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Here $d(x, y)$ denotes the Hamming distance between the two strings $x$ and $y$. We prove\n  1. a variant of {\\em Consensus String with Outliers} where the number of outliers $k$ is fixed and the objective is to minimize the total distance $\\sum_{s_i \\in S^*} d(s_i, s)$ admits a simple PTA"},"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":"1111.0376","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-02T03:13:55Z","cross_cats_sorted":[],"title_canon_sha256":"426387eb15fb57dd7d5b265be59d2343fbeeb1c9e3c5d079c2792ae74278e744","abstract_canon_sha256":"61f9593ec76d53213cc6f5cb65a7d1344b0148832f84a94907261da7ad9c16eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:24.946044Z","signature_b64":"JSc6k2/cKTb+xNTMdd4MFi80+Kfcn1MYC0/HR20jsdWOBJaKZmJqEV4sbT/2O7zTB19orxR6hguQCitOPqvhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76fbe765adb00fd68a7dfef2f6d18c0b515629d50821136b650389b580c51a29","last_reissued_at":"2026-05-18T04:09:24.945367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:24.945367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Outlier Detection for DNA Fragment Assembly","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christina Boucher, Christine Lo, Daniel Lokshtanov","submitted_at":"2011-11-02T03:13:55Z","abstract_excerpt":"Given $n$ length-$\\ell$ strings $S =\\{s_1, ..., s_n\\}$ over a constant size alphabet $\\Sigma$ together with parameters $d$ and $k$, the objective in the {\\em Consensus String with Outliers} problem is to find a subset $S^*$ of $S$ of size $n-k$ and a string $s$ such that $\\sum_{s_i \\in S^*} d(s_i, s) \\leq d$. Here $d(x, y)$ denotes the Hamming distance between the two strings $x$ and $y$. We prove\n  1. a variant of {\\em Consensus String with Outliers} where the number of outliers $k$ is fixed and the objective is to minimize the total distance $\\sum_{s_i \\in S^*} d(s_i, s)$ admits a simple PTA"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0376","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.0376","created_at":"2026-05-18T04:09:24.945483+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.0376v2","created_at":"2026-05-18T04:09:24.945483+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0376","created_at":"2026-05-18T04:09:24.945483+00:00"},{"alias_kind":"pith_short_12","alias_value":"O356OZNNWAH5","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"O356OZNNWAH5NCT5","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"O356OZNN","created_at":"2026-05-18T12:26:37.096874+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O356OZNNWAH5NCT573ZPNUMMBN","json":"https://pith.science/pith/O356OZNNWAH5NCT573ZPNUMMBN.json","graph_json":"https://pith.science/api/pith-number/O356OZNNWAH5NCT573ZPNUMMBN/graph.json","events_json":"https://pith.science/api/pith-number/O356OZNNWAH5NCT573ZPNUMMBN/events.json","paper":"https://pith.science/paper/O356OZNN"},"agent_actions":{"view_html":"https://pith.science/pith/O356OZNNWAH5NCT573ZPNUMMBN","download_json":"https://pith.science/pith/O356OZNNWAH5NCT573ZPNUMMBN.json","view_paper":"https://pith.science/paper/O356OZNN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.0376&json=true","fetch_graph":"https://pith.science/api/pith-number/O356OZNNWAH5NCT573ZPNUMMBN/graph.json","fetch_events":"https://pith.science/api/pith-number/O356OZNNWAH5NCT573ZPNUMMBN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O356OZNNWAH5NCT573ZPNUMMBN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O356OZNNWAH5NCT573ZPNUMMBN/action/storage_attestation","attest_author":"https://pith.science/pith/O356OZNNWAH5NCT573ZPNUMMBN/action/author_attestation","sign_citation":"https://pith.science/pith/O356OZNNWAH5NCT573ZPNUMMBN/action/citation_signature","submit_replication":"https://pith.science/pith/O356OZNNWAH5NCT573ZPNUMMBN/action/replication_record"}},"created_at":"2026-05-18T04:09:24.945483+00:00","updated_at":"2026-05-18T04:09:24.945483+00:00"}