{"paper":{"title":"A Theory of Network Equivalence, Parts I and II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Michelle Effros, Muriel Medard, Ralf Koetter","submitted_at":"2010-07-07T01:35:17Z","abstract_excerpt":"A family of equivalence tools for bounding network capacities is introduced. Part I treats networks of point-to-point channels. The main result is roughly as follows. Given a network of noisy, independent, memoryless point-to-point channels, a collection of communication demands can be met on the given network if and only if it can be met on another network where each noisy channel is replaced by a noiseless bit pipe with throughput equal to the noisy channel capacity. This result was known previously for the case of a single-source multicast demand. The result given here treats general demand"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1033","kind":"arxiv","version":2},"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"}