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From a dynamic programming point of view, Dijkstra's algorithm for the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method.
The Held–Karp algorithm, also called the Bellman–Held–Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman [1] and by Held and Karp [2] to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour that visits each city exactly once before returning to ...
From a dynamic programming point of view, Dijkstra's algorithm is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method. [33] [34] [35] In fact, Dijkstra's explanation of the logic behind the algorithm: [36] Problem 2.
For the class of interval graphs, an ()-time algorithm is known, which uses a dynamic programming approach. [19] This dynamic programming approach has been exploited to obtain polynomial-time algorithms on the greater classes of circular-arc graphs [20] and of co-comparability graphs (i.e. of the complements of comparability graphs, which also ...
Differential dynamic programming (DDP) is an optimal control algorithm of the trajectory optimization class. The algorithm was introduced in 1966 by Mayne [1] and subsequently analysed in Jacobson and Mayne's eponymous book. [2] The algorithm uses locally-quadratic models of the dynamics and cost functions, and displays quadratic convergence ...
Decremental algorithms are algorithms in which only deletions of elements are allowed, starting with the initialization of a full data structure. If both additions and deletions are allowed, the algorithm is sometimes called fully dynamic .
Like the Needleman–Wunsch algorithm, of which it is a variation, Smith–Waterman is a dynamic programming algorithm. As such, it has the desirable property that it is guaranteed to find the optimal local alignment with respect to the scoring system being used (which includes the substitution matrix and the gap-scoring scheme).
Dynamic programming – Problem optimization method; Hamilton–Jacobi–Bellman equation – An optimality condition in optimal control theory; Markov decision process – Mathematical model for sequential decision making under uncertainty; Optimal control theory – Mathematical way of attaining a desired output from a dynamic system