Top Ten Algorithms
Algorithms for the Ages
"Great algorithms are the poetry of computation," says Francis Sullivan
of the Institute for Defense Analyses' Center for Computing Sciences in
Bowie, Maryland. He and Jack Dongarra of the University of Tennessee
and Oak Ridge National Laboratory have put together a sampling that
might have made Robert Frost beam with pridehad the poet been a
computer jock. Their list of 10 algorithms having "the greatest
influence on the development and practice of science and engineering in
the 20th century" appears in the January/February issue of Computing in
Science & Engineering. If you use a computer, some of these algorithms
are no doubt crunching your data as you read this. The drum roll,
please:

1946: The Metropolis Algorithm for Monte Carlo. Through the use of
random processes, this algorithm offers an efficient way to stumble
toward answers to problems that are too complicated to solve exactly.

1947: Simplex Method for Linear Programming. An elegant solution to a
common problem in planning and decisionmaking.

1950: Krylov Subspace Iteration Method. A technique for rapidly solving
the linear equations that abound in scientific computation.

1951: The Decompositional Approach to Matrix Computations. A suite of
techniques for numerical linear algebra.

1957: The Fortran Optimizing Compiler. Turns highlevel code into
efficient computerreadable code.

1959: QR Algorithm for Computing Eigenvalues. Another crucial matrix
operation made swift and practical.

1962: Quicksort Algorithms for Sorting. For the efficient handling of
large databases.

1965: Fast Fourier Transform. Perhaps the most ubiquitous algorithm in
use today, it breaks down waveforms (like sound) into periodic
components.

1977: Integer Relation Detection. A fast method for spotting simple
equations satisfied by collections of seemingly unrelated numbers.

1987: Fast Multipole Method. A breakthrough in dealing with the
complexity of nbody calculations, applied in problems ranging from
celestial mechanics to protein folding.
From Random Samples, Science page 799, February 4, 2000.