Abstract
In this paper, we consider parallelizability of some P-complete problems. First we propose a parameter which indicates parallelizability for a convex layers problem. We prove P-completeness of the problem and propose a cost optimal parallel algorithm, according to the parameter. Second we consider a lexicographically first maximal 3 sums problem. We prove P-completeness of the problem by reducing a lexicographically first maximal independent set problem, and propose two cost optimal parallel algorithms for related problems. The above results show that some P-complete problems have efficient cost optimal parallel algorithms.
Research supported in part by the Scientific Research Grant-in-Aid from Ministry of Education, Science, Sports and Culture of Japan (Scientific research of Priority Areas(B)10205218)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. Chazelle. On the convex layers of a planar set. IEEE Transactions on Information Theory, IT-31(4):509–517, 1985.
D. Z. Chen. Efficient geometric algorithms on the EREW PRAM. IEEE transactions on parallel and distributed systems, 6(1):41–47, 1995.
W. Chen. Parallel Algorithm and Data Structures for Geometric Problems. PhD thesis, Osaka University, 1993.
R. Cole. Parallel merge sort. SIAM Journal of Computing, 17(4):770–785, 1988.
A. Dessmark, A. Lingas, and A. Maheshwari. Multi-list ranking: complexity and applications. In 10th Annual Symposium on Theoretical Aspects of Computer Science (LNCS665), pages 306–316, 1993.
J. Erickson and R. Seidel. Better lower bounds on detecting affine and spherical degeneracies. In 34th Annual IEEE Symposium on Foundations of Computer Science (FOCS’ 93), pages 528–536, 1993.
A. Fujiwara, M. Inoue, and M. Toshimitsu. Practical parallelizability of some P-complete problems. Technical Report of IPSF, Vol. 99, No. 72 (AL-69-2), September 1999.
A. Gajentaan and M. H. Overmars. On a class of O(n 2) problems in computational geometry. Computational geometry, 5:165–185, 1995.
R. Greenlaw, H.J. Hoover, and W.L. Ruzzo. Limits to Parallel Computation: P-Completeness Theory. Oxford university press, 1995.
C. Kruskal. Searching, merging and sorting in parallel computation. IEEE Transactions. on Computers, C-32(10):942–946, 1983.
S. Miyano. The lexicographically first maximal subgraph problems: P-completeness and NC algorithms. Mathematical Systems Theory, 22:47–73, 1989.
J.S. Vitter and R.A. Simons. New classes for parallel complexity: A study of unification and other complete problems for P. IEEE Transactions of Computers, C-35(5):403–418, 1986.
A. C. Yao. A lower bound to finding convex hulls. Journal of the ACM, 28(4):780–787, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fujiwara, A., Inoue, M., Masuzawa, T. (2000). Parallelizability of some P-complete problems. In: Rolim, J. (eds) Parallel and Distributed Processing. IPDPS 2000. Lecture Notes in Computer Science, vol 1800. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45591-4_14
Download citation
DOI: https://doi.org/10.1007/3-540-45591-4_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67442-9
Online ISBN: 978-3-540-45591-2
eBook Packages: Springer Book Archive