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(1)-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) over tilde (n).