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Dynamic programming is both a mathematical optimization method and an algorithmic paradigm. ... For example, given a graph G=(V,E), ...
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 ...
Bellman flow chart. A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. [1]
Minor testing (checking whether an input graph contains an input graph as a minor); the same holds with topological minors; Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in polynomial time.) Modularity maximization [5]
Dynamic programming is used when we compute the maximum-weight independent set for each . This dynamic program works because each is a -outerplanar graph. Many NP-complete problems can be solved with dynamic programming on -outerplanar graphs. Baker's technique can be interpreted as covering the given planar graphs with subgraphs of this type ...
If the graph is planar and has low branch-width (or is nonplanar but with a known branch decomposition), then it can be solved in polynomial time using dynamic programming. In general, the time required is polynomial in the graph size, but exponential in the branch-width.
Dynamic problems in computational complexity theory are problems stated in terms of changing input data. In its most general form, a problem in this category is usually stated as follows: In its most general form, a problem in this category is usually stated as follows: