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In the {\\sc Bandwidth} problem we are given as input a graph $G$ and integer $b$, and asked whether the bandwidth of $G$ is at most $b$. We present two results concerning the parameterized complexity of the {\\sc Bandwidth} problem on trees.\n  First we show that an algorithm for {\\sc Bandwidth} with running time $f(b)n^{o(b)}$ would violate the Exponential Time H"},"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":"1404.7810","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-30T17:44:03Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"560845be0e0eb09701260007116edb50ce1dbb0b10f0c3997f06f3b017c7aa09","abstract_canon_sha256":"8251b1eb8b764926f1883c38204cdfeb8e9b7377757ef5c24fe336e73f64e426"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:49.882232Z","signature_b64":"mX2dL6xiPKRW88AmYVQu93s/qJ9GHvnUirAhmvoyVQQqHd6fceMtKpE9GPOXU1R7uEHWQBRQ72094/sR1yN3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dbaa5f07a6cc61562993e38868f654533ee4f21aa81a43b427f4f347d67bedf","last_reissued_at":"2026-05-18T02:52:49.881735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:49.881735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parameterized Complexity of Bandwidth on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Daniel Lokshtanov, Markus Sortland Dregi","submitted_at":"2014-04-30T17:44:03Z","abstract_excerpt":"The bandwidth of a $n$-vertex graph $G$ is the smallest integer $b$ such that there exists a bijective function $f : V(G) \\rightarrow \\{1,...,n\\}$, called a layout of $G$, such that for every edge $uv \\in E(G)$, $|f(u) - f(v)| \\leq b$. In the {\\sc Bandwidth} problem we are given as input a graph $G$ and integer $b$, and asked whether the bandwidth of $G$ is at most $b$. We present two results concerning the parameterized complexity of the {\\sc Bandwidth} problem on trees.\n  First we show that an algorithm for {\\sc Bandwidth} with running time $f(b)n^{o(b)}$ would violate the Exponential Time H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7810","kind":"arxiv","version":1},"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":"1404.7810","created_at":"2026-05-18T02:52:49.881804+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.7810v1","created_at":"2026-05-18T02:52:49.881804+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7810","created_at":"2026-05-18T02:52:49.881804+00:00"},{"alias_kind":"pith_short_12","alias_value":"HW5KL4D2NTDB","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HW5KL4D2NTDBKYUZ","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HW5KL4D2","created_at":"2026-05-18T12:28:30.664211+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/HW5KL4D2NTDBKYUZHY4IND3FIU","json":"https://pith.science/pith/HW5KL4D2NTDBKYUZHY4IND3FIU.json","graph_json":"https://pith.science/api/pith-number/HW5KL4D2NTDBKYUZHY4IND3FIU/graph.json","events_json":"https://pith.science/api/pith-number/HW5KL4D2NTDBKYUZHY4IND3FIU/events.json","paper":"https://pith.science/paper/HW5KL4D2"},"agent_actions":{"view_html":"https://pith.science/pith/HW5KL4D2NTDBKYUZHY4IND3FIU","download_json":"https://pith.science/pith/HW5KL4D2NTDBKYUZHY4IND3FIU.json","view_paper":"https://pith.science/paper/HW5KL4D2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.7810&json=true","fetch_graph":"https://pith.science/api/pith-number/HW5KL4D2NTDBKYUZHY4IND3FIU/graph.json","fetch_events":"https://pith.science/api/pith-number/HW5KL4D2NTDBKYUZHY4IND3FIU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HW5KL4D2NTDBKYUZHY4IND3FIU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HW5KL4D2NTDBKYUZHY4IND3FIU/action/storage_attestation","attest_author":"https://pith.science/pith/HW5KL4D2NTDBKYUZHY4IND3FIU/action/author_attestation","sign_citation":"https://pith.science/pith/HW5KL4D2NTDBKYUZHY4IND3FIU/action/citation_signature","submit_replication":"https://pith.science/pith/HW5KL4D2NTDBKYUZHY4IND3FIU/action/replication_record"}},"created_at":"2026-05-18T02:52:49.881804+00:00","updated_at":"2026-05-18T02:52:49.881804+00:00"}