## Monte Carlo Algorithms for Hard Counting Problems

*Monte-Carlo Algorithms for Enumeration and Reliability Problems*

Richard Karp, Michael Luby

**24th STOC**, 1983, pp. 56-64.

*Monte-Carlo Approximation Algorithms for Enumeration Problems*

Richard Karp, Michael Luby, Neal Madras

**J. of Algorithms**, Vol. 10, No. 3, Sept. 1989, pp. 429-448.

*Monte-Carlo Methods for Estimating System Reliability*

Michael Luby,

**Ph.D. thesis**, U.C. Berkeley, September 1983.

*Monte-Carlo Algorithms for the Planar Multiterminal Network
Reliability Problem*

Richard Karp, Michael Luby

**J. of Complexity**, 1, pp. 45-64, 1985.

*A Monte-Carlo Algorithm for Estimating the Permanent*
(189K)

Narindra Karmarkar, Richard Karp, Richard Lipton,
Laslo Lovasz, Michael Luby

**SIAM J. on Computing**, 1993, Vol. 22, No. 2, pp. 284-293.

*Polytopes, Permanents and Graphs with Large Factors*

Paul Dagum, Michael Luby, Milena Mihail, Umesh Vazirani

**29th FOCS**, 1988.

*Approximating the Permanent of Graphs with Large Factors*
(333K)

Paul Dagum, Michael Luby

**Theretical Computer Science**, Part A, Vol. 102, Nov. 1992, pp. 283-305.

*A Survey of Approximation Algorithms for the Permanent*

Michael Luby

Proceedings of the **Advanced International Workshop on Sequences:**

Combinatorics, Compression, Security and Transmission,
Springer-Verlag, 1988.

*Approximating the Number of Solutions to a GF[2] Formula*
(134K)

Marek Karpinski, Michael Luby

Preliminary version in **2nd Annual Symposium on Discrete Algorithms**,
1991.

Final version in **Journal of Algorithms**, Vol. 14, No. 2,
March 1993, pp. 280-287.

*Markov Chain Algorithms for Planar Lattice Structures*

Michael Luby, Dana Randall, Alistair Sinclair

**36th FOCS**, 1995, pp. 150-159.

*Approximately Counting Up To Four*
(177K)

Michael Luby, Eric Vigoda

To appear in 29th STOC, May 1997.