{"paper":{"title":"Two-Level Rectilinear Steiner Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Nicolas K\\\"ammerling, Stephan Held","submitted_at":"2015-01-05T17:39:34Z","abstract_excerpt":"Given a set $P$ of terminals in the plane and a partition of $P$ into $k$ subsets $P_1, ..., P_k$, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree $T_i$ connecting the terminals in each set $P_i$ ($i=1,...,k$) and a top-level tree $T_{top}$ connecting the trees $T_1, ..., T_k$. The goal is to minimize the total length of all trees. This problem arises naturally in the design of low-power physical implementations of parity functions on a computer chip.\n  For bounded $k$ we present a polynomial time approximation scheme (PTAS) that is based on Arora's PTAS for rectili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00933","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"}