Multicast communication constrained by end-to-end and interdestination delay variation is known as delay and delay variation-bounded multicast. These constraints are salient for real-time multicast communications. In this paper, we propose a directional core selection algorithm for core selection and delay variation-bounded multicast tree generation. Another algorithm, based on k-shortest paths, is proposed to further decrease the interdestination delay variation of the trees generated by directional core selection. We also propose the dynamic version of both algorithms that respond to dynamic join and leave requests to the ongoing multicast session by reorganizing the tree and avoiding session disruption. Simulations show that the proposed algorithms surpass existing algorithms in end-to-end delay, interdestination delay variation, execution time, and failure probability.