Drawing graphs on rectangular grids

24Citations
Citations of this article
9Readers
Mendeley users who have this article in their library.

Abstract

We consider the problem of embedding undirected graphs G = (V, E) with n vertices of maximum degree 4 (4-graphs) into rectangular grids. The problems of minimizing the grid area (Kramer and van Leeuwen, 1984; Formann and Wagner, 1991) as well as minimizing the total number of bends are NP-hard (Storer, 1984). It is well known that such a graph can be embedded in a rectangular grid with at most 2n columns and 2n rows such that any edge is embedded with at most 5 bends (Lengauer, 1990, p. 249). We present an /oO(n2)-algorithm constructing an embedding for arbitrary 4-graphs with n vertices in a rectangular grid with at most 2n columns and 2n rows bending every edge at most twice. Note that two is a lower bound on the maximum number of bends per embedded edge since the graph K5 cannot be embedded with less than 2 bends per embedded edge. © 1995.

Cite

CITATION STYLE

APA

Schäffter, M. (1995). Drawing graphs on rectangular grids. Discrete Applied Mathematics, 63(1), 75–89. https://doi.org/10.1016/0166-218X(94)00020-E

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free