# Random Generation of Combinatorial Structures from a Uniform Distribution

@article{Jerrum1986RandomGO, title={Random Generation of Combinatorial Structures from a Uniform Distribution}, author={Mark Jerrum and Leslie G. Valiant and Vijay V. Vazirani}, journal={Theor. Comput. Sci.}, year={1986}, volume={43}, pages={169-188} }

## 977 Citations

### Random Generation and Approximate Counting of Combinatorial Structures

- Computer ScienceArXiv
- 2010

A limit of an heuristic for combinatorial optimization problems based on the random initialization of local search algorithms showing that derandomizing such heuristic can be, in some cases, #P-hard.

### Random Generation and Approximate Counting of Ambiguously Described Combinatorial Structures

- Computer ScienceSTACS
- 2000

A uniform random generation algorithm for finitely ambiguous context-free languages of the same time complexity of the best known algorithm for the unambiguous case is given.

### Randomised algorithms for counting and generating combinatorial structures

- Mathematics
- 1988

The thesis studies the computational complexity of two natural classes of combinatorial problems: counting the elements of a finite set of structures and generating them uniformly at random. For each…

### Approximate Counting, Uniform Generation and Rapidly Mixing Markov Chains

- MathematicsWG
- 1987

The general techniques of the paper are used to derive an almost uniform generation procedure for labelled graphs with a given degree sequence which is valid over a much wider range of degrees than previous methods: this in turn leads to randomised approximate counting algorithms for these graphs with very good asymptotic behaviour.

### Counting and random generation of strings in regular languages

- Computer ScienceSODA '95
- 1995

We study the problems of counting and random generation of strings of a fixed length in regular languages. The regular language is described by a non-deterministic finite automaton or regular…

### On the Circuit Complexity of Random Generation Problems for Regular and Context-Free Languages

- Computer ScienceSTACS
- 2001

It is proved that, for every language accepted in polynomial time by 1-NAuxPDA of polynomially bounded ambiguity, the problem is solvable by a logspace-uniform family of probabilistic boolean circuits of poynomial size and O(log2 n) depth.

### The distance approach to approximate combinatorial counting

- Mathematics, Computer Science
- 2000

This paper derives asymptotically sharp cardinality bounds in the case of the Hamming distance and shows that for small subsets a suitably defined “randomized” Hamming Distance allows one to get tighter estimates of the cardinality.

### Algorithms for Almost-uniform Generation with an Unbiased Binary Source

- Computer Science, MathematicsCOCOON
- 1998

A new algorithm is presented which is based on a circulant, symmetric, rapidly mixing Markov chain, and its rate of convergence is superior to the estimates obtainable by commonly used methods of bounding the mixing rate of Markov chains such as conductance, direct canonical paths, and couplings.

### On the Random Generation and Counting of Matchings in Dense Graphs

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1998

### Fast Uniform Generation of Regular Graphs

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1990

## References

SHOWING 1-10 OF 16 REFERENCES

### The complexity of approximate counting

- Computer Science, MathematicsSTOC
- 1983

The complexity of computing approximate solutions to problems in #P is classified in terms of the polynomial-time hierarchy (for short, P-hierarchy) in order to study a class of restricted, but very natural, probabilistic sampling methods motivated by the particular counting problems.

### The Complexity of Combinatorial Computations: An Introduction

- Computer Science, MathematicsGI Jahrestagung
- 1978

The search for mechanizable procedures or algorithms for solving problems has been an integral part of mathematics from the beginning, and such algorithms as Gaussian elimination for solving linear equations, Newton's iteration for algebraic equations, and Euclid's algorithm for greatest common divisors appear very efficient even now after centuries of further investigation.

### How to generate random integers with known factorization

- Mathematics, Computer ScienceSTOC
- 1983

A probabilistic algorithm that produces a random k-bit integer in factored form that is equally likely to appear, and under reasonable assumptions about the speed of primality testing, is a polynomial time process.

### Monte-Carlo algorithms for enumeration and reliability problems

- Mathematics24th Annual Symposium on Foundations of Computer Science (sfcs 1983)
- 1983

A simple but very general Monte-Carlo technique for the approximate solution of enumeration and reliability problems and several applications are given.

### On the Difference Between One and Many (Preliminary Version)

- Computer ScienceICALP
- 1977

It is shown, that in specific cases, the question, ‘Given a problem, is it more difficult to tell how many solutions the problem has than just deciding whether it has a solution?’ can be put into a mathematically meaningful form.

### The Complexity of Computing the Permanent

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1979

### A complexity theoretic approach to randomness

- Computer Science, MathematicsSTOC
- 1983

We study a time bounded variant of Kolmogorov complexity. This notion, together with universal hashing, can be used to show that problems solvable probabilistically in polynomial time are all within…

### NP is as easy as detecting unique solutions

- Mathematics, Computer ScienceSTOC '85
- 1985

It is shown that the problems of distinguishing between instances of SAT having zero or one solution, or finding solutions to instances of SOTA having unique solutions, are as hard as SAT itself.