Abstract
Mobile sensors are located on a barrier represented by a line segment. Each sensor has a single energy source that can be used for both moving and sensing. A sensor consumes energy in movement in proportion to distance traveled, and it expends energy per time unit for sensing in direct proportion to its radius raised to a constant exponent. We address the problem of energy efficient coverage. The input consists of the initial locations of the sensors and a coverage time requirement \(t\). A feasible solution consists of an assignment of destinations and coverage radii to all sensors such that the barrier is covered. We consider two variants of the problem that are distinguished by whether the radii are given as part of the input. In the fixed radii case, we are also given a radii vector \(\rho \), and the radii assignment \(r\) must satisfy \(r_i \in \{0,\rho _i\}\), for every \(i\), while in the variable radii case the radii assignment is unrestricted. We consider two objective functions. In the first the goal is to minimize the sum of the energy spent by all sensors and in the second the goal is to minimize the maximum energy used by any sensor.
We present FPTASs for the problem of minimizing the energy sum with variable radii and for the problem of minimizing the maximum energy with variable radii. We also show that the latter can be approximated within any additive constant \(\varepsilon >0\). We show that the problem of minimizing the energy sum with fixed radii cannot be approximated within a factor of \(O(n^c)\), for any constant \(c\), unless P\(=\)NP. The problem of minimizing the maximum energy with fixed radii is shown to be strongly NP-hard. Additional results are given for three special cases: (i) sensors are stationary, (ii) free movement, and (iii) uniform fixed radii.
D. Rawitz—Supported by the Israel Science Foundation (grant no. 497/14).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agnetis, A., Grande, E., Mirchandani, P.B., Pacifici, A.: Covering a line segment with variable radius discs. Computers & OR 36(5), 1423–1436 (2009)
Anastasi, G., Conti, M., Di Francesco, M., Passarella, A.: Energy conservation in wireless sensor networks: A survey. Ad Hoc Networks 7(3), 537–568 (2009)
Bar-Noy, A., Baumer, B.: Maximizing Network Lifetime on the Line with Adjustable Sensing Ranges. In: Erlebach, T., Nikoletseas, S., Orponen, P. (eds.) ALGOSENSORS 2011. LNCS, vol. 7111, pp. 28–41. Springer, Heidelberg (2012)
Bar-Noy, A., Baumer, B., Rawitz, D.: Changing of the Guards: Strip Cover with Duty Cycling. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 36–47. Springer, Heidelberg (2012)
Bar-Noy, A., Baumer, B., Rawitz, D.: Set it and forget it: Approximating the set once strip cover problem. Tech. Rep. 1204.1082, CoRR (2012)
Bar-Noy, A., Brown, T., Johnson, M.P., Liu, O.: Cheap or Flexible Sensor Coverage. In: Krishnamachari, B., Suri, S., Heinzelman, W., Mitra, U. (eds.) DCOSS 2009. LNCS, vol. 5516, pp. 245–258. Springer, Heidelberg (2009)
Bar-Noy, A., Rawitz, D., Terlecky, P.: Maximizing Barrier Coverage Lifetime with Mobile Sensors. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 97–108. Springer, Heidelberg (2013)
Bhattacharya, B.K., Burmester, M., Hu, Y., Kranakis, E., Shi, Q., Wiese, A.: Optimal movement of mobile sensors for barrier coverage of a planar region. Theor. Comput. Sci. 410(52), 5515–5528 (2009)
Buchsbaum, A.L., Efrat, A., Jain, S., Venkatasubramanian, S., Yi, K.: Restricted strip covering and the sensor cover problem. In: SODA, pp. 1056–1063 (2007)
Chen, D.Z., Gu, Y., Li, J., Wang, H.: Algorithms on Minimizing the Maximum Sensor Movement for Barrier Coverage of a Linear Domain. In: Fomin, F.V., Kaski, P. (eds.) SWAT 2012. LNCS, vol. 7357, pp. 177–188. Springer, Heidelberg (2012)
Czyzowicz, J., et al.: On Minimizing the Maximum Sensor Movement for Barrier Coverage of a Line Segment. In: Ruiz, P.M., Garcia-Luna-Aceves, J.J. (eds.) ADHOC-NOW 2009. LNCS, vol. 5793, pp. 194–212. Springer, Heidelberg (2009)
Czyzowicz, J., Kranakis, E., Krizanc, D., Lambadaris, I., Narayanan, L., Opatrny, J., Stacho, L., Urrutia, J., Yazdani, M.: On Minimizing the Sum of Sensor Movements for Barrier Coverage of a Line Segment. In: Nikolaidis, I., Wu, K. (eds.) ADHOC-NOW 2010. LNCS, vol. 6288, pp. 29–42. Springer, Heidelberg (2010)
Demaine, E.D., Hajiaghayi, M.T., Mahini, H., Sayedi-Roshkhar, A.S., Gharan, S.O., Zadimoghaddam, M.: Minimizing movement. ACM Transactions on Algorithms 5(3) (2009)
Dobrev, S., Durocher, S., Eftekhari, M., Georgiou, K., Kranakis, E., Krizanc, D., Narayanan, L., Opatrny, J., Shende, S., Urrutia, J.: Complexity of Barrier Coverage with Relocatable Sensors in the Plane. In: Spirakis, P.G., Serna, M. (eds.) CIAC 2013. LNCS, vol. 7878, pp. 170–182. Springer, Heidelberg (2013)
Fan, H., Li, M., Sun, X., Wan, P., Zhao, Y.: Barrier coverage by sensors with adjustable ranges. ACM Transactions on Sensor Networks 11(1) (2014)
Gibson, M., Varadarajan, K.: Decomposing coverings and the planar sensor cover problem. In: FOCS, pp. 159–168 (2009)
Lev-Tov, N., Peleg, D.: Polynomial time approximation schemes for base station coverage with minimum total radii. Computer Networks 47(4), 489–501 (2005)
Mehrandish, M., Narayanan, L., Opatrny, J.: Minimizing the number of sensors moved on line barriers. In: WCNC, pp. 653–658 (2011)
Phelan, B., Terlecky, P., Bar-Noy, A., Brown, T., Rawitz, D.: Should I stay or should I go? Maximizing lifetime with relays. In: 8th DCOSS, pp. 1–8 (2012)
Tan, X., Wu, G.: New Algorithms for Barrier Coverage with Mobile Sensors. In: Lee, D.-T., Chen, D.Z., Ying, S. (eds.) FAW 2010. LNCS, vol. 6213, pp. 327–338. Springer, Heidelberg (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Bar-Noy, A., Rawitz, D., Terlecky, P. (2015). “Green” Barrier Coverage with Mobile Sensors. In: Paschos, V., Widmayer, P. (eds) Algorithms and Complexity. CIAC 2015. Lecture Notes in Computer Science(), vol 9079. Springer, Cham. https://doi.org/10.1007/978-3-319-18173-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-18173-8_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18172-1
Online ISBN: 978-3-319-18173-8
eBook Packages: Computer ScienceComputer Science (R0)