dorsal/arxiv
View SchemaShorelines of islands of tractability: Algorithms for parsimony and minimum perfect phylogeny haplotyping problems
| Authors | Leo van Iersel, Judith Keijsper, Steven Kelk, Leen Stougie |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0605024 |
| URL | https://arxiv.org/abs/q-bio/0605024 |
Abstract
The problem Parsimony Haplotyping (PH) asks for the smallest set of haplotypes which can explain a given set of genotypes, and the problem Minimum Perfect Phylogeny Haplotyping (MPPH) asks for the smallest such set which also allows the haplotypes to be embedded in a perfect phylogeny, an evolutionary tree with biologically-motivated restrictions. For PH, we extend recent work by further mapping the interface between ``easy'' and ``hard'' instances, within the framework of (k,l)-bounded instances where the number of 2's per column and row of the input matrix is restricted. By exploring, in the same way, the tractability frontier of MPPH we provide the first concrete, positive results for this problem, and the algorithms underpinning these results offer new insights about how MPPH might be further tackled in the future. In addition, we construct for both PH and MPPH polynomial time approximation algorithms, based on properties of the columns of the input matrix. We conclude with an overview of intriguing open problems in PH and MPPH.
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"abstract": "The problem Parsimony Haplotyping (PH) asks for the smallest set of\nhaplotypes which can explain a given set of genotypes, and the problem Minimum\nPerfect Phylogeny Haplotyping (MPPH) asks for the smallest such set which also\nallows the haplotypes to be embedded in a perfect phylogeny, an evolutionary\ntree with biologically-motivated restrictions. For PH, we extend recent work by\nfurther mapping the interface between ``easy\u0027\u0027 and ``hard\u0027\u0027 instances, within\nthe framework of (k,l)-bounded instances where the number of 2\u0027s per column and\nrow of the input matrix is restricted. By exploring, in the same way, the\ntractability frontier of MPPH we provide the first concrete, positive results\nfor this problem, and the algorithms underpinning these results offer new\ninsights about how MPPH might be further tackled in the future. In addition, we\nconstruct for both PH and MPPH polynomial time approximation algorithms, based\non properties of the columns of the input matrix. We conclude with an overview\nof intriguing open problems in PH and MPPH.",
"arxiv_id": "q-bio/0605024",
"authors": [
"Leo van Iersel",
"Judith Keijsper",
"Steven Kelk",
"Leen Stougie"
],
"categories": [
"q-bio.OT",
"q-bio.PE"
],
"title": "Shorelines of islands of tractability: Algorithms for parsimony and minimum perfect phylogeny haplotyping problems",
"url": "https://arxiv.org/abs/q-bio/0605024"
},
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