The concept of rectangle-of-influence (RI) drawings is old and well-studied in the area of graph drawing. A graph has such a drawing if we can assign points to its vertices such that for every edge (v, w) the supporting rectangle (i.e., the minimal closed axis-aligned rectangle R(v, w) containing v and w) contains no other points. In the original setup, the graph had to have an edge for every p...

In document processing, segmentation is done to uniquely identify each foreground connected region of an image by specifying its minimum containing rectangle (MCR). MCR is the rectangle with minimum dimensions that completely encloses a geometric pattern. In this paper, we present a two-step MCR detection algorithm and its parallelization method. The first step determines the boundary of each c...

Given a set S of n points in the plane, the disjoint two-rectangle covering problem is to find a pair of disjoint rectangles such that their union contains S and the area of the larger rectangle is minimized. In this paper we consider two variants of this optimization problem: (1) the rectangles are free to rotate but must remain parallel to each other, and (2) one rectangle is axis-parallel bu...