{"id":"https://openalex.org/W7154279871","doi":"https://doi.org/10.48550/arxiv.2604.11027","title":"Parameterized Algorithms and Complexity for Function Merging with Branch Reordering","display_name":"Parameterized Algorithms and Complexity for Function Merging with Branch Reordering","publication_year":2026,"publication_date":"2026-04-13","ids":{"openalex":"https://openalex.org/W7154279871","doi":"https://doi.org/10.48550/arxiv.2604.11027"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.11027","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11027","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.11027","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007636554","display_name":"Amir K. Goharshady","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Goharshady, Amir K.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092825186","display_name":"Kerim Kochekov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kochekov, Kerim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133561307","display_name":"Tian Shu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shu, Tian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133582466","display_name":"Ahmed Khaled Zaher","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zaher, Ahmed Khaled","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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.36160001158714294,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.36160001158714294,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.1818999946117401,"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/T11269","display_name":"Algorithms and Data Compression","score":0.09309999644756317,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.8159999847412109},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.48910000920295715},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4837999939918518},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4796000123023987},{"id":"https://openalex.org/keywords/nesting","display_name":"Nesting (process)","score":0.4763999879360199},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4722999930381775},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4571000039577484},{"id":"https://openalex.org/keywords/factor","display_name":"Factor (programming language)","score":0.42910000681877136}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.8159999847412109},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6140000224113464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5142999887466431},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.48910000920295715},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4837999939918518},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4796000123023987},{"id":"https://openalex.org/C2776937656","wikidata":"https://www.wikidata.org/wiki/Q2229669","display_name":"Nesting (process)","level":2,"score":0.4763999879360199},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4722999930381775},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4571000039577484},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.42910000681877136},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42590001225471497},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.3982999920845032},{"id":"https://openalex.org/C3017489831","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Running time","level":2,"score":0.39320001006126404},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3691999912261963},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3296999931335449},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C97542219","wikidata":"https://www.wikidata.org/wiki/Q497863","display_name":"SIMPLE algorithm","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.259799987077713}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.11027","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11027","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.11027","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11027","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Binary":[0],"size":[1,149],"reduction":[2],"is":[3,14,35,160,206,253,270],"an":[4,236,282],"increasingly":[5],"important":[6],"optimization":[7],"objective":[8],"for":[9,81],"compilers.":[10],"One":[11],"emerging":[12],"technique":[13],"function":[15,276],"merging,":[16],"where":[17,40,109,145],"multiple":[18],"similar":[19],"functions":[20,41,142,234],"are":[21,42,50,190],"merged":[22],"into":[23],"one,":[24],"thereby":[25],"eliminating":[26],"redundancy.":[27],"The":[28],"SOTA":[29],"approach":[30],"to":[31,161,212,258],"perform":[32],"the":[33,69,93,102,115,127,163,176,204,233,240,251,264,271],"merging":[34,277],"based":[36],"on":[37],"sequence":[38,178],"alignment,":[39],"viewed":[43],"as":[44,191],"linear":[45],"sequences":[46],"of":[47,68,74,104,114,133,140,165,232,266,275],"instructions":[48],"that":[49,90,117,172,203,228,250],"then":[51],"matched":[52],"in":[53,169,198,223,243],"a":[54,64,170],"way":[55,171],"maximizing":[56],"their":[57],"alignment.":[58,179],"In":[59],"this":[60,91,269],"paper,":[61],"we":[62,98,110],"consider":[63],"significantly":[65],"generalized":[66],"formulation":[67],"problem":[70,94,205,241,252],"by":[71],"allowing":[72,80],"reordering":[73,280],"branches":[75,164],"within":[76],"each":[77,146],"function,":[78],"subsequently":[79],"more":[82],"flexible":[83],"matching":[84],"and":[85,96,107,130,154,167,183],"better":[86],"merging.":[87],"We":[88,121],"show":[89],"makes":[92],"NP-hard,":[95],"thus":[97],"study":[99,274],"it":[100],"through":[101],"lens":[103],"parameterized":[105],"algorithms":[106],"complexity,":[108],"identify":[111],"certain":[112],"parameters":[113,215],"input":[116,134,138],"govern":[118],"its":[119],"complexity.":[120],"look":[122],"at":[123],"two":[124,141],"natural":[125],"parameters:":[126],"branching":[128,151],"factor":[129,152],"nesting":[131,155,238],"depth":[132,156],"functions.":[135],"Concretely,":[136],"our":[137,267],"consists":[139],"$F_1,":[143],"F_2,$":[144],"$F_i$":[147],"has":[148,235],"$n_i,$":[150],"$b_i,$":[153],"$d_i.$":[157],"Our":[158,188],"task":[159],"reorder":[162],"$F_1$":[166],"$F_2$":[168],"yields":[173],"linearizations":[174],"achieving":[175],"maximum":[177],"Let":[180],"$n=\\max(n_1,":[181],"n_2),$":[182],"define":[184],"$b,":[185],"d$":[186],"similarly.":[187],"results":[189],"follows:":[192],"-":[193,219,245],"A":[194,246],"simple":[195],"algorithm":[196,221],"running":[197,222],"time":[199,224],"$2^{O(bd)}":[200],"n^2,$":[201],"establishing":[202],"fixed-parameter":[207],"tractable":[208],"(FPT)":[209],"with":[210,278],"respect":[211],"all":[213],"four":[214],"$b_1,d_1,":[216],"b_2,":[217,261],"d_2.$":[218,262],"An":[220],"$2^{O(bd_2)}":[225],"n^7,$":[226],"showing":[227,249],"even":[229,255],"when":[230,256],"one":[231],"unbounded":[237],"depth,":[239],"remains":[242],"FPT.":[244],"hardness":[247],"result":[248],"NP-hard":[254],"constrained":[257],"constant":[259],"$d_1,":[260],"To":[263],"best":[265],"knowledge,":[268],"first":[272],"systematic":[273],"branch":[279],"from":[281],"algorithmic":[283],"or":[284],"complexity-theoretic":[285],"perspective.":[286]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-15T00:00:00"}
