Color-spanning localized query

Smallest Color-Spanning Objects

Motivated by questions in location planning, we show for a set of colored point sites in the plane how to compute the smallest (by perimeter or area) axis-parallel rectangle, the narrowest strip, and other smallest objects enclosing at least one site of each color.

Shortest Color-Spanning Intervals

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.

Related Work : Color - Spanning Set

Recognition of Minimum Width Color-Spanning Corridor and Minimum Area Color-Spanning Rectangle

Given a set of n colored points with a total of m > 3 colors in 2D, the problem of identifying the smallest color-spanning object is studied. We have considered two different shapes: (i) corridor, and (ii) rectangle of arbitrary orientation. Our proposed algorithm identifies the narrowest color-spanning corridor in O(n2 log n) time using O(n) space. Our proposed algorithm for identifying minimu...