Abstract. Most diagram editors and graph construction tools provide some form of automatic connector routing, typically providing orthogonal or poly-line connectors. Usually the editor provides an initial automatic route when the connector is created and then modifies this when the connector end-points are moved. None that we know of ensure that the route is of minimal length while avoiding other objects in the diagram. We study the problem of incrementally computing minimal length object-avoiding poly-line connector routings. Our algorithms are surprisingly fast and allow us to recalculate optimal connector routings fast enough to reroute connectors even during direct manipulation of an object’s position, thus giving instant feedback to the diagram author. 1

The cluster connecting problem inside a simple polygon is introduced in this paper. The problem is shown to be NP-complete. A log n-factor approximation algorithm is proposed. 1