Efficient algorithms for solving the center problems in weighted cactus networks are presented. In particular, we have proposed the following algorithms for the weighted cactus networks of size n: an O(n log n) time algorithm to solve the 1-center problem, an O(n log 3 n) time algorithm to solve the weighted continuous 2-center problem. We have also provided improved solutions to the general p-center problems in cactus networks. The developed ideas are then applied to solve the obnoxious 1-center problem in weighted cactus networks.
For this general model, they REF presented an O(n log n) time algorithm to solve the node weighted 1-center problem, and an O(n log 3 n) time algorithm to solve the continuous node weighted 2-center problem.
Efficient algorithms for center problems in cactus networks
THEOR COMPUT. SCI
Mathematics Computer Science