This paper presents a variation on the reverse p-median problem that does not require that the facilities are placed as an input to the problem. The variation, which will be referred to as the p-median problem with edge reduction, requires solving the p-median problem and the reverse p-median problem together. This paper presents a series of algorithms for solving the 1- and 2-median problems with edge reduction on trees. For the 1-median on a tree, where the location problem can be solved in O(n) time and the reverse problem in O(n log n) time, an algorithm is presented to solve the combined problem in O(n log n) time as well. The 2-median combined problem on a tree, for which each individual problem requires O(n log n) time, can be solved in O(n2 log n) time.
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