{"id":"https://openalex.org/W4389820898","doi":"https://doi.org/10.48550/arxiv.2312.08776","title":"Approximate Integer Solution Counts over Linear Arithmetic Constraints","display_name":"Approximate Integer Solution Counts over Linear Arithmetic Constraints","publication_year":2023,"publication_date":"2023-12-14","ids":{"openalex":"https://openalex.org/W4389820898","doi":"https://doi.org/10.48550/arxiv.2312.08776"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2312.08776","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.08776","pdf_url":"https://arxiv.org/pdf/2312.08776","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2312.08776","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066997484","display_name":"Cunjing Ge","orcid":"https://orcid.org/0000-0002-8249-1397"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ge, Cunjing","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066997484"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9983999729156494,"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/T11106","display_name":"Data Management and Algorithms","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/polytope","display_name":"Polytope","score":0.9348995089530945},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6289069652557373},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5874795317649841},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5869117975234985},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5274895429611206},{"id":"https://openalex.org/keywords/integer-lattice","display_name":"Integer lattice","score":0.5214623808860779},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49671775102615356},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.45019933581352234},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.43903109431266785},{"id":"https://openalex.org/keywords/counting-problem","display_name":"Counting problem","score":0.42607182264328003},{"id":"https://openalex.org/keywords/integer-factorization","display_name":"Integer factorization","score":0.4219023287296295},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39242255687713623},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3159964680671692},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25735366344451904},{"id":"https://openalex.org/keywords/half-integer","display_name":"Half-integer","score":0.0587591826915741}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9348995089530945},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6289069652557373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5874795317649841},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5869117975234985},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5274895429611206},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.5214623808860779},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49671775102615356},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.45019933581352234},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.43903109431266785},{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.42607182264328003},{"id":"https://openalex.org/C119677069","wikidata":"https://www.wikidata.org/wiki/Q4846249","display_name":"Integer factorization","level":4,"score":0.4219023287296295},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39242255687713623},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3159964680671692},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25735366344451904},{"id":"https://openalex.org/C56863137","wikidata":"https://www.wikidata.org/wiki/Q743139","display_name":"Half-integer","level":2,"score":0.0587591826915741},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2312.08776","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.08776","pdf_url":"https://arxiv.org/pdf/2312.08776","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.2312.08776","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2312.08776","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2312.08776","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2312.08776","pdf_url":"https://arxiv.org/pdf/2312.08776","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389820898.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1778780361","https://openalex.org/W1959574478","https://openalex.org/W2950397665","https://openalex.org/W2514213955","https://openalex.org/W2962839429","https://openalex.org/W2950610433","https://openalex.org/W2561312639","https://openalex.org/W2017624835","https://openalex.org/W4287079425","https://openalex.org/W4389820898"],"abstract_inverted_index":{"Counting":[0],"integer":[1],"solutions":[2],"of":[3,19,40,92],"linear":[4],"constraints":[5],"has":[6,70],"found":[7],"interesting":[8],"applications":[9],"in":[10],"various":[11],"fields.":[12],"It":[13],"is":[14],"equivalent":[15],"to":[16,50],"the":[17,52],"problem":[18,31],"counting":[20],"lattice":[21,53],"points":[22],"inside":[23,55],"a":[24,37,47,56,59,76],"polytope.":[25],"However,":[26],"state-of-the-art":[27,97],"algorithms":[28],"for":[29,35],"this":[30,43],"become":[32],"too":[33],"slow":[34],"even":[36],"modest":[38],"number":[39],"variables.":[41],"In":[42],"paper,":[44],"we":[45],"propose":[46],"new":[48,60],"framework":[49],"approximate":[51],"counts":[54,65],"polytope":[57],"with":[58,90],"random-walk":[61],"sampling":[62],"method.":[63],"The":[64],"computed":[66],"by":[67,75],"our":[68,85],"approach":[69],"been":[71],"proved":[72],"approximately":[73],"bounded":[74],"$(\u03b5,":[77],"\u03b4)$-bound.":[78],"Experiments":[79],"on":[80],"extensive":[81],"benchmarks":[82],"show":[83],"that":[84],"algorithm":[86],"could":[87],"solve":[88],"polytopes":[89],"dozens":[91],"dimensions,":[93],"which":[94],"significantly":[95],"outperforms":[96],"counters.":[98]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}