We study two packing problems that arise in the area of dissemination-based information systems; a second theme is the study of distributed approximation algorithms. The problems considered have the property that the space occupied by a collection of objects together could be significantly less than the sum of the sizes of the individual objects. In the Channel Allocation Problem, there are users who request subsets of items. There are a fixed number of channels that can carry an arbitrary amount of information. Each user must get all of the requested items from one channel, i.e., all the data items of each request must be broadcast on some channel. The load on any channel is the number of items that are broadcast on that channel; the objective is to minimize the maximum load on any channel. We present approximation algorithms for this problem and also show that the problem is MAX-SNP hard. The second problem is the Edge Partitioning Problem addressed by Goldschmidt, Hochbaum, Levin, and Olinick (Networks, 41:13-23, 2003). Each channel here can deliver information to at most k users, and we aim to minimize the total load on all channels. We present an O(n1/3)-approximation algorithm and also show that the algorithm can be made fully distributed with the same approximation guarantee; we also generalize to the case of hypergraphs.