Abstract
Consider a set of intervals S=I 1, I 2, ..., I n , where I i = (l i , r i ), l i , and r i are real numbers, and l i < r i . We study a restricted track assignment problem (RTAP): if an interval I a contains another interval I b then I a must be assigned to a higher track than I b , and the goal is to minimize the number of tracks used. The problem RTAP is shown to be NP-hard. An approximation algorithm that produces a solution within twice of the optimal is also presented and the bound is shown to be tight. The algorithm, uses a segment tree as the basic structure, runs in O(nlogn) time and requires linear space. The proposed approximation algorithm is employed to solve the problem of finding a maximum-weighted independent set in a circle graph, and related problems.
Supported in part by the National Science Foundation under Grants MIP-8921540 and CCR-8901815.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Apostolico, A., Atallah, M.J., and Hambrusch, S.E., “New Clique and Independent Set Algorithms for Circle Graphs,” to appear in Discrete Applied Mathematics.
Asano, T, Asano, T., and Imai, H., “Partitioning a Polygonal Region into Trapezoids,” Journal of the ACM, Vol. 33, No. 2, April 1986, pp. 290–312.
Buckingham, M., Circle Graphs, Ph. D. Thesis (Report No. NSO-21), Courant Institute of Mathematical Sciences, Computer Science Department, October 1980.
Danny Z. Chen, Private communication.
Cong, J., Routing Algorithms in Physical Design of VLSI Circuits, Ph. D. Thesis. University of Illinois at Urbana-Champaign, Department of Computer Science, August 1990.
Garey, M.R., Johnson, D.S, Miller, G.L., and Papadimitriou, C.H., “The Complexity of Coloring Circular Arcs and Chords,” SIAM Journal on Algebraic Discrete Methods, Vol. 1, No. 20, June 1980, pp. 216–227.
Gavril, F. “Algorithms for a Maximum Clique and a Maximum Independent Set of a Circle Graph,” Networks, Vol. 3, 1973, pp. 261–273.
Golumbic, M.C., Algorithmic Graph Theory and Perfect Graphs, Academic Press, 1980.
Gupta, U., Lee, D.T., Leung, J., “An Optimal Solution for the Channel Assignment Problem,” IEEE Transactions on Computers, November 1979, pp. 807–810.
LaPaugh, A. S., Algorithms for Integrated Circuit Layout: An Analytic Approach, Department of Electrical Engineering and Computer Science, M.I.T. 1980.
G. Manacher, personal communication.
Preparata, F. and Shamos, M. I., Computational Geometry: an Introduction, Springer-Verlag, 1986.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sarrafzadeh, M., Lee, D.T. (1992). Restricted track assignment with applications. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_97
Download citation
DOI: https://doi.org/10.1007/3-540-56279-6_97
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56279-5
Online ISBN: 978-3-540-47501-9
eBook Packages: Springer Book Archive