Incremental channelization

Channelization is the problem of forming multicast groups from inputs of a set of flows, a set of users and a set of user preferences, along with an upper bound on the number of groups. Channelization aims to construct groups such that the network cost is substantially smaller than using a single multicast group which delivers all flows to all users. In this paper we introduce an incremental version of channelization wherein the input may change over time. When such a change occurs, one approach is to totally recompute the channelization solution. In contrast, in the incremental approach taken here, the solution for the original channelization instance is updated to become a solution for the modified channelization instance. The goal is to produce a solution of high quality in substantially less time than it would take to do a full recomputation. In this context we study incremental channelization problems corresponding to adding a flow and adding a user. For these two problems we provide complexity results and incremental algorithms. Specifically we show: 1) that natural incremental approaches are NP-hard; 2) that approximating the optimal solution within a log factor is unlikely; and 3) give a greedy algorithm with a performance within a log factor of the optimal (in light of our result 2, this is the best possible approximation result). In addition to the theoretical results, a case study is given for the problem of adding a flow, providing simulation results comparing the effectiveness of the solutions produced by our incremental algorithms with solutions from algorithms doing full recomputation.