{"paper":{"title":"The structure and topology of rooted weighted trees modeling layered cyber-security systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Geir Agnarsson, Raymond Greenlaw, Sanpawat Kantabutra","submitted_at":"2016-05-11T19:25:31Z","abstract_excerpt":"In this paper we consider a layered-security model in which the containers and their nestings are given in the form of a rooted tree $T$. A {\\em cyber-security model\\/} is an ordered three-tuple $M = (T, C, P)$ where $C$ and $P$ are multisets of {\\em penetration costs\\/} for the containers and {\\em target-acquisition values\\/} for the prizes that are located within the containers, respectively, both of the same cardinality as the set of the non-root vertices of $T$. The problem that we study is to assign the penetration costs to the edges and the target-acquisition values to the vertices of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03569","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"}