Abstract
Network localization is important for networks with no prefixed positions of network nodes such as sensor networks. We are given a subset of the set of \(\binom{n}{2}\) pairwise distances among n sensors in some Euclidean space. We want to determine the positions of each sensors from the (partial) distance information. The input can be seen as an edge weighted graph. In this paper, we present some efficient algorithms that solve this problem using the structures of input graphs, which we call the cores of them. For instance, we present a polynomial-time algorithm solving the network localization problem for graphs with connected dominating sets of bounded size. This algorithm allows us to have an FPT algorithm for some restricted instances such as graphs with connected vertex covers of bounded size.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arkin, E.M., Halldórsson, M.M., Hassin, R.: Approximating the tree and tour covers of a graph. Inform. Process. Lett. 47, 275–282 (1993)
Aspnes, J., Eren, T., Goldenberg, D.K., Morse, A.S., Whiteley, W., Yang, Y.R., Anderson, B.D.O., Belhumeur, P.N.: A theory of network localization. IEEE Trans. Mobile Comput. 5, 1663–1678 (2006)
Aspvall, B., Plass, M.F., Tarjan, R.E.: A linear-time algorithm for testing the truth of certain quantified boolean formulas. Inform. Process. Lett. 8, 121–123 (1979)
Bhatt, S.N., Cosmadakis, S.S.: The complexity of minimizing wire lengths in VLSI layouts. Inform. Process. Lett. 25, 263–267 (1987)
Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Discrete Math. 86, 165–177 (1990)
Corke, P., Hrabar, S., Peterson, R., Rus, D., Saripalli, S., Sukhatme, G.: Autonomous deployment and repair of a sensor network using an unmanned aerial vehicle. In: IEEE International Conference on Robotics and Automation (2004)
Corneil, D.G., Lerchs, H., Burlingham, L.S.: Complement reducible graphs. Discrete Appl. Math. 3, 163–174 (1981)
Courcelle, B., Olariu, S.: Upper bounds to the clique width of graphs. Discrete Appl. Math. 101, 77–114 (2000)
Dargie, W., Poellabauer, C.: Fundamentals of Wireless Sensor Networks: Theory and Practice. Wiley (2010)
Downey, R.G., Estivill-Castro, V., Fellows, M.R., Prieto, E., Rosamond, F.A.: Cutting up is hard to do: the parameterized complexity of k-cut and related problems. Electron. Notes Theor. Comput. Sci. 78, 209–222 (2003)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1998)
Feder, T., Motwani, R.: On the graph turnpike problem. Inform. Process. Lett. 109, 774–776 (2009)
Fulkerson, D.R., Gross, O.A.: Incidence matrices and interval graphs. Pacific J. Math. 15, 835–855 (1965)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman (1979)
Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs, 2nd edn. Annals of Discrete Mathematics, vol. 57. North Holland (2004)
Graver, J., Servatius, B., Servatius, H.: Combinatorial Rigidity. AMS (1993)
Guo, J., Niedermeier, R., Wernicke, S.: Parameterized complexity of vertex cover variants. Theory Comput. Syst. 41, 501–520 (2007)
Harary, F.: Graph Theory. Addison-Wesley, Reading (1969)
Hliněný, P., Oum, S., Seese, D., Gottlob, G.: Width parameters beyond tree-width and their applications. Comput. J. 51, 326–362 (2008)
Jackson, B., Jordán, T.: Connected rigidity matroids and unique realizations of graphs. J. Combin. Theory Ser. B 94, 1–29 (2005)
Laman, G.: On graphs and rigidity of plane skeletal structures. J. Eng. Math. 4, 331–340 (2002)
Laurent, M.: Polynomial instances of the positive semidefinite and euclidean distance matrix completion problems. SIAM J. Matrix Anal. Appl. 22, 874–894 (2000)
Rose, D.J., Tarjan, R.E., Lueker, G.S.: Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput. 5, 266–283 (1976)
Saxe, J.B.: Embeddability of weighted graphs in k-space is strongly NP-hard. In: 17th Allerton Conf. Commun. Control Comput., pp. 480–489 (1979)
Saxe, J.B.: Two papers on graph embedding problems. Technical Report CMU-CS-80-102, Department of Computer Science, Carnegie-Mellon University (1980)
Sohraby, K., Minoli, D., Znati, T.: Wireless Sensor Networks: Technology, Protocols, and Applications. Wiley-Interscience (2007)
Tarjan, R.E., Yannakakis, M.: Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM J. Comput. 13, 566–579 (1984)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, M., Otachi, Y., Tokuyama, T. (2012). Efficient Algorithms for Network Localization Using Cores of Underlying Graphs. In: Erlebach, T., Nikoletseas, S., Orponen, P. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2011. Lecture Notes in Computer Science, vol 7111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28209-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-28209-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28208-9
Online ISBN: 978-3-642-28209-6
eBook Packages: Computer ScienceComputer Science (R0)