Scientific Communication
Outline

An Improved Implementation of the Nijenhuis-Wilf Random K-Subset Algorithm
John Burkardt

Abstract
  (written already)

Introduction
  The task is common to many computations.
  This is a widely used algorithm with special advantages in storage and work.
  It uses a clever but complicated trick to avoid O(K^2) work.
  The resulting algorithm is subtle.
  The published implementation is obsolete, unreadable and undocumented.

The Random K Subset Problem
  Requires a random number generator
  Storage, Work, Sorting.
  Uses
    cryptography
    statistical sampling
    a robust cluster has N servers, a user asks for K, need to 
    pick K at random to guarantee work is evenly assigned.
    reliability simulation: a system is required to continue to function
    if up to K out of N subsystems fail.

Alternative Algorithms
  Drawing with replacement
  Drawing without replacement
  Reservoir
  Assign index to every K-subset, choose index at random.

The Nijenhuis-Wilf Algorithm
  Discuss steps, try to be clear.
  
The Published Implementation 
  Defects
  Proposed Improvements

Performance Measurements
  K = 1, 2, 3,
  K = M versus K = N - M, 
  K = N - 2, N - 1, N
  Average work = O(K)?
  Comparison to other methods.

Uniformity Measurements
  Histogram of number of times each element occurred
  Chi-Squared test

Sample Codes
  Original F77 code
  Revised F77 code
  C and Python versions

References
  N & W book
  Kreher and Stinson
  Pemmaraju & Skiena (Mathematica, Combinatorica) RandomKSubset(I,k)