The amount of time needed by a graphics device in drawing a set of vectors comprising a single-frame picture depends on the order and directions in which the vectors are drawn and can generally be reduced by reordering and redirecting them. The reduction of the drawing time is achieved more effectively by the manipulation of line groups, each line group consisting of a set of line segments all of which are drawn by uninterrupted vector drawing operations without any move operation. This thesis presents a technique for reducing the drawing time by the manipulation of line groups. An algorithm for this along with test results is presented. The algorithm is implemented in PASCAL on a VAX-11/780 running under UNIX(BSD 4.2) operating system.