Localized Geometric Query Problems
  A new class of geometric query problems are studied in this paper. We are required to preprocess a set of geometric objects $P$ in the plane, so that for any arbitrary query point $q$, the largest circle that contains $q$ but does not contain any member of $P$, can be reported efficiently. The geometric sets that we consider are point sets and boundaries of simple polygons. 
John Augustine and Sandip Das and Anil Maheshwari and Subhas C. Nandy   and Sasanka Roy and Swami Sarvattomananda
cs.CG