{"id":"https://openalex.org/W2185746685","doi":null,"title":"Computing Persistent Homology via Discrete Morse Theory","display_name":"Computing Persistent Homology via Discrete Morse Theory","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2185746685","mag":"2185746685"},"language":"en","primary_location":{"id":"mag:2185746685","doi":null,"is_oa":false,"landing_page_url":"https://www.math.ku.dk/~moller/students/brian_brost.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091111581","display_name":"Jesper M. Mller","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jesper Michael Mller","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030887041","display_name":"Pawe\u0142 Winter","orcid":"https://orcid.org/0000-0003-2669-0524","observed_orcids":["https://orcid.org/0000-0003-2669-0524"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Winter","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2669-0524","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"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/T12923","display_name":"Digital Image Processing Techniques","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/persistent-homology","display_name":"persistent homology","score":0.8769999742507935},{"id":"https://openalex.org/keywords/discrete-morse-theory","display_name":"discrete Morse theory","score":0.996999979019165},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"topological data analysis","score":0.800000011920929},{"id":"https://openalex.org/keywords/simulated-annealing","display_name":"simulated annealing","score":0.871999979019165},{"id":"https://openalex.org/keywords/homology-computation","display_name":"homology computation","score":0.8769999742507935},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"simplicial complexes","score":0.8289999961853027},{"id":"https://openalex.org/keywords/computational-topology","display_name":"computational topology","score":0.8040000200271606}],"concepts":[{"id":"https://openalex.org/C170315498","wikidata":"https://www.wikidata.org/wiki/Q5282039","display_name":"Discrete Morse theory","level":3,"score":0.872214674949646},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.7193289399147034},{"id":"https://openalex.org/C135783237","wikidata":"https://www.wikidata.org/wiki/Q3139850","display_name":"Morse homology","level":4,"score":0.7019644975662231},{"id":"https://openalex.org/C181576044","wikidata":"https://www.wikidata.org/wiki/Q4129926","display_name":"Computational topology","level":3,"score":0.6721833348274231},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.6572710275650024},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6300249099731445},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.5622335076332092},{"id":"https://openalex.org/C140031139","wikidata":"https://www.wikidata.org/wiki/Q79897","display_name":"Morse code","level":2,"score":0.514623761177063},{"id":"https://openalex.org/C34736171","wikidata":"https://www.wikidata.org/wiki/Q918333","display_name":"Preprocessor","level":2,"score":0.5124323964118958},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.4768596589565277},{"id":"https://openalex.org/C139962677","wikidata":"https://www.wikidata.org/wiki/Q1095056","display_name":"Singular homology","level":3,"score":0.4199843108654022},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41621559858322144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40737760066986084},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.39735114574432373},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.39649391174316406},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28823286294937134},{"id":"https://openalex.org/C55537702","wikidata":"https://www.wikidata.org/wiki/Q3139849","display_name":"Cellular homology","level":3,"score":0.2837579548358917},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24311086535453796},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23237019777297974},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20248925685882568},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.13837546110153198},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.07261583209037781},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2185746685","doi":null,"is_oa":false,"landing_page_url":"https://www.math.ku.dk/~moller/students/brian_brost.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W181649851","https://openalex.org/W327529882","https://openalex.org/W1496383623","https://openalex.org/W1978174880","https://openalex.org/W1979273469","https://openalex.org/W1986644591","https://openalex.org/W1987227236","https://openalex.org/W2002165972","https://openalex.org/W2008581147","https://openalex.org/W2021125686","https://openalex.org/W2022805865","https://openalex.org/W2033902599","https://openalex.org/W2037613900","https://openalex.org/W2038073775","https://openalex.org/W2042847888","https://openalex.org/W2064020260","https://openalex.org/W2081349787","https://openalex.org/W2087841994","https://openalex.org/W2094796465","https://openalex.org/W2101570837","https://openalex.org/W2113957471","https://openalex.org/W2144044408","https://openalex.org/W2153986241","https://openalex.org/W2154477220","https://openalex.org/W2157878484","https://openalex.org/W2167574130","https://openalex.org/W2215934091","https://openalex.org/W2276999326","https://openalex.org/W2336259629","https://openalex.org/W3013843370","https://openalex.org/W3040586665","https://openalex.org/W3043060850"],"related_works":["https://openalex.org/W7097175069","https://openalex.org/W7134959209","https://openalex.org/W6924163864","https://openalex.org/W2526131644","https://openalex.org/W2762398509","https://openalex.org/W2025892619","https://openalex.org/W2052322350","https://openalex.org/W2029833645","https://openalex.org/W2900648503","https://openalex.org/W7098934043"],"abstract_inverted_index":{"This":[0,136],"report":[1],"provides":[2],"theoretical":[3],"justification":[4],"for":[5,12,28,37,60,77,115],"the":[6,13,23,26,29,45,73,78,123,130,133,158],"use":[7,152],"of":[8,15,22,25,31,47,49,82,125,132,145,153,161],"discrete":[9,32,62,154,165],"Morse":[10,33,63,120,155,166],"theory":[11,121,156],"computation":[14,30,81,127,160],"homology":[16,83,86,111,126],"and":[17,35,84,106,142],"persistent":[18,85],"homology,":[19],"an":[20,38,89],"overview":[21],"state":[24],"art":[27],"matchings":[34,64],"motivation":[36],"interest":[39],"in":[40,92,97],"these":[41],"computations,":[42],"particularly":[43],"from":[44,139],"point":[46,144],"view":[48],"topological":[50,101],"data":[51,102],"analysis.":[52],"Additionally,":[53],"a":[54,140],"new":[55],"simulated":[56],"annealing":[57],"based":[58],"method":[59],"computing":[61,110],"is":[65,112,137,157],"presented.":[66],"For":[67],"several":[68],"problem":[69],"instances":[70],"this":[71],"outperforms":[72],"best":[74],"known":[75],"heuristics":[76],"task.":[79],"The":[80,147],"has":[87],"become":[88],"important":[90],"task":[91],"computational":[93],"topology,":[94],"with":[95],"applications":[96],"fields":[98],"such":[99],"as":[100],"analysis,":[103],"computer":[104],"vision":[105],"materials":[107],"science.":[108],"Unfortunately":[109],"currently":[113],"infeasible":[114],"large":[116],"input":[117,134],"complexes.":[118,135],"Discrete":[119],"enables":[122],"preprocessing":[124],"by":[128],"reducing":[129],"size":[131],"advantageous":[138],"memory":[141],"performance":[143],"view.":[146],"key":[148],"to":[149],"making":[150],"efficient":[151],"quick":[159],"optimal,":[162],"or":[163],"good,":[164],"matchings.":[167]},"counts_by_year":[],"updated_date":"2026-09-26T08:19:03.415552","created_date":"2016-06-24T00:00:00"}