Improved approximations for tour and tree covers

A tree (tour) cover of an edge-weighted graph is a set of edges which forms a tree (closed walk) and covers every other edge in the graph. Arkin, Halldorsson and Hassin (Information Processing Letters 47:275- 282, 1993) give approximation algorithms with ratio 3.55 (tree cover) and 5.5 (tour cover). We present algorithms with worst-case ratio 3 for both problems.