A heuristic for the p-center problems in graphs

New heuristic algorithms for the rectangular $p$-cover problem

“…A2 is a modification of an O(n 2 logn) algorithm given by Plesnik [16] for points in a network and adapted later for any metric space in [14]. In [14,16] the search is in the set D = {d(Pu Pk) : Pu Pk e M, i < fc}, which clearly contains L*, but this is time consuming as it is shown in [15], for instance for n = 1 000, p -6 the run time on an Olivetti M-300 (with an 80386SX processor and 16 Mhz) was 1534 sec.…”

“…The problem (pC) has been proved to be NP-Hard, even for m -2 and the Rectangular norm [11,12], and so only heuristic algorithms can be used to obtain good solutions of (RpC) for large problems [2,6,7,14,16]. Most of the heuristic algorithms proposed for (pC) can be used for any metric [14], and consequently for the problem (RpC).…”

“…With the new rule each algorithm is this class becomes a new algorithm, creating a new class of algorithms. In particular, modifications of two algorithms given in [6,16] are considered. In section 3, we give two new algorithms based on partitions, the first is a modification of the heuristic given in [13], and the second is a modification of the well known Location-Allocation algorithm, which requires the évaluation of F (Mj) many times, but this is not time consuming for F (Mj) -L (Mj), Le.…”

An Optimal Algorithm for the Weighted Backup 2-Center Problem on a Tree

“…A point of a graph is a location on an edge of the graph, and is identified with the edge it locates on and the distance to an end vertex of the edge. The p-center problem in general graphs, for arbitrary p, is NP-hard [9], and the best possible approximation ratio is 2, unless NP=P [11]. When p is fixed or the network topology is specific, many efficient algorithms were proposed [4,5,7].…”

The minimum weight t-composition of an integer

“…The p-median [7] and the p-center [8] are classical examples of location problems. These problems are N P -hard and several heuristic methods have been developed, some of them exploiting the close relationship with another N P -hard problem designated the dominating set problem [6,9,10]. Since practical location problems have in general a huge dimension, it is a common procedure to decompose the problem into t smaller location problems [2], and produce a solution from the outcomes of each sub-problem.…”