An extreme routing problem connected with observing the areas where some potentially dangerous occurrences may appear is considered; this circumstance imposes the requirement for the fastest revealing of the considered occurrences with the aim to liquidate the consequences (forest fire, radiation, chemical contamination). All these circumstances require the qualitative routing of the "observer". This article is devoted to the development of dynamic programming ideas for the considered applied problem. The theory of the article takes shape in optimal (accurate to the correspondent discretization) algorithm for a parallel computer and the respective experiment is conducted.