Abstract
We present a fast derandomization scheme for the PROFIT/COST problem. Through the application of this scheme we show the time complexity O(log2 n log log n) for the Δ+1 vertex coloring problem using O ((m+n)/log log n) processors on the CREW PRAM. The power of this fast derandomization scheme also allows us to obtain fast and efficient parallel algorithms for the maximal independent set problem and the maximal matching problem.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
N. Alon, L. Babai, A. Itai. A fast and simple randomized parallel algorithm for the maximal independent set problem. J. of Algorithms 7, 567–583(1986).
B. Berger, J. Rompel. Simulating (logc n)-wise independence in NC. Proc. 1989 IEEE FOCS, 2–7.
B. Berger, J. Rompel, P. Shor. Efficient NC algorithms for set cover with applications to learning and geometry. Proc. 1989 IEEE FOCS, 54–59.
M. Goldberg, T. Spencer. Constructing a maximal independent set in parallel. SIAM J. Dis. Math., Vol 2, No. 3, 322–328(Aug. 1989).
Y. Han. A parallel algorithm for the PROFIT/COST problem. To appear in Proc. of 1991 Int. Conf. on Parallel Processing, (AUg. 1991).
Y. Han. A fast derandomization scheme and its applications. Tech. Report, TR No. 180–90, Computer Science Dept., University of Kentucky, Lexington, Kentucky.
Y. Han and Y. Igarashi. Derandomization by exploiting redundancy and mutual independence. Proc. SIGAL 1990, LNCS 450, 328–337.
A. Israeli, Y. Shiloach. An improved parallel algorithm for maximal matching. Information Processing Letters 22(1986), 57–60.
R. Karp, A. Wigderson. A fast parallel algorithm for the maximal independent set problem. JACM 32:4, Oct. 1985, 762–773.
M. Luby. A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput. 15:4, Nov. 1986, 1036–1053.
M. Luby. Removing randomness in parallel computation without a processor penalty. Proc. 1988 IEEE FOCS, 162–173.
M. Luby. Removing randomness in parallel computation without a processor penalty. TR-89-044, Int. Comp. Sci. Institute, Berkeley, California.
G. L. Miller and J. H. Reif. Parallel tree contraction and its application. Proc. 26th Symp. on Foundations of Computer Science, IEEE, 291–298(1985).
R. Motwani, J. Naor, M. Naor. The probabilistic method yields deterministic parallel algorithms. Proc. 1989 IEEE FOCS, 8–13.
G. Pantziou, P. Spirakis, C. Zaroliagis. Fast parallel approximations of the maximum weighted cut problem through Derandomization. FST&TCS 9: 1989, Bangalore, India, LNCS 405, 20–29.
P. Raghavan. Probabilistic construction of deterministic algorithms: approximating packing integer programs. JCSS 37:4, Oct. 1988, 130–143.
J. Spencer. Ten Lectures on the Probabilistic Method. SIAM, Philadelphia, 1987.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Han, Y. (1991). A fast derandomization scheme and its applications. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028260
Download citation
DOI: https://doi.org/10.1007/BFb0028260
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54343-5
Online ISBN: 978-3-540-47566-8
eBook Packages: Springer Book Archive