Accelerating the shortest-path calculation using cut nodes for problem reduction and division

摘要

The shortest-path algorithm is one of the most important algorithms in geographical information systems. Bellman?s principle of optimization (BPO) is implicit in the shortest-path problem; that is, any involved node must be located in the simple paths between source and destination nodes. Unfortunately, BPO has never been explicitly used to exclude irrelevant nodes in existing methods, potentially leading to unnecessary searches among irrelevant nodes. To address this problem, we propose a BPO-based shortest-path acceleration algorithm (BSPA). In BSPA, a high-level graph is built to locate the necessary nodes and is used to partition the graph and divide a given task into independent subtasks. This allows the speed of any existing method to be improved using parallel computing. In a test using random graphs, on average, at most only 1.209% of the nodes need to be involved in the calculation. When compared with existing algorithms in real-world road networks, the BSPA shows faster preprocessing and query times, being respectively 118 and 463 times faster in the best case. In the worst case, they remain slightly faster.