{
  "abstract": "Computation of zigzag persistence has progressed in recent years, with results showing that complexities of many problems closely align with those in the non-zigzag setting. The major efficiency gap now lies in the updating of zigzag representatives. In this paper, we propose efficient algorithms for updating zigzag representatives based on a recent algorithm for extracting zigzag representatives from a $R=DV$ decomposition of a constructed non-zigzag. The main difficulty for designing our update algorithms lies in the adjacency change occurring in two operations that lengthen or shorten a filtration. Despite the adjacency change, we find that the update can still be done efficiently in quadratic time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.16153",
  "author_total": 3,
  "authors": [
    {
      "name": "Tamal K. Dey"
    },
    {
      "name": "Tao Hou"
    },
    {
      "name": "Dmitriy Morozov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/63txwta8ct2zz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.16153",
  "fulltext_url": null,
  "id": "63txwta8ct2zz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.16153",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7169796770",
  "pdf_url": "https://arxiv.org/pdf/2607.16153",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/63txwta8ct2zz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2607.16153",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.16153"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Updating zigzag representatives efficiently",
  "title_text": "Updating zigzag representatives efficiently",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/63txwta8ct2zz",
  "venue": "arXiv",
  "versions": []
}