# Searching a solid pseudo 3-sided orthoconvex grid

## Abstract

In this paper we examine the edge searching problem on pseudo 3-sided solid orthoconvex grids. We obtain a closed formula that expresses the minimum number of searchers required to search a pseudo 3-sided solid orthoconvex grid. From that formula and a rather straight forward algorithm we show that the problem is in P. We obtain a parallel version of that algorithm that places the problem in NC. For the case of sequential algorithms, we derive an optimal algorithm that solves the problem in O(*m*) time where *m* is the number of points necessary to describe the orthoconvex grid. Another important feature of our method is that it also suggests an optimal searching strategy that consists of O(*n*) steps, where *n* is the number of nodes of the grid.

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