Local PTAS for dominating and connected dominating set in location aware unit disk graphs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5426 LNCS, Issue , 2009, Pages 227-240

  Wiese, Andreas ^a   Kranakis, Evangelos ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b CARLETON UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DISKS (STRUCTURAL COMPONENTS); GRAPH THEORY; TELECOMMUNICATION NETWORKS;

APPROXIMATION RATIOS; BEST APPROXIMATIONS; CONNECTED DOMINATING SETS; GEOGRAPHIC COORDINATES; GRAPH MODELS; LOCATION-AWARE; NUMBER OF HOPS; PROCESSING TIME; UNIT DISK GRAPHS;

APPROXIMATION ALGORITHMS;

EID: 60349086141     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-93980-1_18     Document Type: Conference Paper

References (19)

1. Alzoubi, K., Wan, P., Frieder, O.: Message-optimal connected dominating sets in mobile ad hoc networks. In: MobiHoc 2002: Proceedings of the 3rd ACM international symposium on Mobile Ad Hoc Networking & Computing, pp. 157-164. ACM Press, New York (2002)
2. Breu, H., Kirkpatrick, D.G.: Unit disk graph recognition is NP-hard. Computational Geometry. Theory and Applications 9(1-2), 3-24 (1998)
3. Cheng, X., Huang, X., Li, D., Wu, W., Du, D.-Z.: A polynomial-time approximation scheme for the minimum-connected dominating set in ad hoc wireless networks. Networks 42(4), 202-208 (2003)
4. Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Discrete Math. 86(1-3), 165-177 (1990)
5. Czyzowicz, J., Dobrev, S., Fevens, T., González-Aguilar, H., Kranakis, E., Opatrny, J., Urrutia, J.: Local algorithms for dominating and connected dominating sets of unit disk graphs with location aware nodes. In: Laber, E.S., Bornstein, C, Nogueira, L.T., Faria, L. (eds.) LATIN 2008. LNCS, vol. 4957, pp. 158-169. Springer, Heidelberg (2008)
6. Gfeller, B., Vicari, E.: A faster distributed approximation scheme for the connected dominating set problem for growth-bounded graphs. In: Kranakis, E., Opatrny, J. (eds.) ADHOC-NOW 2007. LNCS, vol. 4686, pp. 59-73. Springer, Heidelberg (2007)
7. Hunt III, H.B., Marathe, M.V., Radhakrishnan, V., Ravi, S.S., Rosenkrantz, D.J., Stearns, R.E.: NC-approximation schemes for NP- and PSPACE-hard problems for geometric graphs. J. Algorithms 26(2), 238-274 (1998)
8. Johnson, D.S.: Approximation algorithms for combinatorial problems. In: Proc. 5th Ann. ACM Symp. Theory Computing, NY, pp. 38-49.
9. ACM Press, New York (1973); Also in J. Comput. Syst. Sci. 9(3), 256-278 (1974)
10. Kuhn, F., Moscibroda, T., Nieberg, T., Wattenhofer, R.: Fast deterministic distributed maximal independent set computation on growth-bounded graphs. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 273-287. Springer, Heidelberg (2005)
11. Kuhn, F., Moscibroda, T., Wattenhofer, R.: Unit disk graph approximation. In: DIALM-POMC 2004: Proceedings of the 2004 joint workshop on Foundations of mobile computing, pp. 17-23. ACM Press, New York (2004)
12. Kuhn, F., Moscibroda, T., Wattenhofer, R.: On the locality of bounded growth. In: Proceedings of the twenty-fourth annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing, pp. 60-68 (2005)
13. Kuhn, F., Moscibroda, T., Wattenhofer, R.: The price of being near-sighted. In: SODA 2006: Proceedings of the seventeenth annual ACM-SIAM Symposium on Discrete Algorithms, pp. 980-989. ACM Press, New York (2006)
14. Kuhn, F., Nieberg, T., Moscibroda, T., Wattenhofer, R.: Local approximation schemes for ad hoc and sensor networks. In: DIALM-POMC 2005: Proceedings of the 2005 Joint Workshop on Foundations of Mobile Computing, pp. 97-103. ACM Press, New York (2005)
15. Linial, N.: Locality in distributed graph algorithms. SIAM J. Comput. 21(1), 193-201 (1992)
16. Marathe, M.V., Breu, H., Hunt III, H.B., Ravi, S.S., Rosenkrantz, D.J.: Simple heuristics for unit disk graphs. Networks 25(1), 59-68 (1995)
17. Nieberg, T., Hurink, J.L.: A PTAS for the minimum dominating set problem in unit disk graphs. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 296-306. Springer, Heidelberg (2006)
18. Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a subconstant error-probability PCP characterization of NP. In: Proceedings of the 29th Annual ACM Symposium on the Theory of Computing (STOC 1997), New York, May 1997, pp. 475-484. Association for Computing Machinery (1997)
19. Wiese, A., Kranakis, E.: Local ptas for dominating and connected dominating set in location aware unit disk graphs. Technical Report TR-07-17, Carleton University, School of Computer Science, Ottawa (December 2007)