{"paper":{"title":"Exact Solution for Optimal Navigation with Total Cost Restriction","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Dong Zhou, Jiang Zhang, Yanqing Hu, Yong Li, Zengru Di","submitted_at":"2010-07-08T02:35:31Z","abstract_excerpt":"Recently, Li \\textit{et al.} have concentrated on Kleinberg's navigation model with a certain total length constraint $\\Lambda = cN$, where $N$ is the number of total nodes and $c$ is a constant. Their simulation results for the 1- and 2-dimensional cases indicate that the optimal choice for adding extra long-range connections between any two sites seems to be $\\alpha=d+1$, where $d$ is the dimension of the lattice and $\\alpha$ is the power-law exponent. In this paper, we prove analytically that for the 1-dimensional large networks, the optimal power-law exponent is $\\alpha=2$ Further, we stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1281","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}