Graph graphics: Theory and practice

Abstract Many graph drawing problems are NP-complete. Most of the problems described in this expository survey have constraints that relate to either minimizing the number of crossings or minimizing some function of the edge lengths. Nevertheless, these problems are sufficiently common in some areas that polynomial-time algorithms for special cases and heuristics for more general cases have been developed. A graph-theoretic characterization of some of these problems is given, followed by a discussion of their complexity. Finally, several algorithms and heuristics for graph layout [some with applications to very large scale integration (VLSI)] will be discussed.