On-Line Navigation in a Room

We consider the problem of navigating through an unknownenvironment in which the obstacles are disjoint oriented rectanglesenclosed in an <?Pub Fmt italic>n<?Pub Fmt /italic> x<?Pub Fmt italic>n<?Pub Fmt /italic> square room. The task of navigatingalgorithm is to reach the center of the room starting from one of thecorners. While there always exists a path of length<?Pub Fmt italic>n<?Pub Fmt /italic>, the best previously knownnavigating algorithm finds paths of length <inline-equation><f>n<inf>2^{0<fen lp="par"><rad><rcd>1nn</rcd></rad><rp post="par"></fen>}</inf></f><?Pub Caret></inline-equation>. We give an efficient deterministicalgorithm which finds a path of length<?Pub Fmt italic>O<?Pub Fmt /italic>(<?Pub Fmt italic>n<?Pub Fmt /italic>ln <?Pub Fmt italic>n<?Pub Fmt /italic>); this algorithm uses tactileinformation only. Moreover, we prove that any deterministic algorithmcan be forced to traverse a distance of&OHgr;(<?Pub Fmt italic>n<?Pub Fmt /italic> ln<?Pub Fmt italic>n<?Pub Fmt /italic>), even if it uses visualinformation.