# Phenotype space and kinship assignment for the Simpson index

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2008)

- Volume: 42, Issue: 2, page 323-333
- ISSN: 0988-3754

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topLitow, Bruce, and Konovalov, Dmitry. "Phenotype space and kinship assignment for the Simpson index." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 42.2 (2008): 323-333. <http://eudml.org/doc/245441>.

@article{Litow2008,

abstract = {We investigate the computational structure of the biological kinship assignment problem by abstracting away all biological details that are irrelevant to computation. The computational structure depends on phenotype space, which we formally define. We illustrate this approach by exhibiting an approximation algorithm for kinship assignment in the case of the Simpson index with a priori error bound and running time that is polynomial in the bit size of the population, but exponential in phenotype space size. This algorithm is based on a relaxed version of the assignment problem, where fractional assignments (over the reals) are permitted.},

author = {Litow, Bruce, Konovalov, Dmitry},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {population biology; kinship assignment complexity; Tarski algebra; phenotype space},

language = {eng},

number = {2},

pages = {323-333},

publisher = {EDP-Sciences},

title = {Phenotype space and kinship assignment for the Simpson index},

url = {http://eudml.org/doc/245441},

volume = {42},

year = {2008},

}

TY - JOUR

AU - Litow, Bruce

AU - Konovalov, Dmitry

TI - Phenotype space and kinship assignment for the Simpson index

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2008

PB - EDP-Sciences

VL - 42

IS - 2

SP - 323

EP - 333

AB - We investigate the computational structure of the biological kinship assignment problem by abstracting away all biological details that are irrelevant to computation. The computational structure depends on phenotype space, which we formally define. We illustrate this approach by exhibiting an approximation algorithm for kinship assignment in the case of the Simpson index with a priori error bound and running time that is polynomial in the bit size of the population, but exponential in phenotype space size. This algorithm is based on a relaxed version of the assignment problem, where fractional assignments (over the reals) are permitted.

LA - eng

KW - population biology; kinship assignment complexity; Tarski algebra; phenotype space

UR - http://eudml.org/doc/245441

ER -

## References

top- [1] A. Almudevar, A simulated annealing algorithm for maximum likelihood pedigree reconstruction. Theor. Popul. Biol. 63 (2003) 63–75. Zbl1104.62115
- [2] A. Almudevar and C. Field, Estimation of single-generation sibling relationships based on dna markers. J. Agr. Biol. Envir. St. 4 (1999) 136–165. MR1812079
- [3] S. Basu, R. Pollack and M-F. Roy, Algorithms in Real Algebraic Geometry. Springer (2005). Zbl1102.14041MR1998147
- [4] T.Y. Berger-Wolf, B. DasGupta, W. Chaovalitwongse and M. Ashley, Combinatorial reconstructions of sibling relationships. In 6th International Symposium on Computational Biology and Genome Informatics (CBGI), Salt Lake City, Utah (2005) 1252–1255.
- [5] G. Collins, Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Automata theory and formal languages. Springer (1975) 134–183. Zbl0318.02051MR403962
- [6] L. Csanky, Fast parallel matrix inversion algorithms. In 16th IEEE FOCS (1975) 11–12. Zbl0353.68063MR428785
- [7] H. Ebbinghaus, J. Flum and W. Thomas, Mathematical Logic. Springer (1984). Zbl0556.03001MR736838
- [8] K.F. Goodnight and D.C. Queller. Computer software for performing likelihood tests of pedigree relationship using genetic markers. Mol. Ecol. 8 (1999) 1231–1234.
- [9] D.Yu. Grigoriev, Complexity of deciding Tarski algebra. J. Symb. Comput. 5 (1988) 65–108. Zbl0689.03021MR949113
- [10] N. Jacobson, Basic Algebra, Vol. I. Freeman, 2nd edn. (1985). Zbl0557.16001MR780184
- [11] A.G. Jones and W.R. Arden, Methods of parentage analysis in natural populations. Mol. Ecol. 12 (2003) 2511–2523.
- [12] D.A. Konovalov, Accuracy of four heuristics for the full sibship reconstruction problem in the presence of genotype errors. In The Fourth Asia Pacific Bioinformatics Conference, 13-16 Feb, 2006, Taiwan (2006) 7-16.
- [13] D.A. Konovalov, C. Manning and M.T. Henshaw, Kingroup: a program for pedigree relationship reconstruction and kin group assignments using genetic markers. Mol. Ecol. Notes 4 (2004) 779–782.
- [14] D.A. Konovalov, N. Bajema and B. Litow, Modified simpson o(n3) algorithm for the full sibship reconstruction problem. Bioinformatics 21 (2005) 3912–3917.
- [15] D.A. Konovalov, B. Litow and N. Bajema, Partition-distance via the assignment problem. Bioinformatics 21 (2005) 2463–2468.
- [16] B. Mishra, Algorithmic Algebra. Springer (1993). Zbl0804.13009MR1239443
- [17] P.T. O’Reilly, C. Herbinger and J.M. Wright, Analysis of parentage determination in atlantic salmon (salmo salar) using microsatellites. Anim. Genet. 29 (1998) 363–370.
- [18] A. Tarski, Sur les ensembles définissables de nombres réels. Fundamenta Mathematicae 17 (1931) 210–239. Zbl57.0060.02JFM57.0060.02
- [19] A. Tarski, A decision method for elementary algebra and geometry. Technical report, Rand Corp. (1948). Zbl0035.00602MR28796
- [20] J.L. Wang, Sibship reconstruction from genetic data with typing errors. Genetics 166 (2004) 1963–1979.

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