Paths, trees, and minimum latency tours

We give improved approximation algorithms for a variety of latency minimization problems. In particular, we give a 3.59-approximation to the minimum latency problem, improving on previous algorithms by a multiplicative factor of 2. Our techniques also give similar improvements for related problems like k-traveling repairmen and its multiple depot variant. We also observe that standard techniques can be used to speed up the previous and this algorithm by a factor of O^˜(n).