Efficient Algorithms for Geometric Shortest Path Query Problems

Computing shortest paths in a geometric environment is a fundamental topic in computational geometry and finds applications in many other areas. The problem of processing geometric shortest path queries is concerned with constructing an efficient data structure for quickly answering on-line queries for shortest paths connecting any two query points in a geometric setting. This problem is a generalization of the well-studied problem of computing a geometric shortest path connecting only two specified points. This paper covers the newly-developed algorithmic paradigms for processing geometric shortest path queries and related problems. These general paradigms have led to efficient techniques for designing algorithms and data structures for processing a variety of queries on exact and approximate shortest paths in a number of geometric and graphical settings. Some open problems and promising directions for future research are also discussed.

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