Dynamic programming is a technique for solving problems with overlapping
subproblems.

given n items of known weights w1,...,wn and values v1,...,vn and a knapsack of capacity W, find the most valuable subset of the items that fit into the knapsack.

The goal is to get a method that solves only subproblems that ar necessary and does so only once. Such a method exists; it is based on using memory functions.

its practicality is limited by dependence on the instance parameters being relatively small.

Although approximation algorithms run a gamut in level of sophistication, most of them are based on some problem-specific heuristic.

A polynomial-time approximation algorithm is said to be a capproximation algorithm,

Greedy Algorithms for the TSP The simplest approximation algorithms for the
traveling salesman problem are based on the greedy technique.

Minimum-Spanning-Tree–Based Algorithms There are approximation algorithms for the traveling salesman problem that exploit a connection between Hamiltonian circuits and spanning trees of the same graph