Title page for ETD etd-05062004-232310

Type of Document

Thesis

Author

Patarasuk, Pitch

URN

etd-05062004-232310

Title

Crossing Reduction for Layered Hierarchical Graph Drawing

Degree

Master of Science

Department

Computer Science, Department of

Advisory Committee

Advisor Name	Title
Daniel Schwartz	Committee Chair
David Whalley	Committee Member
Lois Hawkes	Committee Member

Keywords

Graph Drawing
Crossing Reduction
Hierarchical Graph
Layered Graph Drawing
Crossing Minimization

Date of Defense

2004-04-29

Availability

unrestricted

Abstract

Graph drawing is widely used in many fields. Good visualization in graph drawing makes it easier for humans to understand the concepts being represented. This thesis deals with what is known as a hierarchical graph and concerns one of the core issues in making graphs look better, that of reducing the number of edge crossings.

The general problem of crossing reduction is discussed, and several approaches are implemented and compared. The overall approach uses the well-known “layer-by-layer sweep” algorithm, where layers are generally considered two at a time and some heuristic is applied for reducing the numbers of edge crossings between just those two layers.

Two specific one-sided 2-level crossing reduction heuristics were implemented: the permutation heuristic and the barycenter heuristic. Both heuristics were each implemented in two ways, with and without randomness. Tests were run which demonstrate that introducing randomness in this manner significantly improves the performance of both heuristics. Moreover, the randomized barycenter method is preferable due to its ability to deal efficiently with large graphs.

Then an alternative, hybrid approach was implemented. This uses the same layer-by-layer-sweep but applies the permutation heuristic when the number of vertices in the given layer is small, and applies the barycenter heuristic otherwise. In general, it did not show significant improvement over the randomized barycenter heuristic. Finally, a new alternative is proposed for future research.

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