{
  "annotation_id": "2e79f8cb-68ea-40e3-a8e6-4d3b87f73d68",
  "date_created": "2026-03-02T18:01:35.649000Z",
  "date_modified": "2026-03-02T18:01:35.649000Z",
  "file_hash": "c4da0ca2b12be299ce342c95a6e69ca209919f663feb4ca760f22b6a0e2f6b6e",
  "private": false,
  "record": {
    "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"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4e4883cb-5b6b-4b2a-8588-387fe0c21152",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}