Approximation algorithms for the mobile piercing set problem with applications to clustering in ad-hoc networks

Mobile Networks and Applications

Volumn 9, Issue 2, 2004, Pages 151-161

  Huang, Hai ^a   Richa, Andréa W ^a   Segal, Michael ^b  

^a Arizona State University   (United States)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Distributed algorithms; Wireless networks

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; PROBLEM SOLVING; SET THEORY; VECTORS;

APPROXIMATION ALGORITHMS; LEAST CLUSTER CHANGE ALGORITHM; MOBILE PIERCING SET PROBLEM;

MOBILE TELECOMMUNICATION SYSTEMS;

EID: 1642405350     PISSN: 1383469X     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:MONE.0000013626.53247.1c     Document Type: Article

References (32)

1. P.K. Agarwal and C.M. Procopiuc, Exact and approximation algorithms for clustering, in: Proc. of 9th ACM-SIAM Sympos. on Discrete Algorithms (1998) pp. 658-667.
2. P.K. Agarwal and M. Sharir, Efficient algorithms for geometric optimization, ACM Comput. Surv. 30 (1998) 412-458.
3. S. Basagni, Distributed and mobility-adaptive clustering for multimedia support in multi-hop wireless networks, in: Proc. of IEEE Vehicular Tech. Conf. (1999) pp. 19-22.
4. S. Basagni, Distributed clustering for ad-hoc networks, in: Proc. of 1999 Int. Sympos. on Parallel Architectures (1999) pp. 310-315.
5. J. Basch, L.J. Guibas and J. Hershberger, Data structures for mobile data, in: Proc. of 8th ACM-SIAM Sympos. on Discrete Algorithms (1997) pp. 747-756.
6. S. Bepamyatnikh, B. Bhattacharya, D. Kirkpatrick and M. Segal, Mobile facility location, in: Proc. of ACM Int. Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (2000) pp. 46-53.
7. C.-C. Chiang, H.-K. Wu, W. Liu and M. Gerla, Routing in clustered multihop, mobile wireless networks with fading channel, in: Proc. of IEEE Singapore Int. Conf. on Networks (1997) pp. 197-211.
8. J.H. Conway and N.J.A. Sloane, Sphere Packings, Lattices, and Groups (Springer, 1999).
9. Z. Drezner, The p-center problem: heuristic and optimal algorithms, J. Oper. Res. Soc. 35 (1984) 741-748.
10. A. Efrat, M.J. Katz, F. Nielsen and M. Sharir, Dynamic data structures for fat objects and their applications, in: Proc. of Workshop on Algorithms and Data Structures (1997) pp. 297-306.
11. T. Feder and D.H. Greene, Optimal algorithms for approximate clustering, in: Proc. of 20th Annu. ACM Sympos. on Theory of Computing (1988) pp. 434-444.
12. R.J. Fowler, M.S. Paterson and S.L. Tanimoto, Optimal packing and covering in the plane are NP-complete, Inform. Process. Lett. 12(3) (1981) 133-137.
13. G.N. Frederickson and D.B. Johnson, Generalized selection and ranking: sorted matrices, SIAM J. Comput. 13 (1984) 14-30.
14. J. Gao, L.J. Guibas, J. Hershburger, L. Zhang and A. Zhu, Discrete mobile centers, in: Proc. of 17th ACM Sympos. on Computational Geometry (2001) pp. 188-196.
15. M. Gerla and J.T.C. Tsai, Multicluster mobile multimedia radio networks, ACM-Baltzer J. Wireless Networks 1(3) (1995) 255-256.
16. M. Golumbic, Algorithmic Graph Theory (Academic Press, New York, 1980).
17. T. Gonzalez, Covering a set of points in multidimensional space, Inform. Process. Lett. 40 (1991) 181-188.
18. S. Har-Peled, Clustering motion, in: Proc. of 42nd Annu. IEEE Sympos. on Foundations of Computer Science (2001) pp. 84-93.
19. D.S. Hochbaum and W. Maas, Approximation schemes for covering and packing problems in image processing and vlsi, J. of the ACM 32 (1985) 130-136.
20. D.S. Hochbaum and D. Shmoys, A best possible heuristic for the k-center problem, Math. Oper. Res. 10 (1985) 180-184.
21. D.S. Hochbaum and D. Shmoys, A unified approach to approximation algorithms for bottleneck problems, J. of the ACM 33 (1986) 533-550.
22. H. Huang, A.W. Richa and M. Segal, Approximation algorithms for the mobile piercing set problem with applications to clustering, Technical Report TR-01-007, Department of Computer Science and Engineering, Arizona State University, Tempe, AZ (2001).
23. R.Z. Hwang, R.C. Chang and R.C.T. Lee, The generalized searching over separators strategy to solve some NP-hard problems in subexponential time, Algorithmica 9 (1993) 398-423.
24. R.Z. Hwang, R.C.T. Lee and R.C. Chang, The slab dividing approach to solve the Euclidean p-center problem, Algorithmica 9 (1993) 1-22.
25. M.J. Katz, F. Nielsen and M. Segal, Maintenance of a piercing set for intervals with applications, in: Proc. of 11th Int. Symp. on Algorithms and Computation (2000) pp. 552-563.
26. M.T. Ko, R.C.T. Lee and J.S. Chang, An optimal approximation algorithm for the rectilinear m-center problem, Algorithmica 5 (1990) 341-352.
27. C.R. Lin and M. Gerla, Adaptive clustering for mobile wireless networks, IEEE J. Selected Areas Commun. 15(7) (1997) 1265-1275.
28. A.B. McDonald and T. Znati, A mobility-based framework for adaptive clustering in wireless ad-hoc networks, IEEE J. Selected Areas Commun. 17(8) (1999).
29. N. Megiddo and K.J. Supowit, On the complexity of some common geometric location problems, SIAM J. Comput. 13(1) (1984) 182-196.
30. F. Nielsen, Fast stabbing of boxes in high dimensions, in: Proc. of 8th Canada Conf. in Computational Geometry (1996) pp. 87-92.
31. R. Ramanathan and M. Steenstrup, Hierarchically-organized, multihop mobile wireless for quality-of-service support, Mobile Networks and Applications 3 (1998) 101-119.
32. M. Sharir and E. Welzl, Rectilinear and polygonal p-piercing and p-center problems, in: Proc. of 12th Annu. ACM Sympos. on Computational Geometry (1996) pp. 122-132.