The Traveling Salesperson Problem asks for, given a complete. weighted graph, the Ila,nilto,iian cycle of minimum weight This i one of the most fanioiedy difficult problems in computer science and graph theory’.
computer science
Description
Part 1: The Traveling Salesperson Problem
The Traveling Salesperson Problem asks for, given a complete. weighted graph, the Ila,nilto,iian cycle of minimum weight This i one of the most fanioiedy difficult problems in computer science and graph theory’.
¡n on-ter to make approxiinaticin more feasible, we consider m.t,* TSP: we round the problem to graphs for whose weights the triangle inequality holds. For example, given: 6V2 Itere, there arc niuhierous Ilansiltonian cvckau of miuilnum weight. One such cycle is (Ob, t’a, t’,, V:,, t’4, Vo).
Part 2: Approximating Metric TSP
Vheii TSP hi restricted to the Iiwtric casc. there then exists a relatively simple 2-approxiinathiti that mus in polynomial time:
1. First, construct au MST, which can be done in lijieanithmic time using Knu,skal’s algorithiii In the graph above. this tree contains the edges {(t’o, o,) ,(v,, v3) , (0:,, 02), (r,, V4)}. An MST is a decent
startluig point for au opproxiunatloui. since Its weight Is a lower bound on that of tut’ optinual cycle.
