Application of Approximate Pattern Matching in Two Dimensional Spaces to Grid Layout for Biochemical Network Maps

Abstract

BackgroundFor visualizing large-scale biochemical network maps, it is important to calculate the coordinates of molecular nodes quickly and to enhance the understanding or traceability of them. The grid layout is effective in drawing compact, orderly, balanced network maps with node label spaces, but existing grid layout algorithms often require a high computational cost because they have to consider complicated positional constraints through the entire optimization process.ResultsWe propose a hybrid grid layout algorithm that consists of a non-grid, fast layout (preprocessor) algorithm and an approximate pattern matching algorithm that distributes the resultant preprocessed nodes on square grid points. To demonstrate the feasibility of the hybrid layout algorithm, it is characterized in terms of the calculation time, numbers of edge-edge and node-edge crossings, relative edge lengths, and F-measures. The proposed algorithm achieves outstanding performances compared with other existing grid layouts.Conclusions Use of an approximate pattern matching algorithm quickly redistributes the laid-out nodes by fast, non-grid algorithms on the square grid points, while preserving the topological relationships among the nodes. The proposed algorithm is a novel use of the pattern matching, thereby providing a breakthrough for grid layout. This application program can be freely downloaded from http://www.cadlive.jp/hybridlayout/hybridlayout.html.

A new grid- and modularity-based layout algorithm for complex biological networks

“…There are six primary extant grid layout algorithms, including the original grid layout [17], LucidDraw [18], hybrid grid layout [20], Cerebral [21], GBL layout [22] and SCCB-grid layout [27]. The hybrid grid layout and GBL are modularity -based algorithms that achieve relatively good performance compared with other grid layouts [20,22]. From this perspective, they have been chosen as the reference algorithms to be compared against GML.…”

“…Connectivity F-measure. The connectivity F-measure evaluates whether nodes with dense connectivities are positioned together [20,37]. It is defined as the weighted harmonic average of precision and recall, which are widely used in the area of information retrieval [37].…”

“…To address the problem, a grid layout algorithm has been proposed to place the nodes on grid points to avoid node overlap, and the interactions among nodes are specified with a cost function that is designed based on the topological structure of the network. Grid layout algorithms generate compact and biologically comprehensible layouts at the expense of computation performance [18–20]. To decrease computation costs, some algorithms are used in rigorous studies to improve the grid-optimization process through special methods (e.g., reoptimization-after-perturbation [18], sweep calculation [19] and subcellular localizations [21]).…”

“…Recently, implicit modular information has been utilized to enhance the performance of grid layout algorithms for the visualization of complex networks. Inoue et al [20] presented a hybrid grid layout algorithm using four different approaches, i.e., Spectral Analysis (H-SA), Kamada-Kawai (H-KK), Fruchterman-Reingold (H-FR) and Gursoy-Atun (H-GA), to preprocess the networks before distributing nodes to grid points. In particular, Spectral Analysis is a clustering algorithm to divide complex networks into modules.…”

Cognitive Societal Human Values of Sports: after the 2011 Disaster of Japan

“…The map layout (Figure 3) was calculated by the Fruchterman-Reingold Algorithm [13], which is a force-directed layout algorithm for centralization of the societal values' positioning. The purpose was to position the vertexes of a graph in two-dimensional space so that all the edges were of more or less equal length and there were as few crossing edges as possible [14,15,16].The force-directed algorithms achieved this by assigning forces among the set of vertexes and the set of edges. The forces were applied to the vertexes, pulling them closer together or pushing them further apart.…”