Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: , a data structure is given for two and higher dimensional shortest path queries. For a set of n axis-parallel rectangles in the plane, or boxes in d-space, and a fixed target, it is possible with this structure to find a shortest rectilinear path avoiding all rectangles or boxes from any point to this target. Alternatively, it is possible to find the length of the path. The metric considered is a generalization of the L1-metric and the link metric, where the length of a path is its L1-length plus some (fixed) constant times the number of turns on the path. The data structure has size O((n log n)d−1), and a query takes O(logd−1 n) time (plus the output size if the path must be reported). As a byproduct, a relatively simple solution to the single shot problem is obtained; the shortest path beten two given points can be computed in time O(ndlog n) for d≥3, and in time O(n2) in the plane.
['Mark de Berg', 'Marc J. van Kreveld', 'Bengt J. Nilsson', 'Mark H. Overmars']
I am writing a research paper on a idea SHORTEST PATH QUERIES IN RECTILINEAR WORLDS
[{"from": "human", "value": "I am writing a research paper on a idea SHORTEST PATH QUERIES IN RECTILINEAR WORLDS"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: , a data structure is given for two and higher dimensional shortest path queries. For a set of n axis-parallel rectangles in the plane, or boxes in d-space, and a fixed target, it is possible with this structure to find a shortest rectilinear path avoiding all rectangles or boxes from any point to this target. Alternatively, it is possible to find the length of the path. The metric considered is a generalization of the L1-metric and the link metric, where the length of a path is its L1-length plus some (fixed) constant times the number of turns on the path. The data structure has size O((n log n)d\u22121), and a query takes O(logd\u22121 n) time (plus the output size if the path must be reported). As a byproduct, a relatively simple solution to the single shot problem is obtained; the shortest path beten two given points can be computed in time O(ndlog n) for d\u22653, and in time O(n2) in the plane."}]