{"id":"https://openalex.org/W1975963573","doi":"https://doi.org/10.1186/1471-2105-15-s9-s5","title":"On the complexity of Minimum Path Cover with Subpath Constraints for multi-assembly","display_name":"On the complexity of Minimum Path Cover with Subpath Constraints for multi-assembly","publication_year":2014,"publication_date":"2014-09-01","ids":{"openalex":"https://openalex.org/W1975963573","doi":"https://doi.org/10.1186/1471-2105-15-s9-s5","mag":"1975963573","pmid":"https://pubmed.ncbi.nlm.nih.gov/25252805"},"language":"en","primary_location":{"id":"doi:10.1186/1471-2105-15-s9-s5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/1471-2105-15-s9-s5","pdf_url":"https://bmcbioinformatics.biomedcentral.com/counter/pdf/10.1186/1471-2105-15-S9-S5","source":{"id":"https://openalex.org/S19032547","display_name":"BMC Bioinformatics","issn_l":"1471-2105","issn":["1471-2105"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC Bioinformatics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://bmcbioinformatics.biomedcentral.com/counter/pdf/10.1186/1471-2105-15-S9-S5","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061874157","display_name":"Rom\u00e9o Rizzi","orcid":"https://orcid.org/0000-0002-2387-0952"},"institutions":[{"id":"https://openalex.org/I119439378","display_name":"University of Verona","ror":"https://ror.org/039bp8j42","country_code":"IT","type":"education","lineage":["https://openalex.org/I119439378"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Romeo Rizzi","raw_affiliation_strings":["Department of Computer Science, University of Verona, Italy","Department of Computer Science, Univ. of Verona, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Verona, Italy","institution_ids":["https://openalex.org/I119439378"]},{"raw_affiliation_string":"Department of Computer Science, Univ. of Verona, Italy","institution_ids":["https://openalex.org/I119439378"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063897224","display_name":"Alexandru I. Tomescu","orcid":"https://orcid.org/0000-0002-5747-8350"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]},{"id":"https://openalex.org/I32943570","display_name":"Helsinki Institute for Information Technology","ror":"https://ror.org/05kph4940","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I32943570","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Alexandru I Tomescu","raw_affiliation_strings":["Helsinki Institute for Information Technology HIIT, Department of Computer Science, University of Helsinki, Helsinki, Finland","Helsinki Institute for Information Technology (HIIT), Department of Computer Science, University of Helsinki, Helsinki, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Helsinki Institute for Information Technology HIIT, Department of Computer Science, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I32943570"]},{"raw_affiliation_string":"Helsinki Institute for Information Technology (HIIT), Department of Computer Science, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I32943570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043558409","display_name":"Veli M\u00e4kinen","orcid":"https://orcid.org/0000-0003-4454-1493"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]},{"id":"https://openalex.org/I32943570","display_name":"Helsinki Institute for Information Technology","ror":"https://ror.org/05kph4940","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I32943570","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Veli M\u00e4kinen","raw_affiliation_strings":["Helsinki Institute for Information Technology HIIT, Department of Computer Science, University of Helsinki, Helsinki, Finland","Helsinki Institute for Information Technology (HIIT), Department of Computer Science, University of Helsinki, Helsinki, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Helsinki Institute for Information Technology HIIT, Department of Computer Science, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I32943570"]},{"raw_affiliation_string":"Helsinki Institute for Information Technology (HIIT), Department of Computer Science, University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I32943570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5063897224"],"corresponding_institution_ids":["https://openalex.org/I133731052","https://openalex.org/I32943570"],"apc_list":{"value":2790,"currency":"USD","value_usd":2790},"apc_paid":{"value":2790,"currency":"USD","value_usd":2790},"fwci":2.3455,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.88340482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"S9","first_page":"S5","last_page":"S5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.5555999875068665,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.5555999875068665,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.193900004029274,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12784","display_name":"Modular Robots and Swarm Intelligence","score":0.045499999076128006,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5254594087600708},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5099793672561646},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.48552680015563965},{"id":"https://openalex.org/keywords/set-cover-problem","display_name":"Set cover problem","score":0.47626492381095886},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.46907395124435425},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.43576177954673767},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4221668243408203},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.410049706697464},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38636770844459534},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33273035287857056},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3054004907608032},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.29686301946640015},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2861427366733551}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5254594087600708},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5099793672561646},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.48552680015563965},{"id":"https://openalex.org/C100808899","wikidata":"https://www.wikidata.org/wiki/Q1192100","display_name":"Set cover problem","level":3,"score":0.47626492381095886},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.46907395124435425},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.43576177954673767},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4221668243408203},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.410049706697464},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38636770844459534},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33273035287857056},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3054004907608032},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.29686301946640015},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2861427366733551},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017423","descriptor_name":"Sequence Analysis, RNA","qualifier_ui":"Q000191","qualifier_name":"economics","is_major_topic":false},{"descriptor_ui":"D017423","descriptor_name":"Sequence