An algorithm for maximising covered area. (English) Zbl 1152.90511
Summary: This paper presents an algorithm for positioning circles in a given region to maximise the covered area. Our algorithm has applications in wireless networks, such as positioning a given number of mobile stations in a given region, one goal of which is to cover the largest area possible. Although the evaluation of the function value, i.e., the total covered area, is difficult, we bypass this difficulty by calculating the gradient of the total covered area directly. As long as nodes continuously move in directions that guarantee increasing coverage, a configuration of node positions corresponding to a maximal covered area can eventually be identified.
References:
| [1] | DOI: 10.1145/1072989.1072992 · doi:10.1145/1072989.1072992 |
| [2] | DOI: 10.1109/18.782168 · Zbl 0959.94036 · doi:10.1109/18.782168 |
| [3] | DOI: 10.1088/0957-0233/10/11/307 · doi:10.1088/0957-0233/10/11/307 |
| [4] | DOI: 10.1109/TIT.2003.809572 · Zbl 1063.94099 · doi:10.1109/TIT.2003.809572 |
| [5] | DOI: 10.1090/S0025-5718-1973-0338937-6 · doi:10.1090/S0025-5718-1973-0338937-6 |
| [6] | Bulusu, N, Heidemann, J and Estrin, D. ”Adaptive beacon placement,”. 21st International Conference on Distributed Computing Systems (ICDCS). pp.489–498. Phoenix, AZ, USA |
| [7] | Convay JH, Sphere Packings, Lattices, and Groups (1998) |
| [8] | Finney J, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 319 pp 479– (1970) |
| [9] | DOI: 10.2307/2689076 · doi:10.2307/2689076 |
| [10] | DOI: 10.1016/S0012-365X(97)00050-2 · Zbl 0901.52017 · doi:10.1016/S0012-365X(97)00050-2 |
| [11] | DOI: 10.1109/18.641544 · Zbl 0904.94020 · doi:10.1109/18.641544 |
| [12] | DOI: 10.1109/18.641545 · Zbl 0904.94021 · doi:10.1109/18.641545 |
| [13] | DOI: 10.1109/TIT.2002.804056 · Zbl 1062.94017 · doi:10.1109/TIT.2002.804056 |
| [14] | Honig ML, IEEE Transactions on Automatic Control 39 pp 1957– (1993) |
| [15] | DOI: 10.1142/9789812384911 · doi:10.1142/9789812384911 |
| [16] | DOI: 10.1109/TWC.2006.04861 · doi:10.1109/TWC.2006.04861 |
| [17] | Huang C, Proceedings of 2nd ACM International Conference on Wireless Sensor Networks and Applications pp 115– (2003) · doi:10.1145/941350.941367 |
| [18] | DOI: 10.1063/1.1511510 · doi:10.1063/1.1511510 |
| [19] | Kershner R, AJM 61 pp 665– (1939) |
| [20] | DOI: 10.1137/0121062 · Zbl 0231.94026 · doi:10.1137/0121062 |
| [21] | DOI: 10.1145/1167935.1167937 · doi:10.1145/1167935.1167937 |
| [22] | DOI: 10.1016/S0378-4371(02)01798-3 · Zbl 1099.82507 · doi:10.1016/S0378-4371(02)01798-3 |
| [23] | DOI: 10.1109/TC.2003.1204831 · doi:10.1109/TC.2003.1204831 |
| [24] | DOI: 10.1016/S0032-5910(97)03207-5 · doi:10.1016/S0032-5910(97)03207-5 |
| [25] | Murty K, Linear Complementarity, Linear and Nonlinear Programming (1988) |
| [26] | Poduri S, IEEE International Conference on Robotics and Automation pp 165– (2004) |
| [27] | DOI: 10.1137/1017046 · Zbl 0307.52007 · doi:10.1137/1017046 |
| [28] | DOI: 10.1080/00268970210125313 · doi:10.1080/00268970210125313 |
| [29] | Szpiro GG, Kepler’s Conjuecture (2003) |
| [30] | Tian D, First ACM International Workshop on Wireless Sensor Networks and Applicaitons (WSNA) (2002) |
| [31] | Zong C, Sphere Packing (1999) |
| [32] | DOI: 10.1364/JOSAA.12.001772 · doi:10.1364/JOSAA.12.001772 |
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