{
  "abstract": "We study the restricted inverse optimal value problem on shortest paths under the weighted $l_\\infty$ norm on trees (RIOVSPT$_\\infty$): adjust edge weights at minimum worst-link cost so that the shortest root--leaf path is lower-bounded by a given value $D$, a restriction on a prescribed path $P_0$. Unlike the $l_1$ version minimizing total adjustment cost, the $l_\\infty$ objective controls the worst link, the criterion relevant in bandwidth pricing. We characterize feasibility through the minimum cost shortest path interdiction problem (MCSPIT$_\\infty$), whose optimal solution $\\hat w$ splits the instance at the first edge of $P_0$ into two independent subproblems. Relative to $\\hat w$, three cases arise. The first two admit closed-form optimal solutions. The third reduces to a parametric subproblem SPIT$^0_\\infty(M)$: minimize the length of $P_0$ on the gate subtree under the budget $C(\\hat w)+M$ with all other root--leaf paths kept at least $D$. It is solved exactly by an iterative greedy procedure. On its value function $V(M)$, the predicate $V(M)\\leq D$ is equivalent to the nonnegativity of truncated-bound margins, which are monotone, continuous and piecewise affine; the smallest such $M$ gives the optimal value, located by binary search over the edge-bound breakpoints with an exact affine threshold evaluation. The same margin test on the full tree gives a uniform algorithm for all cases. Both algorithms run in $O(n\\log n)$ time. Experiments on synthetic trees agree with a linear programming baseline and illustrate the two algorithms' distinct runtime profiles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23710",
  "author_total": 6,
  "authors": [
    {
      "name": "Qiao Zhang"
    },
    {
      "name": "Ying Wang"
    },
    {
      "name": "Xiao Li"
    },
    {
      "name": "Junhua Jia"
    },
    {
      "name": "Xiucui Guan"
    },
    {
      "name": "Panos M. Pardalos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ptnaq193jgfm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23710",
  "fulltext_url": null,
  "id": "8ptnaq193jgfm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23710",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7222933419",
  "pdf_url": "https://arxiv.org/pdf/2610.23710",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ptnaq193jgfm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23710",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23710"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The Restricted Inverse Optimal Value Problem on Shortest Path under $l_\\infty$ Norm on Trees",
  "title_text": "The Restricted Inverse Optimal Value Problem on Shortest Path under l_∞ Norm on Trees",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/8ptnaq193jgfm",
  "venue": "arXiv",
  "versions": []
}