Suppose you are given a graph G = (V,E) that represents homes and the travel tim

Question

Suppose you are given a graph G = (V,E) that represents homes and the travel time between them in some geographic area. Each home can be represented by a v E V and an edge e (vi, vj) E E implies that it is possible to travel directly from home vi to vj. The time to travel between homes will be given by t(eij) Suppose you are in the context of delivering goods to the homes from some starting depot D where vehicles must start and end their day. Further suppose that associated with each home is a time window w = [t1,t2] that indicates when the delivery must be made where 0

Explanation / Answer

Greedy is an algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit. Greedy algorithms are used for optimization problems. An optimization problem can be solved using Greedy if the problem has the following property: At every step, we can make a choice that looks best at the moment, and we get the optimal solution of the complete problem.
If a Greedy Algorithm can solve a problem, then it generally becomes the best method to solve that problem as the Greedy algorithms are in general more efficient than other techniques like Dynamic Programming. But Greedy algorithms cannot always be applied. For example, Fractional Knapsack problem (See this) can be solved using Greedy, but 0-1 Knapsack cannot be solved using Greedy.

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