1

Given a Graph which has vertices as Cities and Edges as the distance between the cities. Each and every city has certain number of holidays associated with it. Initially you are given the starting point. Now the goal is to find a path in a graph such that we need to collect as many holidays as possible while minimizing the distance.

Eg: Consider a graph: Vertex Weights: (City -> Holidays) A -> 30 B -> 35 C -> 45

Edge Weights A -> B (Distance is 2) A -> C (Distance is 8)

If we start from A the maximum holidays we can collect are 65 through the path A -> B with distance "2". We don't choose the path A -> C even though it gives the holidays as 75 since the distance is "8"

Ajantha
  • 33
  • 4
  • 1
    Typical default Traveling Salesman Problem; with no showing effort or whatsoever. – ZF007 Apr 03 '19 at 19:08
  • I don't think so. It has both edge weights and Vertex weights. You need to minimize the total edge weights while maximizing the vertex weights. One thing we can do is converting vertex weights to edge weights by creating Auxiliary vertices and Auxiliary edges and run the traditional Algorithms. Is there any better way than this? – Ajantha Apr 04 '19 at 18:12
  • minimize the total edge weights = TSP default. maximizing the vertex weights = TSP plus issue because.. why only visit cities only once.... and not trade goods.. your case its collecting as many holidays.. What is the difference with picking up packages or deliver packages? Pateto == Patato.. Regardsless, always a nice lunchbreak discussion topic at a logistics department. In the end its optimizing for the best edge weights and Vertex weights ratio. – ZF007 Apr 04 '19 at 22:06

0 Answers0