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Constrained Maximum Weight Paths in Random Geometric Graphs — arXiv:2608.08532

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.08532
License (as archived): CC0-1.0
Archived: 2026-10-19T09:06:59.427Z
SHA-256 of the archived text: facd2537e8e4d4702027717138d4cfa502fe9d5febf4d14d3269e96ca4891f84
Stable URL of this page: https://metraipolis.com/documento/dc_ff23236fa494

How to cite

Constrained Maximum Weight Paths in Random Geometric Graphs — arXiv:2608.08532 — arXiv (en), https://arxiv.org/abs/2608.08532 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ff23236fa494 (Metraipolis archive dc_ff23236fa494, sha256 facd2537e8e4d4702027717138d4cfa502fe9d5febf4d14d3269e96ca4891f84)

BibTeX

@misc{dcff23236fa494,
  title = {Constrained Maximum Weight Paths in Random Geometric Graphs — arXiv:2608.08532},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.08532},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ff23236fa494; sha256 facd2537e8e4d4702027717138d4cfa502fe9d5febf4d14d3269e96ca4891f84},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.08532. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In this paper, we consider a random geometric graph (RGG)~\(G\) formed by~\(n\) vertices distributed uniformly in the unit square~\(S\) on the plane and equip each edge of~\(G\) with an independent weight. We assume that the adjacency distance between vertices is larger than the connectivity threshold and estimate the maximum weight of a path connecting two fixed points~\(O_1\) and~\(O_2\) in~\(S,\) using edges of~\(G\) that satisfy length and weight constraints. Our strategy is to first divide the space between~\(O_1\) and~\(O_2\) into small squares and identify nice squares containing heavy edges. We then use an iterative stitching procedure to connect these heavy edges and estimate the weight of the resulting path~\(P.\) Finally, we invoke a multi-level scaling procedure along with weight segmentation to establish an upper bound for the maximum weight of \emph{any} path between~\(O_1\) and~\(O_2\) and thereby demonstrate the near-optimality of~\(P.\) We also illustrate our results using examples involving edge weights satisfying power law and exponential decay.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-11 in math.PR).
Categorie arXiv: Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2608.08532 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T09:04:32.174Z dalla pagina https://arxiv.org/catchup/math.PR/2026-08-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).