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Barrier coverage in thin strips

Presented by: 
Paul Neville Balister
Wednesday 13th July 2016 - 11:45 to 12:30
INI Seminar Room 1
Suppose sensors are deployed randomly in a long thin strip, and suppose each sensor can detect objects within a fixed distance. We say that the sensors achieve barrier coverage if there is no path across the strip that a small object can follow that avoids detection by the sensors. We give fairly precise results on the probability that barrier coverage is achieved as a function of the range of the sensors, the height and length of the strip, and the number of sensors deployed. In particular, we show that the most likely obstruction - a rectangular region crossing the strip which is devoid of sensors - does not in general dominate the probability of failure of barrier coverage.
Joint work with Bela Bollobas and Amites Sarkar.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons