README.md file of the algorithms module updated

ands/algorithms/README.md

@@ -1,45 +1,200 @@
 # Algorithms
 
-Algorithms I am particularly interested in are:
-
-- Bisection method
-- Fixed-point iteration
-- Secant method
-- [All nearest smaller values](https://en.wikipedia.org/wiki/All_nearest_smaller_values)
-- Jacobi
-- PageRank
-- PowerMethod
-- Kernighan–Lin algorithm (i.e. for partitioning a graph)
-- Conjugate gradient (gradient descent and ascent)
-- Cuthill–McKee algorithm
-- Coppersmith–Winograd algorithm (i.e. for matrix multiplication)
-- Strassen algorithm (i.e. for matrix multiplication), which is theoretically slower than the Coppersmith–Winograd algorithm.
-- Block matrix multiplication (to reduce theoretically, given a certain simplified memory hierarchy model, the memory accesses)
-- Gauss-Newton algorithm
-- Gauss–Seidel method
-- Guassian elimination
-- Guassian elimination with pivoting
-- LU decomposition (or factorization)
-- Cholesky decomposition (for symmetric positive definite matrices)
-- A<sup>*</sup>
-- MCTS
-- Christofides algorithm
-- Fisher–Yates shuffle
-- Alpha-beta pruning
-- Minmax
-- Graham's scan
-- Gift wrapping algorithm 
-- RSA
-- AKS primality test
-- Miller–Rabin primality test
-- Edmonds–Karp algorithm
-- Floyd–Warshall algorithm
-- Mersenne twister (pseudo-random generator)
-- Euclidean algorithm (to compute the greatest common divisor)
-- CYK algorithm
-- Levenshtein edit distance
-- Kosaraju's algorithm
-
-A more exhaustive list of interesting algorithms can be found here:
-
-> [https://en.wikipedia.org/wiki/List_of_algorithms](https://en.wikipedia.org/wiki/List_of_algorithms)
+A few interesting algorithms which may be implemented in the future.
+
+## Combinatorial Algorithms
+
+### Pseudo-random Number Generators 
+
+- [Mersenne Twister](https://en.wikipedia.org/wiki/Mersenne_Twister)
+
+## Cryptography
+
+### Asymmetric Public Key Encryption
+
+- [RSA](https://en.wikipedia.org/wiki/RSA_(cryptosystem)) (Rivest–Shamir–Adleman)
+
+## Geometry
+
+- [Line segment intersection](https://en.wikipedia.org/wiki/Line_segment_intersection)
+
+### Convex Hull
+
+- [Graham's scan](https://en.wikipedia.org/wiki/Graham_scan)
+- [Gift wrapping](https://en.wikipedia.org/wiki/Gift_wrapping_algorithm) (or Jarvis march)
+- [Chan's algorithm](https://en.wikipedia.org/wiki/Chan%27s_algorithm)
+- [Kirkpatrick–Seidel algorithm](https://en.wikipedia.org/wiki/Kirkpatrick%E2%80%93Seidel_algorithm)
+- [Quickhull](https://en.wikipedia.org/wiki/Quickhull)
+- Divide and conquer
+
+## Graph Algorithms
+
+### Search
+
+- [Breadth-first search](https://en.wikipedia.org/wiki/Breadth-first_search)
+- [Depth-first search](https://en.wikipedia.org/wiki/Depth-first_search)
+- [Iterative deepening depth-first search](https://en.wikipedia.org/wiki/Iterative_deepening_depth-first_search)
+- [Best-first Search](https://en.wikipedia.org/wiki/Best-first_search)
+- Uniform-Cost Search
+- [A* search algorithm](https://en.wikipedia.org/wiki/A*_search_algorithm)
+- [Beam search](https://en.wikipedia.org/wiki/Beam_search)
+- [Monte Carlo tree search](https://en.wikipedia.org/wiki/Monte_Carlo_tree_search) (MCTS)
+
+### Shortest Path
+
+- [Dijkstra's algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm)
+- [Bellman–Ford algorithm](https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm)
+- [Floyd–Warshall algorithm](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm)
+
+### Minimum Spanning Tree
+
+- [Kruskal's algorithm](https://en.wikipedia.org/wiki/Kruskal%27s_algorithm)
+- [Prim's algorithm](https://en.wikipedia.org/wiki/Prim%27s_algorithm)
+- [Reverse-delete algorithm](https://en.wikipedia.org/wiki/Reverse-delete_algorithm)
+
+### Strongly Connected Components
+
+- [Kosaraju's algorithm](https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm)
+- [Tarjan's algorithm](https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm)
+
+### Network Theory
+
+#### Network analysis
+
+- [PageRank](https://en.wikipedia.org/wiki/PageRank)
+
+##### Flow Networks
+
+- [Edmonds–Karp algorithm](https://en.wikipedia.org/wiki/Edmonds%E2%80%93Karp_algorithm)
+
+### Partitioning
+
+- [Kernighan–Lin algorithm](https://en.wikipedia.org/wiki/Kernighan%E2%80%93Lin_algorithm)
+
+### Travelling Salesman Problem (TSP)
+
+- [Nearest neighbour algorithm](https://en.wikipedia.org/wiki/Nearest_neighbour_algorithm)
+- [Christofides algorithm](https://en.wikipedia.org/wiki/Christofides_algorithm)
+
+## Number Theory
+
+### Multiplication
+
+- [Karatsuba algorithm](https://en.wikipedia.org/wiki/Karatsuba_algorithm)
+
