By Thomas Kesselheim (auth.), Amotz Bar-Noy, Magnús M. Halldórsson (eds.)
This ebook constitutes the completely refereed post-conference complaints of the eighth overseas Workshop on Algorithms for Sensor structures, instant advert Hoc Networks, and self reliant cellular Entities, ALGOSENSORS 2012, held in Ljubljana, Slovenia, in September 2012. The eleven revised complete papers awarded including invited keynote talks and short bulletins have been conscientiously reviewed and chosen from 24 submissions. The papers are prepared in tracks: sensor networks - protecting subject matters reminiscent of barrier resilience, localization, connectivity with directional antennas, broadcast scheduling, and information aggregation; and advert hoc instant and cellular structures - overlaying subject matters corresponding to: SINR version; geometric routing; cognitive radio networks; video supply; and mapping polygons.
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42–53, 2013. c Springer-Verlag Berlin Heidelberg 2013 Approximating Barrier Resilience for Arrangements 43 region of some sensor si , the start and end of the intersection is considered a sensor entry and exit respectively. The subpath associated with the intersection is considered a sensor crossing, and P is said to cross si . Note that P may have multiple si crossings, and in general no sensors cover S or T so the number of entries, exits and crossings are equivalent. A is said to provide k-barrier coverage if k is the minimum over all S −T paths of the number of distinct sensors crossed.
Second, each antenna is coupled with two of the others; namely, with those whose orientation diﬀers from its own by π/2 and 3π/2, respectively. For example, in Figure 1(a), Wc is coupled with Wb and with Wd . Notice that each such couple covers a half plane. , Wc and Wb cover the appropriate half plane deﬁned by l(ρ c ), and Wc and Wd cover the appropriate half plane deﬁned by l(ρ d ). 2 α < π/2 As observed by Carmi et al. , if α < π/3, then it is not always possible to orient the antennas such that the resulting graph is connected.
Katz, and G. Morgenstern Our goal in this section is to replace the omni-directional antennas with directional antennas of angle π/2 and range r = O(1) and to orient them, such that the induced symmetric communication graph is (i) connected, and (ii) a c-spanner of UDG(P ), with respect to hop distance, √ where c is an appropriate constant. We show that this can be done for r = 14 2 and c = 9. The main idea underlying our construction is to apply Theorem 1 multiple times, each time to a cluster of points within a small region, and to use Theorem 2 to establish that the SCG induced by any two such clusters is connected (assuming unbounded range).