Crossing Minimization Problems of Drawing Bipartite Graphs in Two Clusters
نویسندگان
چکیده
The crossing minimization problem is a classic and very important problem in graph drawing (Pach, Tòth 1997); the results directly affect the effectiveness of the layout, especially for very large scale graphs. But in many cases crossings cannot be avoided. In this paper we present two models for bipartite graph drawing, aiming to reduce crossings that cannot be avoided in the traditional bilayer drawings. We characterize crossing minimization problems in these models, and prove that they are NP-complete.
منابع مشابه
META-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملThe assignment heuristic for crossing reduction
Several applications use algorithms for drawing k-layered networks and, in particular, 2 layered ne tworks ( i . e . b ipart i t e graphs) . Bipartite graphs are commonly drawn in the plane so that all vertices lie on two parallel vertical lines, and an important requirement in drawing such graphs is to minimize edge crossings. Such a problem is NP-complete even when the position of the vertice...
متن کاملA Solution to Bipartite Drawing Problem Using Genetic Algorithm
Crossing minimization problem in a bipartite graph is a well-known NP-Complete problem. Drawing the directed/undirected graphs such that they are easy to understand and remember requires some drawing aesthetics and crossing minimization is one of them. In this paper, we investigate an intelligent evolutionary technique i.e. Genetic Algorithm (GA) for bipartite drawing problem (BDP). Two techniq...
متن کاملBeyond-Planarity: Density Results for Bipartite Graphs
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations. Early research dates back to the 1960s (e.g., Avital and Hanani [14]) for extremal problems on geometric graphs, but is also related to graph drawing problems ...
متن کاملNice Drawings for Planar Bipartite Graphs
Graph drawing algorithms usually attempt to display the characteristic properties of the input graphs. In this paper we consider the class of planar bipartite graphs and try to achieve planar drawings such that the bipartite-ness property is cleary shown. To this aim, we develop several models, give eecient algorithms to nd a corresponding drawing if possible or prove the hardness of the proble...
متن کامل