{"id":"https://openalex.org/W4416371355","doi":"https://doi.org/10.48550/arxiv.2510.03184","title":"On the Hardness of the One-Sided Code Sparsifier Problem","display_name":"On the Hardness of the One-Sided Code Sparsifier Problem","publication_year":2025,"publication_date":"2025-10-03","ids":{"openalex":"https://openalex.org/W4416371355","doi":"https://doi.org/10.48550/arxiv.2510.03184"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2510.03184","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.03184","pdf_url":"https://arxiv.org/pdf/2510.03184","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.03184","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090091569","display_name":"Elena Grigorescu","orcid":"https://orcid.org/0000-0001-9673-4313"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Grigorescu, Elena","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5120459002","display_name":"Alice Moayyedi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Moayyedi, Alice","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.6930999755859375,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.6930999755859375,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.10379999876022339,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.07540000230073929,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/code-word","display_name":"Code word","score":0.8137000203132629},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.678600013256073},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6549999713897705},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4690999984741211},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.31450000405311584},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.3140000104904175},{"id":"https://openalex.org/keywords/parity-check-matrix","display_name":"Parity-check matrix","score":0.2953000068664551}],"concepts":[{"id":"https://openalex.org/C153207627","wikidata":"https://www.wikidata.org/wiki/Q863873","display_name":"Code word","level":3,"score":0.8137000203132629},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.701200008392334},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.678600013256073},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6549999713897705},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5442000031471252},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4690999984741211},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4390999972820282},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.31520000100135803},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3140000104904175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3124000132083893},{"id":"https://openalex.org/C95925971","wikidata":"https://www.wikidata.org/wiki/Q3100414","display_name":"Parity-check matrix","level":4,"score":0.2953000068664551},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2870999872684479},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.28110000491142273},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.27000001072883606},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C112955886","wikidata":"https://www.wikidata.org/wiki/Q5656275","display_name":"Hardness of approximation","level":3,"score":0.25929999351501465},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.251800000667572},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2515000104904175},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2510.03184","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.03184","pdf_url":"https://arxiv.org/pdf/2510.03184","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2510.03184","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.03184","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.03184","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.03184","pdf_url":"https://arxiv.org/pdf/2510.03184","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"notion":[1,21],"of":[2,22,54,78,81,93,103,108,130],"code":[3,41],"sparsification":[4,24],"was":[5],"introduced":[6],"by":[7],"Khanna,":[8],"Putterman":[9],"and":[10,27,72,111],"Sudan":[11],"(arxiv.2311.00788),":[12],"as":[13],"an":[14,34,67],"analogue":[15],"to":[16,66],"the":[17,18,52,59,76,91,100,121],"more":[19],"established":[20],"cut":[23],"in":[25,61],"graphs":[26],"hypergraphs.":[28],"In":[29,95],"particular,":[30],"for":[31,38,84],"$\u03b1\\in":[32],"(0,1)$":[33],"(unweighted)":[35],"one-sided":[36,79,106],"$\u03b1$-sparsifier":[37],"a":[39,46,105,118],"linear":[40,86],"$\\mathcal{C}":[42],"\\subseteq":[43],"\\mathbb{F}_2^n$":[44],"is":[45,63,90,115],"subset":[47],"$S\\subseteq":[48],"[n]$":[49],"such":[50],"that":[51,113],"weight":[53],"each":[55],"codeword":[56,124],"projected":[57],"onto":[58],"coordinates":[60],"$S$":[62],"preserved":[64],"up":[65],"$\u03b1$":[68],"fraction.":[69],"Recently,":[70],"Gharan":[71],"Sahami":[73],"(arxiv.2502.02799)":[74],"show":[75,112,128],"existence":[77],"1/2-sparsifiers":[80],"size":[82],"$n/2+O(\\sqrt{kn})$":[83],"any":[85],"code,":[87],"where":[88],"$k$":[89],"dimension":[92],"$\\mathcal{C}$.":[94],"this":[96],"paper,":[97],"we":[98],"consider":[99],"computational":[101],"problem":[102],"finding":[104],"1/2-sparsifier":[107],"minimal":[109],"size,":[110],"it":[114],"NP-hard,":[116],"via":[117],"reduction":[119],"from":[120],"classical":[122],"nearest":[123],"problem.":[125],"We":[126],"also":[127],"hardness":[129],"approximation":[131],"results.":[132]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}