Given a simple polygon in the plane with two distinguished vertices, s and g, is it possible for two guards to simultaneously walk along the two boundary chains from s to g in such a way that theyâ€¦ (More)

We consider the problem of a robot which has to find a path in an unknown simple polygon from one point <italic>s</italic> to another point <italic>t</italic>, based only on what it has seen so far.â€¦ (More)

We present a competitive strategy for walking into the kernel of an initially unknown star-shaped polygon. From an arbitrary start point, s, within the polygon, our strategy finds a path to theâ€¦ (More)

An important task of computational biology is to identify those parts of a polypeptide chain, which are involved in interactions with other proteins. For this purpose, we have developed the programâ€¦ (More)

A strategy for working with incomplete information is called competitive if it solves each problem instance at a cost not exceeding the cost of an optimal solution (with full information available),â€¦ (More)

We present a new class of curves which are self-approaching in the following sense. For any three consecutive points a, b, c on the curve the point b is closer to c than a to c. This is aâ€¦ (More)

We present an on-line strategy that enables a mobile robot with vision to explore an unknown simple polygon. We prove that the resulting tour is less than 26.5 times as long as the shortest watchmanâ€¦ (More)