Summary: Optimal Graph Orientation with Storage Applications
Oswin Aichholzer
Franz Aurenhammer
Institute for Theoretical Computer Science
Graz University of Technology
Klosterwiesgasse 32/2, A­8010 Graz, Austria
e­mail: foaich,aureng@igi.tu­graz.ac.at
G¨ unter Rote
Institut f¨ ur Mathematik
Technische Universit¨ at Graz
Steyrergasse 30
A­8010 Graz, Austria
e­mail: rote@ftug.dnet.tu­graz.ac.at
Abstract
We show that the edges of a graph with maximum edge density d can always be oriented
such that each vertex has in­degree at most d. Hence, for arbitrary graphs, edges can
always be assigned to incident vertices as uniformly as possible. For example, in­degree
3 is achieved for planar graphs. This immediately gives a space­optimal data structure
that answers edge membership queries in a maximum edge density­d graph in O(log d)
time.

Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz
Technische Universität Graz, Institute for Software Technology

Collections: Computer Technologies and Information Sciences