Open Access Open Badges Methodology article

Application of permanents of square matrices for DNA identification in multiple-fatality cases

Maiko Narahara1, Keiji Tamaki2 and Ryo Yamada1*

Author Affiliations

1 Unit of Statistical Genetics, Center for Genomic Medicine, Graduate School of Medicine, Kyoto University, 53 Shogoin Kawahara-cho, Sakyo-Ku, Kyoto, Japan

2 Department of Forensic Medicine and Molecular Pathology, Graduate School of Medicine, Kyoto University, Yoshida-Konoe-Cho, Sakyo-Ku, Kyoto, Japan

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BMC Genetics 2013, 14:72  doi:10.1186/1471-2156-14-72

Published: 21 August 2013



DNA profiling is essential for individual identification. In forensic medicine, the likelihood ratio (LR) is commonly used to identify individuals. The LR is calculated by comparing two hypotheses for the sample DNA: that the sample DNA is identical or related to a reference DNA, and that it is randomly sampled from a population. For multiple-fatality cases, however, identification should be considered as an assignment problem, and a particular sample and reference pair should therefore be compared with other possibilities conditional on the entire dataset.


We developed a new method to compute the probability via permanents of square matrices of nonnegative entries. As the exact permanent is known as a #P-complete problem, we applied the Huber–Law algorithm to approximate the permanents. We performed a computer simulation to evaluate the performance of our method via receiver operating characteristic curve analysis compared with LR under the assumption of a closed incident. Differences between the two methods were well demonstrated when references provided neither obligate alleles nor impossible alleles. The new method exhibited higher sensitivity (0.188 vs. 0.055) at a threshold value of 0.999, at which specificity was 1, and it exhibited higher area under a receiver operating characteristic curve (0.990 vs. 0.959, P = 9.6E-15).


Our method therefore offers a solution for a computationally intensive assignment problem and may be a viable alternative to LR-based identification for closed-incident multiple-fatality cases.

DNA polymorphism; DNA-based identification; Multiple-fatality cases; Permanent of square matrix; Assignment problem