Capped Alternative-Path Action on Graphs II: Curvature-Guided Capacity Planning and Rapid Failure-Recovery Decision Support for Telecommunications Networks, Validated on 276 Real Topologies
Year: 2026
Type: preprint
Abstract: We transform a validated, regularized graph statistical-mechanics model (Paper I, doi:10.5281/zenodo.20982419) into two practical decision-support tools for telecommunications infrastructure, evaluated on 276 real-world network topologies (Internet Topology Zoo). โข ๐๐ฐ๐จ ๐๐๐๐ข๐ฌ๐ข๐จ๐ง-๐ฌ๐ฎ๐ฉ๐ฉ๐จ๐ซ๐ญ ๐ญ๐จ๐จ๐ฅ๐ฌ are introduced:โ A greedy optimization that ranks candidate links by their improvement of discrete (FormanโRicci) curvature, a validated proxy for structural robustness, under a fixed budget.โ A self-calibrating geographic cost term: distances within a networkโs historical maximum link length are free, while longer links are linearly penalized. โข The geographic term is ๐๐ฎ๐ฅ๐ฅ๐ฒ ๐๐๐ญ๐-๐๐ซ๐ข๐ฏ๐๐ง, requiring no external $/km estimates and adding no measurable computational cost. โข Across all 276 networks:โ Mean curvature: โ3.23โ Median curvature: โ2.59โ Only 3.3% exhibit positive mean curvature, almost exclusively small, near-complete clustersThese values align closely with the synthetic sparse random baseline from the companion model. โข In five case studies (Turkey, Croatia, Latvia, Norway, Greece):โ The most critical node is the national capital in 4/5 networks.โ Its removal fragments the system into 18โ57 disconnected components with no immediate recovery.โ A secondary critical node allows fast recovery (0.04โ0.2 seconds) with realistic link lengths. โข In two cases, unconstrained optimization proposed unrealistically long links; the geographic term ๐๐ฅ๐ข๐ฆ๐ข๐ง๐๐ญ๐๐ฌ ๐๐ฅ๐ฅ ๐ฏ๐ข๐จ๐ฅ๐๐ญ๐ข๐จ๐ง๐ฌ (0/8 and 0/3) without added cost. โข Norwayโs Uninett2010 network shows ๐ง๐จ ๐ฌ๐ข๐ง๐ ๐ฅ๐ ๐๐๐ญ๐๐ฌ๐ญ๐ซ๐จ๐ฉ๐ก๐ข๐ ๐๐๐ข๐ฅ๐ฎ๐ซ๐ ๐ฉ๐จ๐ข๐ง๐ญ, highlighting structural resilience. Scope clarification:Distance is explicitly treated as a proxy for capital cost, not a real economic estimate. The proposed methods provide rapid decision support for network operations, not a replacement for packet-level routing protocols. ๐๐จ๐๐ ๐๐ง๐ ๐๐ฎ๐ฅ๐ฅ ๐ซ๐๐ฉ๐ซ๐จ๐๐ฎ๐๐ข๐๐ข๐ฅ๐ข๐ญ๐ฒ ๐ฆ๐๐ญ๐๐ซ๐ข๐๐ฅ๐ฌ ๐ข๐ง๐๐ฅ๐ฎ๐๐๐.Licensed under PolyForm Noncommercial 1.0.0, covering all algorithms and implementations across languages and hardware platforms.
Author: Pirolo, Andrรฉs Sebastiรกn
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166433028
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