A pursuit-evasion problem on a grid

We consider a two-player (searcher & fugitive) pursuit-evasion game played on an n x m grid, n less than or equal to m. Both players move continously and simultaneously along the edges of the grid; the fugitive has unit maximum speed and the searcher has maximum speed v (a constant). If the searcher is on row i (column j), then only the edges and vertices on row i (column j) are visible to the searcher. The fugitive, on the other hand, has full knowledge. The searcher wins if she can locate the fugitive. R. Dawes (1992) investigated the problem of the minimum speed v(0) by which the searcher can force a win and he showed v(0) less than or equal to n + 1. In this paper we prove an upper bound on v(0) which is essentially 2n/3.