take this into account
hashing background
Hashing Background
  • Straightforward sequential searching impractical for large databases
  • Hashing reduces the database into small subsets
  • Searching subsets reduces search time
  • Predictable time needed for real-time applications
hashing background6
Hashing Background
  • Hashing algorithms are well research, we look to provide new insight base on the probability distribution
  • This work is not concern about collision, each hashing key will have the same number of collision in a link list
  • Hashing using probability background should limit the average number of searches in the link list
linear distribution
Linear Distribution
  • From our capture network traffic we can approximate the non-uniform distribution by a linear probability distribution function
xor hashing for linear distribution
XOR Hashing For Linear Distribution
  • We wanted a straightforward hashing scheme that can be used for any size database and hashing space
  • Define the hashing function as P=(gm-1,gm-2,…,g0)
  • Measure hashing functions against each other by the value δ
  • δ measure how close to uniform the hashing creates
xor hashing observation
XOR Hashing Observation
  • Observations:
    • gi > 1: leads to equal partitioning
    • gi = 1: leads to unequal partitioning
  • δ: difference between highest hash distribution density and mean
  • To find δ: we need to determine highest final hash distribution density
optimal xor hashing for linear distribution
Optimal XOR Hashing for Linear Distribution
  • Hashing consists of m steps (from step m-1 to step 0)
  • pi : highest density value after step i
  • Derive pi from pi+1 at step i
  • pm = A = 1/2n (original mean before hashing)
  • δ = p0 – 1/2m
vs p for linear distribution
δ vs. P for Linear Distribution
  • Optimal solution comes from all groups XORing more than 1 bit
simulation
Simulation
  • Goal: Demonstrate that lower δ leads to better search performance
  • Hashing: map from 2n to 2m
  • Each simulation performs 2m hash lookups
simulation18
Simulation
  • Three performance measurements
    • Number of Empty Bins (NEB)
    • Average maximum Search Length (ASL)
    • Maximum Search Length (MSL)
simulation19
Simulation
  • Improvement from best δ over worst δ
    • NEB: 18%
    • ASL: 12%
    • MSL: 17%
future work
Future Work
  • Find optimal XOR hashing for exponential distribution and partial linear distribution
  • Look more in depth to see if what applications exhibit linear distribution
  • Find performance gain of using this hashing scheme in an intrusion detection system
conclusion
Conclusion
  • Network applications demonstrate non-uniform distribution making known search techniques less than optimal
  • Linear distribution can benefit from the XOR folding property
  • Optimal XOR grouping can be easily identified to minimize error in hashing distribution
  • Theory in linear case can be applied to other non-uniform distributions