where Sn is the symmetric group of permutations on {1, 2, . . . , n}. Unlike the determinant, computing the exact value of the permanent of a given matrix is known to be #P-hard. Thus, most research has focused on finding approximation algorithms for and proving upper and lower bounds for restricted classes of matrices. A sharp upper-bound on the permanent the case of 0− 1 matrices was proved b...

Many hard problems can be solved efficiently for problem instances that can be decomposed by tree decompositions of small width. In particular for problems beyond NP, such as #P-complete counting problems, tree decomposition-based methods are particularly attractive. However, finding an optimal tree decomposition is itself an NP-hard problem. Existing methods for finding tree decompositions of ...

In this paper ZnO nanorods and nanodots (with and without a SiO2 buffer layer) were grown on p-Si, forming p–n heterojunctions. The nanorod devices showed no visible electroluminescence (EL) emission but showed rectifying behavior. Covering around 60% of the length of the nanorods with PMMA produced an ideality factor of 3:91 0:11 together with a reverse saturation current of 6:53 4:2 10 8 A. U...

We consider the computational complexity of the Market equilibrium problem by exploring the structural properties of the Leontief exchange economy. We prove that, for economies guaranteed to have a market equilibrium, finding one with maximum social welfare or maximum individual welfare is NP-hard. In addition, we prove that counting the number of equilibrium prices is #P-hard.

We review Andr\'e Luiz Barbosa's paper"P != NP Proof,"in which the classes P and NP are generalized and claimed to be proven separate. We highlight inherent ambiguities in Barbosa's definitions, and show that attempts to resolve this ambiguity lead to flaws in the proof of his main result.

Voting and assignment are two of the most fundamental settings in social choice theory. For both settings, random serial dictatorship (RSD) is a well-known rule that satisfies anonymity, ex post efficiency, and strategyproofness. Recently, it was shown that computing the resulting probabilities is #P-complete both in the voting and assignment setting. In this paper, we present efficient paramet...