Abstract
Given a graph with positive integer edge weights one may ask whether there exists an edge cut whose weight is bigger than a given number. This problem is NP-Complete. We present here an approximation scheme in NC which provides tight upper bounds to the proportion of edge cuts whose size is bigger than a given number. Our technique is based on the method to convert randomized algorithms into deterinistic ones, introduced by [Luby, 85 and 88]. The basic idea of those methods is to replace an exponentially large sample space by one of polynomial size. Our work examines the statistical distance of random variables of the small sample space to corresponding variables of the exponentially large space, which is the space of all edge cuts taken equiprobably.
This research was supported in part by the ESPRIT Basic Research Action No. 3075 ALCOM, and in part by the Ministry of Education of Greece.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
7 References
[Alon, Babai, Itai, 86] “A fast and simple Randomized parallel Algorithm for the Maximal Independent Set Problem”, J. of Algorithms, 7, 567–583, 1986.
[Bernstein, 45] “Theory of Probability”, (3rd ed.), GTTI, Moscow, 1945.
[Cole, Vishkin, 86] “Deterministic Coin Tossing with Applications to Optimal Parallel List Ranking”, Inform. and Control, Vol.70, N.1, pp. 32–53, July 1986.
[Garey, Johnsn, 79] “Computers and Intractability — A Guide to the Theory of NP-Completeness”, Ed. Freeman and Co, San Francisco, 2nd printing, 1979.
[Garey, Johnson, Stockmeyer, 76] “Some Simplified NP-Complete Graph Problems”, Theor. Comp. Science 1, 237–267, 1976.
[Goldberg, Spencer, 87] “A new Parallel Algorithm for the Maximal Independent Set Problem”, Proc. 28th IEEE FOCS, pp. 161–165, 1987. Also in SIAM J. on Computing, April 1989, pp. 419–427.
[Joffe, 74] “On a set of almost deterministic k-independent random variables”, Ann. Probability, 2 (1974), 161–162.
[Karp, 72] “Reducibility among Combinatorial Problems”, in “Complexity of Computer Computations”, Plenum Press, NY, 1972.
[Karp, Wigderson, 84] “A Fast Parallel Algorithm for the Maximal Independent Set Problem”, Proc. 16th ACM STOC, pp. 266–272, 1984.
[Lancaster, 65] “Pairwise Statistical Independence”, Ann. Math. Stat. 36, (1965), 1313–1317.
[Luby, 85] “A simple Parallel Algorithm for the Maximal Independent Set Problem”, Proc. 17th ACM STOC, pp. 1–10, Providence RI, 1985.
[Luby, 88] “Removing Randomness in Parallel Computation without a Processor Penalty”, Proc. 29th IEEE FOCS, pp. 162–174, 1988.
[Pantziou, Spirakis, Zaroliagis, 89] “Fast Parallel Approximations of the Maximum Weighted Cut Problem through Derandomization”, Techn. Rep. TR-83.04.89, Computer Technology Institute, Patras, 1989.
[Papoulis, 86] “Probability, Random Variables and Stohastic Processes”, 2nd edit., McCraw-Hill, 1986.
[Valiant, 77] “The Complexity of enumeration and reliability problems”, Report No. CSR-15-77, CS Dept, Univ. of Edinburg, Scottland.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pantziou, G., Spirakis, P., Zaroliagis, C. (1989). Fast parallel approximations of the maximum weighted cut problem through derandomization. In: Veni Madhavan, C.E. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1989. Lecture Notes in Computer Science, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52048-1_29
Download citation
DOI: https://doi.org/10.1007/3-540-52048-1_29
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52048-1
Online ISBN: 978-3-540-46872-1
eBook Packages: Springer Book Archive