Comments on the paper: `Heuristic and Special Case Algorithms for Dispersion Problems' by S. S...

This article presents comments by the author on a paper discussing heuristic and special case algorithms for dispersion problems. Problems discussed in this article are the subject of the paper in focus. The results presented in that paper include a simple heuristic for Max-Min Facility Dispersion (MMFD) which provides a performance guarantee of 1/2, and a similar heuristic for Max-Avg Facility Dispersion (MAFD) with a performance guarantee of 1/4. It is also proved there that obtaining a performance guarantee of more than 1/2 for MMFD is NP-hard. The paper also discussed the one- dimensional versions of MMFD and MAFD, where the vertex set V consists of a set of n points on the real line. Section 2 of the paper is devoted to the heuristic for MMPD. It should be noted that this heuristic was analyzed before. In fact, it is shown therein that the performance guarantee of 1/2, holds for a more general model where the selected set p is restricted to be in a compact subset of the network indiced by the edge distances.