We survey the p-median problem and the p-centre problem. Then we investigate two new techniques for continuous optimal partitioning of a tree T with n - 1 edges, where a nonnegative rational valued weight is associated with each edge. The continuous Max-Min tree partition problem (the continuous Min-Max tree partition problem) is to cut the edges in p - 1 places, so as to maximize (respectively minimize) the weight of the lightest (respectively heaviest) resulting subtree. Thus the tree is partitioned into approximately equal components. For each optimization problem, an inefficient implementation of the algorithm is given, which runs in pseudo-polynomial time, using a previously developed algorithm and a construction. We then derive from it a much faster algorithm using a top-down greedy technique, which runs in polynomial time. The algorithms have a variety of applications among others to highway and pipeline maintenance.

Reference:

Chiang, Y. 1995. An algorithmic approach to continuous location. University of Cape Town.

Chiang, Y. B. (1995). An algorithmic approach to continuous location. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/17441

Chiang, Y B. "An algorithmic approach to continuous location." Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1995. http://hdl.handle.net/11427/17441

Chiang YB. An algorithmic approach to continuous location. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1995 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17441