{"paper":{"title":"Codes for Graph Erasures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Eitan Yaakobi, Lev Yohananov","submitted_at":"2017-05-07T15:47:51Z","abstract_excerpt":"Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the information is stored on the edges of an undirected graph, and a code over graphs is a set of graphs. A node failure is the event where all edges in the neighborhood of the failed node have been erased. We say that a code over graphs can tolerate $\\rho$ node failures if it can correct the erased edges of any $\\rho$ failed nodes in the graph. While the constru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02639","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"}