A fast computer algorithm for finding the permanent of adjacency matrices

Cash, Gordon G.

doi:10.1007/bf01164652

Cited by 14 publications

(19 citation statements)

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“…Cash reported a computer algorithm that finds these combinations 1. This algorithm first examines all A i 1 until it finds an A i 1 = 1.…”

Section: Computer Algorithmmentioning

confidence: 99%

“…Cash reported an implementation of the algorithm in the C programming language 1. The code is standard C. The implementation deliberately avoids programming features, such as pointers, that are peculiar to C to facilitate translation into other high‐level languages.…”

Section: Computer Algorithmmentioning

confidence: 99%

“…To calculate per(), therefore, it is not necessary even to add the terms but only to count the nonzero terms. These facts are the key to the computer algorithm presented by Cash 1.…”

Section: Introductionmentioning

confidence: 96%

“…The permanent of a matrix is conceptually similar to the determinant 1. The determinant of an N × N matrix is the sum of all possible products of elements Σ (−1) z A i 1 A j 2 A k 3 … A xN such that i , j , k … are all different and z is odd for half of the terms and even for the other half 2, 3.…”

Section: Introductionmentioning

confidence: 99%

“…Cash determined that per() = K 2 for some hydrocarbons for which || ≠ K 2 , viz. biphenylene, tetraphenylene, pentalene 1, and toroidal polyhex fullerenes 4. However, this equality fails for many nonalternant molecules such as curved polycyclic aromatic hydrocarbons and spherical fullerenes 2, 3.…”

Section: Introductionmentioning

confidence: 99%

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Computing the Kekulé structure count for alternant hydrocarbons

Torrens¹

2002

Int J of Quantum Chemistry

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ABSTRACT:A fast computer algorithm brings computation of the permanents of sparse matrices, specifically, molecular adjacency matrices. Examples and results are presented, along with a discussion of the relationship of the permanent to the Kekulé structure count. A simple method is presented for determining the Kekulé structure count of alternant hydrocarbons. For these hydrocarbons, the square of the Kekulé structure count is equal to the permanent of the adjacency matrix. In addition, for alternant structures the adjacency matrix for N atoms can be written in such a way that only an N/2 ϫ N/2 matrix need be evaluated. The Kekulé structure count correlates with topological indices. The inclusion of the number of cycles improves the fit. When comparing with previous results, the variance decreases 74%. The calculated standard heat of formation correlates with the logarithm of the Kekulé structure count. This heat increments 349 kJ/mol each time the Kekulé structure count increases by one order of magnitude.

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“…Cash reported a computer algorithm that finds these combinations 1. This algorithm first examines all A i 1 until it finds an A i 1 = 1.…”

Section: Computer Algorithmmentioning

confidence: 99%

Section: Computer Algorithmmentioning

confidence: 99%

“…To calculate per(), therefore, it is not necessary even to add the terms but only to count the nonzero terms. These facts are the key to the computer algorithm presented by Cash 1.…”

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%