We consider the channel assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with certain geometric structure. The channel assignment problem can be cast as a variant of the vertex coloring problem (called the distance-2 coloring problem) on the graph that models a given packet radio network. We present efficient approximation algorithms for the distance-2 coloring problem for several classes of graphs including a class of geometric graphs that naturally model a large class of packet radio networks. The classes of graphs considered include (r, s)-civilized graphs, planar graphs, graphs with bounded genus, etc. Many of the approximation results presented here are the first such results in the literature.

A wide number of practical applications would benefit from automatically generated graphical representations of database schemas, in which tables are represented by boxes, and table attributes correspond to distinct stripes inside each table. Links, connecting attributes of two different tables, represent referential constraints or join relationships, and may attach arbitrarily to the left or to the right side of the stripes representing the attributes. To our knowledge no drawing technique is available to automatically produce diagrams in such strongly constrained drawing convention. In this paper we provide a polynomial time algorithm for solving this problem and test its efficiency and effectiveness against a large test suite. Also, we describe an implementation of a system that uses such an algorithm and we study the main methodological problems we faced in developing such a technology.