Traveling Salesman Problem

Definition

Triangle Inequality

c(u,w) $\leq$ c(u,v) + c(v,w)

(generally satisfied)

An approximation algorithm with ratio bound p = 2 exists for TSPs exhibiting triangle inequality.

Approx-TSP-Tour(G, c) $\;\;\;\;\;$ $\;\;\;\;\;$; G = (V, E), c = edge costs
$\;\;\;\;\;$select root vertex r in V
$\;\;\;\;\;$T = MST-Prim(G, c, r)
$\;\;\;\;\;$L = list of vertices in preorder traversal of T
$\;\;\;\;\;$return cycle with vertices ordered as in L