TITLE:
A Note on the Inverse Connected p-Median Problem on Block Graphs
AUTHORS:
Chunsong Bai, Liqi Zhang, Jianjie Zhou
KEYWORDS:
Location Theory, Block Graphs, Inverse Optimization, Connected p-Median
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.4,
April
25,
2023
ABSTRACT: Recently, the inverse connected p-median problem on block graphs G(V,E,w) under various cost functions, say rectilinear norm, Chebyshev norm, and bottleneck Hamming distance. Their contributions include finding a necessary and sufficient condition for the connected p-median problem on block graphs, developing algorithms and showing that these problems can be solved in O(nlogn) time, where n is the number of vertices in the underlying block graph. Using similar technique, we show that some results are incorrect by a counter-example. Then we redefine some notations, reprove Theorem 1 and redescribe Theorem 2, Theorem 3 and Theorem 4.