Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Short Guide To Approximation Preserving Reductions
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Channelization Problem in Large Scale Data Dissemination
ICNP '01 Proceedings of the Ninth International Conference on Network Protocols
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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.