LG-Tree: An Efficient Labeled Index for Shortest Distance Search on Massive Road Networks

Abstract

With the development of mobile Internet technology, the road network in the real world is becoming larger and more complex, and the real-time response to the shortest distance query has become a high requirement for many industrial applications. Many existing approaches, such as G-tree or G*-tree, have been proposed to answer such search problems, however, these approaches are not efficient enough in dealing with very large graphs. To this end, we propose a novel index called LG-tree, which partitions the large graph into sub-graphs, and then indexes these subgraphs using a balanced tree. For each leaf node of LG-tree, a Distance Inverted File (DIF) is constructed, and these DIFs preserve all the connectivity information between the border vertices on the original graph. Inspired by the state-of-the-art label methods, we propose a novel hierarchy computing approach for each border vertex of LG-tree. Based on DIF and the hierarchy of border vertices, the border vertex list for each border is established, which is convenient for us to calculate the shortest distance and path between a query vertex <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$v_{q}$ </tex-math></inline-formula> and a target vertex <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> . Specifically, the number of levels of a vertex hierarchy increases dramatically as the graph size increases, and calculating vertex labels on a very large graph is an NP-hard problem. In order to further improve the calculation efficiency of the shortest distance between vertices, a heuristic method is proposed to limit the level of vertex hierarchy. In addition, a stage-based dynamic programming search method is proposed to divide all search situations between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$v_{q}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> into three cases to guarantee the efficiency of the shortest distance search. Extensive experiments are conducted to show that LG-tree and the stage-based method have better performance than the state-of-the-art approaches.