An Optimal Algorithm for the Minimum Disc Cover Problem

Abstract The minimum disc cover can be used to construct a dominating set on the fly for energy-efficient communications in mobile ad hoc networks, but the approach used to compute the minimum disc cover proposed in previous studies is computationally relatively expensive. In this paper, we show that the disc cover problem is in fact a special case of the general α-hull problem. In spite of being a special case, the disc cover problem is not easier than the general α-hull problem. In addition to applying the existing α-hull algorithm to solve the disc cover problem, we present a simple, yet optimal divide-and-conquer algorithm that constructs the minimum disc cover for arbitrary cases, including those degenerate cases where the α-hull approach would fail.

[1]  Min-Te Sun,et al.  Computing optimal local cover set for broadcast in ad hoc networks , 2002, 2002 IEEE International Conference on Communications. Conference Proceedings. ICC 2002 (Cat. No.02CH37333).

[2]  Anish Arora,et al.  Reliable MAC layer multicast in IEEE 802.11 wireless networks , 2002, Proceedings International Conference on Parallel Processing.

[3]  Anish Arora,et al.  Reliable MAC Layer Multicast in IEEE 802.11 Wireless Networks , 2002, ICPP.

[4]  Nitin H. Vaidya,et al.  Location-aided routing (LAR) in mobile ad hoc networks , 1998, MobiCom '98.

[5]  Richard J. Lipton,et al.  On the Complexity of Computations under Varying Sets of Primitives , 1975, J. Comput. Syst. Sci..

[6]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[7]  Deborah Estrin,et al.  Directed diffusion: a scalable and robust communication paradigm for sensor networks , 2000, MobiCom '00.

[8]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[9]  Leonidas J. Guibas,et al.  Kinetic collision detection between two simple polygons , 2004, SODA '99.

[10]  Wei Peng,et al.  On the reduction of broadcast redundancy in mobile ad hoc networks , 2000, 2000 First Annual Workshop on Mobile and Ad Hoc Networking and Computing. MobiHOC (Cat. No.00EX444).

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12]  Wu-chi Feng,et al.  GPS-based message broadcast for adaptive inter-vehicle communications , 2000, Vehicular Technology Conference Fall 2000. IEEE VTS Fall VTC2000. 52nd Vehicular Technology Conference (Cat. No.00CH37152).

[13]  M. V. Kreveld.  Computational Geometry , 2000, Springer Berlin Heidelberg.

[14]  David G. Kirkpatrick,et al.  On the shape of a set of points in the plane , 1983, IEEE Trans. Inf. Theory.

[15]  Min-Te Sun,et al.  Location aided broadcast in wireless ad hoc network systems , 2002, 2002 IEEE Wireless Communications and Networking Conference Record. WCNC 2002 (Cat. No.02TH8609).

[16]  Yu-Chee Tseng,et al.  The Broadcast Storm Problem in a Mobile Ad Hoc Network , 1999, Wirel. Networks.