| Summary: | Consider a two-dimensional rectangular region guarded by a set of sensors, which may be smart networked surveillance cameras or simpler sensor devices. In order to evaluate the level of security provided by these sensors, it is useful to find and evaluate the path with the lowest level of exposure to the sensors. Then, if desired, additional sensors can be placed at strategic locations to increase the level of security provided. General forms of these two problems are presented in this paper. Next, the minimum exposure path is found by first using the sensing limits of the sensors to compute an approximate “feasible area” of interest, and then using a grid within this feasible area to search for the minimum exposure path in a systematic manner. Two algorithms are presented for the minimum exposure path problem, and an additional subsequently executed algorithm is proposed for sensor deployment. The proposed algorithms are shown to require significantly lower computational complexity than previous methods, with the fastest proposed algorithm requiring <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mrow><mn>2.5</mn></mrow></msup><mo>)</mo></mrow></semantics></math></inline-formula> time, as compared to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo>(</mo><mi>m</mi><msup><mi>n</mi><mn>3</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> for a traditional grid-based search method, where <i>n</i> is the number of sensors, <i>m</i> is the number of obstacles, and certain assumptions are made on the parameter values.
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