data structures and algorithms
building blocks and lego transmogrifiers
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The Unification Algorithm
Conjugate Gradients
Karmarkar's linear programming algorithm
Knuth-Morris-Pratt string matching
Multidimensional scaling
The Kernighan-Lin TSP & graph-partitioning methods
Lempel-Ziv compression
RSA and DH public key algorithms
Fast Fourier Transform
Fast Multipole method
Quine-McCluskey optimization
Celine/Gosper/Zeilberger/Wilf algorithm for hypergeometric identities
Simulated Annealing or Genetic Algorithm
Simplex Method
Space Time Adaptation Protocol
Red-Black Trees
Tree Comparison
Skip Lists
KD trees
graph based
algorithms of the ages
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 decision-making.
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 high-level code into efficient computer-readable 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 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 n-body calculations, applied in problems ranging from celestial mechanics to protein folding.