Semi-Yao graph


The k-semi-Yao graph of a set of n objects P is a geometric proximity graph, which was first described to present a kinetic data structure for maintenance of all the nearest neighbors on moving objects. It is named for its relation to the Yao graph, which is named after Andrew Yao.

Construction

The k-SYG is constructed as follows. The space around each point p in P is partitioned into a set of polyhedral cones of opening angle ', meaning the angle of each pair of rays inside a polyhedral cone emanating from the apex is at most ', and then p connects to k points of P in each of the polyhedral cones whose projections on the cone axis is minimum.

Properties