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In Section 3, we show that MCLP is APX-complete on monochromatic-diamond-free graphs with maximum degree 6.
3 Inapproximability of MCLP on monochromatic-diamond-free graphs
It is easily seen that PIC is a special case of the decision version of MCLP if the graph G is colored by a unique color.
Hence, if the input graph for MCLP is monochromatic-diamond-free with the size of a maximum monochromatic clique bounded by a constant, we have an approximation algorithm with constant performance ratio.
The MCLP was first introduced by Church and ReVelle (1974).
The MSAP is created as a modification of the MCLP which makes use of the capability of GIS to generate service areas of facilities as travel time zones.
Both the MCLP and MSAP concern with the problem of selecting p facility sites out of n candidate sites that achieve the best objective function value of the problem.
Both Add and GAS were chosen as they have been tested workable to solve the MCLP (Church and ReVelle, 1974), easy to understand, relatively fast and easy to integrate with existing data structures in the GIS.