Abstract
Graph drawing, or the automatic layout of graphs, is a challenging problem. There are several search based methods for graph drawing which are based on optimizing an objective function which is formed from a weighted sum of multiple criteria. In this paper, we propose a new neighbourhood search method which uses a tabu search coupled with path relinking to optimize such objective functions for general graph layouts with undirected straight lines. To our knowledge, before our work, neither of these methods have been previously used in general multi-criteria graph drawing. Tabu search uses a memory list to speed up searching by avoiding previously tested solutions, while the path relinking method generates new solutions by exploring paths that connect high quality solutions. We use path relinking periodically within the tabu search procedure to speed up the identification of good solutions. We have evaluated our new method against the commonly used neighbourhood search optimization techniques: hill climbing and simulated annealing. Our evaluation examines the quality of the graph layout (objective function’s value) and the speed of layout in terms of the number of evaluated solutions required to draw a graph. We also examine the relative scalability of each method. Our experimental results were applied to both random graphs and a real-world dataset. We show that our method outperforms both hill climbing and simulated annealing by producing a better layout in a lower number of evaluated solutions. In addition, we demonstrate that our method has greater scalability as it can layout larger graphs than the state-of-the-art neighbourhood search methods. Finally, we show that similar results can be produced in a real world setting by testing our method against a standard public graph dataset.
Highlights
Graph drawing is the process of transforming a graph into a visual representation that is called a graph layout [1]
In this paper we show that tabu search alone outperforms hill climbing, but not simulated annealing, we show that when tabu is combined with path relinking it outperforms simulated annealing
The rest of this paper is organized as follows: Section 2 describes some background in search based techniques; Section 3 describes our method that couples tabu search with path relinking; Section 4 describes parameters tuning process along with experimental results for applying hill climbing, simulated annealing, tabu search, and tabu search with path relinking on random graphs, and for testing the scalability of our method; Section 5 describes experimental results of applying the same approaches on real world public graph datasets; Section 6 discusses and analyses the results; in Section 7 we give our conclusions in addition to directions for future work
Summary
Graph drawing is the process of transforming a graph into a visual representation that is called a graph layout [1]. Many graph layout algorithms in the literature use neighbourhood search based methods for drawing multi-criteria graph layouts with Simulated Annealing (SA) [2, 8, 9, 10] and Hill Climbing (HC) [3, 6, 11], and single-criterion graph layouts with Tabu search (TS) [12] and Path Relinking (PR) [13]. The addition of applying path relinking within the tabu search procedure speeds up the identification of good solutions and outperforms simulated annealing by producing graph layouts with better values of objective function. The rest of this paper is organized as follows: Section 2 describes some background in search based techniques; Section 3 describes our method that couples tabu search with path relinking; Section 4 describes parameters tuning process along with experimental results for applying hill climbing, simulated annealing, tabu search, and tabu search with path relinking on random graphs, and for testing the scalability of our method; Section 5 describes experimental results of applying the same approaches on real world public graph datasets; Section 6 discusses and analyses the results; in Section 7 we give our conclusions in addition to directions for future work
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