TY - JOUR
T1 - K-center and K-median problems in graded distances
AU - Lin, Guo Hui
AU - Xue, Guoliang
N1 - Funding Information:
* Corresponding author. Email: xue@cs.uvm.edu. ’ The research of this author was supported in part by the National Natural Science Foundation of China grant 1933 1050, and by the Presidential Chuang Xin Foundation of the Chinese Academy of Sciences. 2 The research of this author was supported in part by the Army Research Office grant DAAH04-9610233 and by the National Science Foundation grants ASC-9409285 and OSR-9350540.
PY - 1998/10/28
Y1 - 1998/10/28
N2 - Graded distances are generalizations of the Euclidean distance on points in R1. They have been used in the study of special cases of NP-hard problems. In this paper, we study the k-center and k-median problems with graded distance matrices. We first prove that the k-center problem is polynomial time solvable when the distance matrix is graded up the rows or graded down the rows. We then prove that the k-median problem is NP-complete when the distance matrix is graded up the rows or graded down the rows. An easy special case of the k-median problem with graded distance matrices is also discussed.
AB - Graded distances are generalizations of the Euclidean distance on points in R1. They have been used in the study of special cases of NP-hard problems. In this paper, we study the k-center and k-median problems with graded distance matrices. We first prove that the k-center problem is polynomial time solvable when the distance matrix is graded up the rows or graded down the rows. We then prove that the k-median problem is NP-complete when the distance matrix is graded up the rows or graded down the rows. An easy special case of the k-median problem with graded distance matrices is also discussed.
KW - Computational complexity
KW - Graded distance matrix
KW - The k-center problem
KW - The k-median problem
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U2 - 10.1016/s0304-3975(98)00063-2
DO - 10.1016/s0304-3975(98)00063-2
M3 - Article
AN - SCOPUS:0345767117
SN - 0304-3975
VL - 207
SP - 181
EP - 192
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 1
ER -