A New Framework for Solving the Spatial Network Problems Based on Line Graphs

Abstract

In this article we define inverse line graphs of directed graphs as a new framework for solving some classical network analysis problems. The extraction method and theories of inverse line graphs are explained in this article. It is shown that by changing the analysis space from the original directed graph to the inverse line graph, complex problems can be changed into simpler problems. We show the usefulness of the proposed framework in two particular applications: shortest path computations and the more general route planning. Considering the implementation result, we expect that this framework could be used in many more network analysis problems.

An Evaluation Model for Analyzing Robustness and Spatial Closeness of 3D Indoor Evacuation Networks

“…Unlike outdoor navigation, indoor navigation occurs in 3D spaces and requires both the topological and geometric 3D information of route planning environments. Many efforts have shed light on developing models and methods for the efficient representation of 3D data for indoor navigation purposes [7][8][9][10][11]. In recent decades, with the increased attention paid to indoor emergencies, many researchers have directed their interests to indoor navigation in disastrous situations and have developed new models and methods to support routing in indoor environments.…”

Unveil key functions in socio-technical systems: mapping FRAM into a multilayer network

“…In terms of graph theory, this second matricial encoding corresponds to the matrix of adjacency obtained from the transformation of the graph in a line graph, i.e., the graph built by replacing new nodes to the existing arcs, and arcs (lines) instead of the old nodes. It can be demonstrated that the same search can be carried out with a different algorithm based on power of the adjacency matrix of the starting graph; the two descriptions are in fact equivalent in substance (Saberian et al 2014). Bellini et al (2017) proposed the most explicit attempt in the context of the resilience of the urban transport system.…”

A Faster R-CNN Approach for Extracting Indoor Navigation Graph From Building Designs

“…Whilst the research topic is interesting, two major gaps have to be filled in order to achieve a sounding automation process for providing high quality indoor navigation graphs (Qian et al, 2015, Saberian et al, 2014, Ricker et al, 2014, Guex, 2014. One is that the data source quality cannot not be maintained due to inconsistent data formats and variant resolutions of building blueprints.…”