Parallel algorithm to find minimum vertex guard set in a triangulated irregular network

Abstract

This paper presents a new serial algorithm for selecting a nearly minimum number of vertex-guards so that all parts of a geographical surface modeled by a TIN (Triangulated Irregular Networks) is covered. Our algorithm selects fewer guards than the best existing algorithms on the average. Based on this approach, a new coarse-grain parallel algorithm for this problem is proposed. It has been showed that the upper bound for total number of guards, selected by this algorithm, is where n is number of vertices in the TIN. Average case analysis and implementation results show that in real TINs even fewer than guards (proved upper bound of needed guards in worse-case) are selected by our serial and parallel algorithms. © 2008 Springer-Verlag Berlin Heidelberg.