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The most na\\\"ive way to construct an additive $k$-spanner of $G$ is the following: As long as $H$ is not an additive $k$-spanner repeat: Find a pair $(u,v) \\in H$ that violates the spanner-condition and a shortest path from $u$ to $v$ in $G$. Add the edges of this path to $H$.\n  We show that, with a very simple initial graph $H$, this na\\\"ive method gives additive $6$- and $2$-spanners of sizes matching the best known upper bounds. For additive $2$-spanners we start with $H=\\emptyset$ a"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.0178","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-03-02T09:33:30Z","cross_cats_sorted":[],"title_canon_sha256":"43737635de5f56da1e2c05f86e344870567e7d6de3bdf80f0e6c669ac6cd3516","abstract_canon_sha256":"ba3ae6a5b1e55b68ee6cd4a964af2e3777dc4bf00e539e673bfa2b4abde2fea0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:01.288567Z","signature_b64":"G+JcaTNHQmpqeFRsDblDxR0iQHl3RzlJcDtFo1Pb5l9ufyyoZ9+oMNTZrPZ06lUMFO69IhV/K8MILDeYJAYzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58a71d859937a0d3a34556167b6857b574da7149242e7dac43fd934c4f472de1","last_reissued_at":"2026-05-18T02:33:01.288224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:01.288224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Additive Spanners: A Simple Construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Mathias B{\\ae}k Tejs Knudsen","submitted_at":"2014-03-02T09:33:30Z","abstract_excerpt":"We consider additive spanners of unweighted undirected graphs. 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