3-Dimensional Shortest Path Searching and Chasing in the Volumes

Abstract

This paper presents the 3D shortest path searching algorithms in the volumes with O(N) of time and memory space complexities based on the nuclear fission chain reactions scheme, where N is the number of voxels in the grid space. Fur- thermore, the proposed algorithm is extended to the 3D shortest path searching for multiple pairs based on the concept of the aircraft domain to avoid collision and chasing algorithm in the volumes with the time complexity of O(qN) and O(N2/a), respectively, where q is the number of aircraft and a is the relative speed ratio of chaser to target. The concept of these algorithms can be applied to GIS (Geographic Information Sys- tem), search and interception for aircrafts, and cruise missile interception system.