Topic
Counting problem
About: Counting problem is a research topic. Over the lifetime, 1321 publications have been published within this topic receiving 36050 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: It is shown that the permanent function of (0, 1)-matrices is a complete problem for the class of counting problems associated with nondeterministic polynomial time computations.
3,373 citations
Book•
1 Jan 1983
TL;DR: In this article, problem complexity and method efficiency in optimisation are discussed in terms of problem complexity, method efficiency, and method complexity in the context of OO optimization, respectively.
Abstract: (1984). Problem Complexity and Method Efficiency in Optimization. Journal of the Operational Research Society: Vol. 35, No. 5, pp. 455-455.
2,869 citations
Book•
1 Jan 2010
TL;DR: Fixed-Parameter Tractability.
Abstract: Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- The W-Hierarchy.- The A- Hierarchy.- Kernelization and Linear Programming Techniques.- The Automata-Theoretic Approach.- Tree Width.- Planarity and Bounded Local Tree Width.- Homomorphisms and Embeddings.- Parameterized Counting Problems.- Bounded Fixed-Parameter Tractability.- Subexponential Fixed-Parameter Tractability.- Appendix, Background from Complexity Theory.- References.- Notation.- Index.
2,733 citations
TL;DR: For a large number of natural counting problems for which there was no previous indication of intractability, that they belong to the class of computationally eqivalent counting problems that are at least as difficult as the NP-complete problems.
Abstract: The class of $# P$-complete problems is a class of computationally eqivalent counting problems (defined by the author in a previous paper) that are at least as difficult as the $NP$-complete problems. Here we show, for a large number of natural counting problems for which there was no previous indication of intractability, that they belong to this class. The technique used is that of polynomial time reduction with oracles via translations that are of algebraic or arithmetic nature.
2,431 citations
TL;DR: The class of combinatorial problems involving the random generation from a uniform distribution is considered in this article, where it is shown that almost uniform generation and randomized approximate counting are inter-reducible, and hence, of similar complexity.
1,051 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 5 |
| 2024 | 4 |
| 2023 | 23 |
| 2022 | 36 |
| 2021 | 55 |