thm (thm 3.8 in text): The above algorithm is a 2-approximation algorithm.
1.5-approximation algorithm for TST in metric graph
thm (Euler): Given an Eulerian graph, an Eulerian tour can be found in polynomial time.
thm (shortcutting): Given an Eulerian tour T in a metric graph, a Traveling Salesman Tour (TST) T' such that cost(T') ≤ cost(T) can be found in polynomial time.
thm: Given an even-sized subset S of vertices of a metric graph, the cost of the minimum-cost perfect matching on S is at most 1/2 the cost of the minimum cost TST.
corollary (thm 3.12 in text): The above algorithm is a 1.5-approximation algorithm.