Computational geometry John Hershberger has been a significant contributor to computational geometry and the algorithms community since the mid-1980s. His earliest work focused on shortest paths and visibility. With
Leonidas Guibas and by himself, he devised optimal linear-time algorithms to compute
visibility polygons,
shortest path trees,
visibility graphs, and data structures for logarithmic-time shortest path queries in simple polygons. With
Jack Snoeyink he extended the algorithms for simple polygons to compute
homotopic shortest paths among
polygonal obstacles in the
plane. He also invented
parallel algorithms to solve several
shortest path and
visibility problems. One of the most significant achievement of this period is his algorithm (joint work with
Subhash Suri) to compute
shortest paths among
polygonal obstacles in the
plane using only
O(n log n) time. This algorithm was a vast improvement over the roughly
quadratic running time achievable by
visibility-graph-based methods, and resolved a problem that had been open and intensely studied for years. Data structure for "Pedestrian ray shooting", devised by John and
Subhash Suri, answers ray shooting queries in a
simple polygon. It consists of a special
triangulation such that any
line segment inside the
polygon intersects only O(log
n) triangles; ray shoot-ing queries can be answered simply by walking from triangle to triangle until the query ray hits the polygon boundary.
Kinetic data structures, proposed by
Leonidas Guibas,
Julien Basch and Hershberger, have been and continue to be influential in computational geometry. Working by himself and with a variety of co-authors, John devised kinetic data structures to maintain the extent of moving points; the connected components of moving unit disks, rectangles, and hypercubes; clusters for sets of moving points; and data structures to detect collisions between polygons in motion. ==Selected publications==