Abstract
The point location problem is to determine the position of n distinct points on a line, up to translation and reflection by the fewest possible pairwise (adversarial) distance queries. In this paper we report on an experimental study of a number of deterministic point placement algorithms and an incremental randomized algorithm, with the goal of obtaining a greater insight into the behavior of these algorithms, particularly of the randomized one.
A. Mukhopadhyay—Research supported by an NSERC Discovery Grant.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Mukhopadhyay, A., Rao, S.V., Pardeshi, S., Gundlapalli, S.: Linear layouts of weakly triangulated graphs. In: Pal, S.P., Sadakane, K. (eds.) WALCOM 2014. LNCS, vol. 8344, pp. 322–336. Springer, Heidelberg (2014)
Young, G., Householder, A.S.: Discussion of a set of points in terms of their mutual distances. Psychometrika 3(1), 19–22 (1938)
Blumenthal, L.M.: Theory and applications of distance geometry, 2nd edn. Chelsea, New York (1970)
Crippen, G., Havel, T.: Distance Geometry and Molecular Conformation. John Wiley and Sons (1988)
Damaschke, P.: Point placement on the line by distance data. Discrete Applied Mathematics 127(1), 53–62 (2003)
Skiena, S.S., Smith, W.D., Lemke, P.: Reconstructing sets from interpoint distances (extended abstract). In: Proceedings of the Sixth Annual Symposium on Computational Geometry, SCG 1990, pp. 332–339. ACM, New York (1990)
Daurat, A., Gérard, Y., Nivat, M.: The chords’ problem. Theor. Comput. Sci. 282(2), 319–336 (2002)
Smith, H., Wilcox, K.: A restriction enzyme from hemophilus influenzae. i. purification and general properties. Journal of Molecular Biology 51, 379–391 (1970)
Redstone, J., Ruzzo, W.L.: Algorithms for a simple point placement problem. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds.) CIAC 2000. LNCS, vol. 1767, pp. 32–43. Springer, Heidelberg (2000)
Alam, M.S., Mukhopadhyay, A.: Three paths to point placement. In: Ganguly, S., Krishnamurti, R. (eds.) CALDAM 2015. LNCS, vol. 8959, pp. 33–44. Springer, Heidelberg (2015)
Chin, F.Y.L., Leung, H.C.M., Sung, W.K., Yiu, S.M.: The point placement problem on a line – improved bounds for pairwise distance queries. In: Giancarlo, R., Hannenhalli, S. (eds.) WABI 2007. LNCS (LNBI), vol. 4645, pp. 372–382. Springer, Heidelberg (2007)
Alam, M.S., Mukhopadhyay, A.: More on generalized jewels and the point placement problem. J. Graph Algorithms Appl. 18(1), 133–173 (2014)
Alam, M.S., Mukhopadhyay, A.: Improved upper and lower bounds for the point placement problem. CoRR abs/1210.3833 (2012)
Damaschke, P.: Randomized vs. deterministic distance query strategies for point location on the line. Discrete Applied Mathematics 154(3), 478–484 (2006)
Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, New York (1995)
Emiris, I.Z., Psarros, I.D.: Counting euclidean embeddings of rigid graphs. CoRR abs/1402.1484 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Mukhopadhyay, A., Sarker, P.K., Kannan, K.K.V. (2015). Randomized Versus Deterministic Point Placement Algorithms: An Experimental Study. In: Gervasi, O., et al. Computational Science and Its Applications -- ICCSA 2015. ICCSA 2015. Lecture Notes in Computer Science(), vol 9156. Springer, Cham. https://doi.org/10.1007/978-3-319-21407-8_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-21407-8_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21406-1
Online ISBN: 978-3-319-21407-8
eBook Packages: Computer ScienceComputer Science (R0)