- to the needs of the application. Alpha should be enough large to prevent
- undercoverage and so to reach the highest possible coverage ratio. Beta
- should be enough large to prevent overcoverage and so to activate a minimum
- number of sensors. The values of $\alpha_{i}^{j}$ can be identical for all
- coverage intervals $i$ of one sensor $j$ in order to express that the
- perimeter of each sensor should be uniformly covered, but $\alpha_{i}^{j}$
- values can be differentiated between sensors to force some regions to be
- better covered than others. The choice of $\beta \gg \alpha$ prevents the
- overcoverage, and so limit the activation of a large number of sensors, but
- as $\alpha$ is low, some areas may be poorly covered. This explains the
- results obtained for $Lifetime_{50}$ with $\beta \gg \alpha$: a large number
- of periods with low coverage ratio. With $\alpha \gg \beta$, we favor the
- coverage even if some areas may be overcovered, so high coverage ratio is
- reached, but a large number of sensors are activated to achieve this goal.
- Therefore network lifetime is reduced. The choice $\alpha=0.6$ and
- $\beta=0.4$ seems to achieve the best compromise between lifetime and
- coverage ratio.}}\\
+ to the needs of the application. Alpha should be large enough to prevent
+ undercoverage and thus to reach the highest possible coverage ratio. Beta
+ should be large enough to prevent overcoverage and thus to activate a
+ minimum number of sensors. The values of $\alpha_{i}^{j}$ can be identical
+ for all coverage intervals $i$ of one sensor $j$ in order to express that
+ the perimeter of each sensor should be uniformly covered, but
+ $\alpha_{i}^{j}$ values can be differentiated between sensors to force some
+ regions to be better covered than others. The choice of $\beta \gg \alpha$
+ prevents the overcoverage, and so limit the activation of a large number of
+ sensors, but as $\alpha$ is low, some areas may be poorly covered. This
+ explains the results obtained for $Lifetime_{50}$ with $\beta \gg \alpha$: a
+ large number of periods with low coverage ratio. With $\alpha \gg \beta$,
+ we favor the coverage even if some areas may be overcovered, so a high
+ coverage ratio is reached, but a large number of sensors are activated to
+ achieve this goal. Therefore the network lifetime is reduced. The choice
+ $\alpha=0.6$ and $\beta=0.4$ seems to achieve the best compromise between
+ lifetime and coverage ratio.}}\\
