A Survey on graph layout problems

Abstract

In this paper we survey results on several graph layout problems from an algorithmic point of view. Graph layout problems are a particular class of combinatorial optimization problems whose goal is to find a linear layout of an input graph in such way that a certain objective cost is optimized. A linear layout is a labeling of the nodes of a graph with distinct integers. A large amount of relevant problems in different areas can be formulated as graph layout problems. These include network optimization, VLSI circuit design, information retrieval, numerical analysis, computational biology, graph theory, scheduling, archaeology, etc. On the other hand, the minimal values of some layout costs are also related to interesting graph theoretic invariants of graphs. Most of the graph layout problems are NP-complete, but, in many of their applications, feasible solutions with an almost optimal cost are sufficient and, thus, approximation algorithms or effective heuristics can be used.