Incremental bipartite drawing problem

Abstract Layout strategies that strive to preserve perspective from earlier drawings are called incremental. In this paper we study the incremental arc crossing minimization problem for bipartite graphs. We develop a greedy randomized adaptive search procedure (GRASP) for this problem. We have also developed a branch-and-bound algorithm in order to compute the relative gap to the optimal solution of the GRASP approach. Computational experiments are performed with 450 graph instances to first study the effect of changes in grasp search parameters and then to test the efficiency of the proposed procedure. Scope and purpose Many information systems require graphs to be drawn so that these systems are easy to interpret and understand. Graphs are commonly used as a basic modeling tool in areas such as project management, production scheduling, line balancing, business process reengineering, and software visualization. Graph drawing addresses the problem of constructing geometric representations of graphs. Although the perception of how good a graph is in conveying information is fairly subjective, the goal of limiting the number of arc crossings is a well-admitted criterion for a good drawing. Incremental graph drawing constructions are motivated by the need to support the interactive updates performed by the user. In this situation, it is helpful to preserve a “mental picture” of the layout of a graph over successive drawings. It would not be very intuitive or effective for a user to have a drawing tool in which after a slight modification of the current graph, the resulting drawing appears very different from the previous one. Therefore, generating incrementally stable layouts is important in a variety of settings. Since “real-world” graphs tend to be large, an automated procedure to deal with the arc crossing minimization problem in the context of incremental strategies is desirable. In this article, we develop a procedure to minimize arc crossings that is fast and capable of dealing with large graphs, restricting our attention to bipartite graphs.