Topic
#P-complete
About: #P-complete is a research topic. Over the lifetime, 59 publications have been published within this topic receiving 800 citations.
Papers published on a yearly basis
Papers
TL;DR: By using the model of linear-optical quantum computing and a universality theorem owing to Knill, Laflamme and Milburn, one can give a different and arguably more intuitive proof of Valiant's theorem that computing the permanent of an n×n matrix is #P-hard.
Abstract: One of the crown jewels of complexity theory is Valiant9s theorem that computing the permanent of an n × n matrix is # P -hard. Here we show that, by using the model of linear-optical quantum computing —and in particular, a universality theorem owing to Knill, Laflamme and Milburn—one can give a different and arguably more intuitive proof of this theorem.
70 citations
TL;DR: This paper presents the first formal proof that the problem of counting the number of maximal frequent itemsets in a database of transactions, given an arbitrary support threshold, is #P-complete, thereby providing theoretical evidence that theproblem of mining maximalrequent itemsets is NP-hard.
42 citations
7 Jun 1993
TL;DR: It is proved that a polynomially bounded function can not be not=P-complete under 'reasonable' complexity assumptions.
Abstract: Valiant (1979) proved that computing the permanent of a 01-matrix is not=P-complete. The authors present another proof for the same result. The proof uses 'black box' methodology, which facilitates its presentation. They also prove that deciding whether the permanent is divisible by a small prime is not=P-hard. They conclude by proving that a polynomially bounded function can not be not=P-complete under 'reasonable' complexity assumptions. >
30 citations
11 Oct 1989
29 citations
TL;DR: It is proved that counting the number of phylogenetic trees inferred by a (binary) phylogenetic network is \#P-complete.
Abstract: Answering a problem posed by Nakhleh, we prove that counting the number of phylogenetic trees inferred by a (binary) phylogenetic network is \#P-complete. An immediate consequence of this result is that counting the number of phylogenetic trees commonly inferred by two (binary) phylogenetic networks is also \#P-complete.
25 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 2 |
| 2018 | 1 |
| 2017 | 1 |
| 2016 | 1 |
| 2015 | 1 |
| 2013 | 6 |