Searching a solid pseudo 3-sided orthoconvex grid
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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