Optimal receiver scheduling algorithms for a multicast problem

This paper studies a multicast problem arising in wavelength division multiplexing single-hop lightwave networks, as well as in Video-on-Demand systems. In this problem, the same message of duration ΔΔ has to be transmitted to a set of nn receivers which are not all available simultaneously. The receivers can be partitioned into subsets, each served by a different transmission, with the objective of minimizing their overall waiting cost. When there is a single data channel available for transmission, a dynamic programming algorithm is devised which finds an optimal solution in O(nlogn+min{n2,nΔ2})O(nlogn+min{n2,nΔ2}) time, improving over a previously known O(n3)O(n3) time algorithm. When multiple data channels are available for transmission, an optimal O(n)O(n) time algorithm is proposed which finds an optimal solution if the message has constant transmission duration, whereas an NP-completeness proof is given if the message has arbitrary transmission duration.