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 AbstractGraph 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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