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- A. Frieze
- Mathematics, Computer ScienceSODA '06
- 22 January 2006
Some of the major results in random graphs and some of the more challenging open problems are reviewed, including those related to the WWW.
Min-Wise Independent Permutations
- A. Broder, M. Charikar, A. Frieze, M. Mitzenmacher
- Mathematics, Computer ScienceJ. Comput. Syst. Sci.
- 1 June 2000
This research was motivated by the fact that such a family of permutations is essential to the algorithm used in practice by the AltaVista web index software to detect and filter near-duplicate documents.
Quick Approximation to Matrices and Applications
The matrix approximation is generalized to multi-dimensional arrays and from that derive approximation algorithms for all dense Max-SNP problems and the Regularity Lemma is derived.
Improved Approximation Algorithms for MAX k-CUT and MAX BISECTION
Polynomial-time approximation algorithms with non-trivial performance guarantees are presented for the problems of (a) partitioning the vertices of a weighted graph into k blocks so as to maximise…
Fast Monte-Carlo algorithms for finding low-rank approximations
- A. Frieze, R. Kannan, S. Vempala
- Computer ScienceProceedings 39th Annual Symposium on Foundations…
- 8 November 1998
This paper develops an algorithm which is qualitatively faster provided the entries of the matrix are sampled according to a natural probability distribution and the algorithm takes time polynomial in k, 1//spl epsiv/, log(1//spl delta/) only, independent of m, n.
Introduction to Random Graphs
All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.
A random polynomial-time algorithm for approximating the volume of convex bodies
The proof of correctness of the algorithm relies on recent theory of rapidly mixing Markov chains and isoperimetric inequalities to show that a certain random walk can be used to sample nearly uniformly from within K within Euclidean space.
Analysis of Two Simple Heuristics on a Random Instance of k-SAT
We consider the performance of two algorithms, GUC and SC studied by M. T. Chao and J. Franco SIAM J. Comput.15(1986), 1106?1118;Inform. Sci.51(1990), 289?314 and V. Chvatal and B. Reed…
On the worst-case performance of some algorithms for the asymmetric traveling salesman problem
This work considers the asymmetric traveling salesman problem for which the triangular inequality is satisfied, and constructs examples to show that the worst-case ratio of length of tour found to minimum length tour is (n) for n city problems.
The regularity lemma and approximation schemes for dense problems
The central point here is that the Regularity Lemma provides an explanation of why these Max-SNP hard problems turn out to be easy in dense graphs.