{"paper":{"title":"Diameter Constrained Reliability: Computational Complexity in terms of the diameter and number of terminals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Eduardo Canale, Pablo Romero","submitted_at":"2014-04-14T18:29:48Z","abstract_excerpt":"Let $G=(V,E)$ be a simple graph with $|V|=n$ nodes and $|E|=m$ links, a subset $K \\subseteq V$ of \\emph{terminals}, a vector $p=(p_1,\\ldots,p_m) \\in [0,1]^m$ and a positive integer $d$, called \\emph{diameter}. We assume nodes are perfect but links fail stochastically and independently, with probabilities $q_i=1-p_i$. The \\emph{diameter-constrained reliability} (DCR for short), is the probability that the terminals of the resulting subgraph remain connected by paths composed by $d$ links, or less. This number is denoted by $R_{K,G}^{d}(p)$.\n  The general DCR computation is inside the class of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3684","kind":"arxiv","version":1},"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"}