+### Greatest Common Divisor
+
+- [Euclidean algorithm](https://en.wikipedia.org/wiki/Euclidean_algorithm) (or Euclid's algorithm)
+
+### Primality Tests
+
+- [AKS primality test](https://en.wikipedia.org/wiki/AKS_primality_test)
+- [Miller–Rabin primality test](https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test)
+- [Sieve of Eratosthenes](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)
+- [Sieve of Atkin](https://en.wikipedia.org/wiki/Sieve_of_Atkin)
+
+## Numerical algorithms
+
+### Differential Equations
+
+- [Runge–Kutta methods](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods)
+
+### Interpolation
+
+- [De Casteljau's algorithm](https://en.wikipedia.org/wiki/De_Casteljau%27s_algorithm)
+- [De Boor algorithm](https://en.wikipedia.org/wiki/De_Boor%27s_algorithm)
+
+### Linear algebra
+
+#### Linear System of Equations
+
+- [Jacobi method](https://en.wikipedia.org/wiki/Jacobi_method)
+- [Conjugate gradient method](https://en.wikipedia.org/wiki/Conjugate_gradient_method)
+- [Guassian elimination](https://en.wikipedia.org/wiki/Gaussian_elimination)
+- [Guassian elimination with pivoting](https://en.wikipedia.org/wiki/Pivot_element)
+- [Gauss–Seidel method](https://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method)
+- [LU decomposition](https://en.wikipedia.org/wiki/LU_decomposition) (or factorization)
+- [Cholesky decomposition](https://en.wikipedia.org/wiki/Cholesky_decomposition)
+
+#### Sparse Matrix Algorithms
+
+- [Cuthill–McKee algorithm](https://en.wikipedia.org/wiki/Cuthill%E2%80%93McKee_algorithm)
+
+#### Matrices
+
+##### Multiplication
+
+- [Strassen algorithm](https://en.wikipedia.org/wiki/Strassen_algorithm)
+- [Cannon's algorithm](https://en.wikipedia.org/wiki/Cannon%27s_algorithm)
+- [Coppersmith–Winograd algorithm](https://en.wikipedia.org/wiki/Coppersmith%E2%80%93Winograd_algorithm)
+- [Block matrix multiplication](https://en.wikipedia.org/wiki/Block_matrix#Block_matrix_multiplication)
+
+##### Eigenvalues
+
+- [Rayleigh quotient iteration](https://en.wikipedia.org/wiki/Rayleigh_quotient_iteration)
+- [Power Method](https://en.wikipedia.org/wiki/Power_iteration)
+- [QR algorithm](https://en.wikipedia.org/wiki/QR_algorithm)
+- [Inverse iteration](https://en.wikipedia.org/wiki/Inverse_iteration)
+
+#### Orthogonalization
+
+- [Gram–Schmidt process](https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process)
+
+### Roots Finding
+
+- [Bisection method](https://en.wikipedia.org/wiki/Bisection_method)
+- [Secant method](https://en.wikipedia.org/wiki/Secant_method)
+- [Halley's method](https://en.wikipedia.org/wiki/Halley%27s_method)
+
+## Optimization Algorithms
+
+- [Alpha-beta pruning](https://en.wikipedia.org/wiki/Alpha%E2%80%93beta_pruning)
+- [Minmax](https://en.wikipedia.org/wiki/Minimax#Minimax_algorithm_with_alternate_moves)
+- [Simulated annealing](https://en.wikipedia.org/wiki/Simulated_annealing)
+
+### Non-linear Least Squares
+
+- [Gauss-Newton algorithm](https://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm)
+
+### Evolutionary computation
+
+#### Genetic Algorithms
+
+- [Fitness proportionate selection](https://en.wikipedia.org/wiki/Fitness_proportionate_selection)
+- [Truncation selection](https://en.wikipedia.org/wiki/Truncation_selection)
+- [Tournament selection](https://en.wikipedia.org/wiki/Tournament_selection)
+
+#### Swarm Intelligence
+
+- [Ant colony optimization](https://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms)
+- [Bees algorithm](https://en.wikipedia.org/wiki/Bees_algorithm)
+- [Particle swarm optimization](https://en.wikipedia.org/wiki/Particle_swarm_optimization)
+
+## Programming Language Theory
+
+## Parsing
+
+- [CYK algorithm](https://en.wikipedia.org/wiki/CYK_algorithm)
+- [LL parser](https://en.wikipedia.org/wiki/LL_parser)
+- [LR parser](https://en.wikipedia.org/wiki/LR_parser)
+- [Earley parser](https://en.wikipedia.org/wiki/Earley_parser)
+- [Recursive descent parser](https://en.wikipedia.org/wiki/Recursive_descent_parser)
+
+## Sequence Algorithms
+
+### Approximate Sequence Matching
+
+#### String Metrics
+
+- [Levenshtein edistance](https://en.wikipedia.org/wiki/Levenshtein_distance) (or edit distance)
+- [Hamming distance](https://en.wikipedia.org/wiki/Hamming_distance)
+
+### Sequence Permutations
+
+- [Fisher–Yates shuffle](https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle)
+
+----
+
+An article listing other possibly interesting algorithms can be found at the following URL.
+
+> [https://en.wikipedia.org/wiki/List\_of\_algorithms](https://en.wikipedia.org/wiki/List_of_algorithms)