{"paper":{"title":"On the length of Golomb Ruler: A function construction approach based on difference triangle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NT","authors_text":"Xiaoming Li, Yanqing Wang","submitted_at":"2014-01-22T05:25:16Z","abstract_excerpt":"Since the significance of Golomb Ruler Problem in some context, we proposes a function construction approach based on difference triangle to generate near-optimal Golomb rulers. Let x1, x2, ..., xn be an increasing sequence of integers, where x1 = 0, which satisfies the following conditions: if abs(xi-xj) = abs(xp-xq) then {i, j} = {p,q}. Our objective is to find the order of minimum xn for any given n. In this paper, the two results in a paper are both improved. In addition, it will be shown that the length of Golomb Ruler have been shortened to a half, and that the satisfying sequence can no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5556","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"}