Efficient algorithms for center problems in cactus networks

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$n$: an O(nlogn)$O(nlogn)$ time algorithm to solve the 1-center problem, and an O(nlog³n)$O\left(n{log}^{3}n\right)$ time algorithm to solve the weighted continuous 2-center problem. We have also provided improved solutions to the general p$p$-center problems in cactus networks. The developed ideas are then applied to solve the obnoxious 1-center problem in weighted cactus networks.