Analysis, RNA","qualifier_ui":"Q000191","qualifier_name":"economics","is_major_topic":false},{"descriptor_ui":"D017423","descriptor_name":"Sequence Analysis, RNA","qualifier_ui":"Q000191","qualifier_name":"economics","is_major_topic":false},{"descriptor_ui":"D017423","descriptor_name":"Sequence Analysis, RNA","qualifier_ui":"Q000191","qualifier_name":"economics","is_major_topic":false},{"descriptor_ui":"D017423","descriptor_name":"Sequence Analysis, RNA","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D017423","descriptor_name":"Sequence Analysis, RNA","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D017423","descriptor_name":"Sequence Analysis, RNA","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D017423","descriptor_name":"Sequence Analysis, RNA","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D059014","descriptor_name":"High-Throughput Nucleotide Sequencing","qualifier_ui":"Q000191","qualifier_name":"economics","is_major_topic":false},{"descriptor_ui":"D059014","descriptor_name":"High-Throughput Nucleotide Sequencing","qualifier_ui":"Q000191","qualifier_name":"economics","is_major_topic":false},{"descriptor_ui":"D059014","descriptor_name":"High-Throughput Nucleotide Sequencing","qualifier_ui":"Q000191","qualifier_name":"economics","is_major_topic":false},{"descriptor_ui":"D059014","descriptor_name":"High-Throughput Nucleotide Sequencing","qualifier_ui":"Q000191","qualifier_name":"economics","is_major_topic":false},{"descriptor_ui":"D059014","descriptor_name":"High-Throughput Nucleotide Sequencing","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D059014","descriptor_name":"High-Throughput Nucleotide Sequencing","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D059014","descriptor_name":"High-Throughput Nucleotide Sequencing","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D059014","descriptor_name":"High-Throughput Nucleotide Sequencing","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D059467","descriptor_name":"Transcriptome","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D059467","descriptor_name":"Transcriptome","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D059467","descriptor_name":"Transcriptome","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D059467","descriptor_name":"Transcriptome","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":4,"locations":[{"id":"doi:10.1186/1471-2105-15-s9-s5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/1471-2105-15-s9-s5","pdf_url":"https://bmcbioinformatics.biomedcentral.com/counter/pdf/10.1186/1471-2105-15-S9-S5","source":{"id":"https://openalex.org/S19032547","display_name":"BMC Bioinformatics","issn_l":"1471-2105","issn":["1471-2105"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC Bioinformatics","raw_type":"journal-article"},{"id":"pmid:25252805","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25252805","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC bioinformatics","raw_type":null},{"id":"pmh:oai:helda.helsinki.fi:10138/162778","is_oa":true,"landing_page_url":"http://hdl.handle.net/10138/162778","pdf_url":null,"source":{"id":"https://openalex.org/S4210213322","display_name":"Ty\u00f6v\u00e4entutkimus Vuosikirja","issn_l":"0784-1272","issn":["0784-1272","1459-7780"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:pubmedcentral.nih.gov:4168716","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4168716","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"BMC Bioinformatics","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1186/1471-2105-15-s9-s5","is_oa":true,"landing_page_url":"https://doi.org/10.1186/1471-2105-15-s9-s5","pdf_url":"https://bmcbioinformatics.biomedcentral.com/counter/pdf/10.1186/1471-2105-15-S9-S5","source":{"id":"https://openalex.org/S19032547","display_name":"BMC Bioinformatics","issn_l":"1471-2105","issn":["1471-2105"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320256","host_organization_name":"BioMed Central","host_organization_lineage":["https://openalex.org/P4310320256","https://openalex.org/P4310319965"],"host_organization_lineage_names":["BioMed Central","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BMC Bioinformatics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5600000023841858,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[{"id":"https://openalex.org/G3187257985","display_name":null,"funder_award_id":"#250345","funder_id":"https://openalex.org/F4320321108","funder_display_name":"Academy of Finland"}],"funders":[{"id":"https://openalex.org/F4320321108","display_name":"Academy of Finland","ror":"https://ror.org/05k73zm37"},{"id":"https://openalex.org/F4320321726","display_name":"Suomen Kulttuurirahasto","ror":"https://ror.org/027xav248"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1975963573.pdf","grobid_xml":"https://content.openalex.org/works/W1975963573.grobid-xml"},"referenced_works_count":66,"referenced_works":["https://openalex.org/W162544871","https://openalex.org/W938539187","https://openalex.org/W1487612538","https://openalex.org/W1565354039","https://openalex.org/W1640263478","https://openalex.org/W1784600267","https://openalex.org/W1794348287","https://openalex.org/W1921404173","https://openalex.org/W1968475238","https://openalex.org/W1969357318","https://openalex.org/W1971332228","https://openalex.org/W1977545325","https://openalex.org/W1981509058","https://openalex.org/W1983383464","https://openalex.org/W1983924599","https://openalex.org/W1988245212","https://openalex.org/W1989047664","https://openalex.org/W1990061958","https://openalex.org/W1992442812","https://openalex.org/W2000875411","https://openalex.org/W2006046315","https://openalex.org/W2009329319","https://openalex.org/W2011039300","https://openalex.org/W2011753019","https://openalex.org/W2012660994","https://openalex.org/W2014286596","https://openalex.org/W2028599385","https://openalex.org/W2030646320","https://openalex.org/W2038230536","https://openalex.org/W2044935944","https://openalex.org/W2047617069","https://openalex.org/W2061043894","https://openalex.org/W2061884336","https://openalex.org/W2063382533","https://openalex.org/W2063556310","https://openalex.org/W2071442384","https://openalex.org/W2075322358","https://openalex.org/W2084224084","https://openalex.org/W2091299439","https://openalex.org/W2101199515","https://openalex.org/W2101548835","https://openalex.org/W2102813686","https://openalex.org/W2107079154","https://openalex.org/W2112232553","https://openalex.org/W2114348990","https://openalex.org/W2118395479","https://openalex.org/W2126766730","https://openalex.org/W2126924325","https://openalex.org/W2133459862","https://openalex.org/W2134800079","https://openalex.org/W2141458291","https://openalex.org/W2143513235","https://openalex.org/W2151265018","https://openalex.org/W2154431984","https://openalex.org/W2155804510","https://openalex.org/W2155839887","https://openalex.org/W2157529519","https://openalex.org/W2163326395","https://openalex.org/W2170765088","https://openalex.org/W2291195346","https://openalex.org/W2300684981","https://openalex.org/W2560367415","https://openalex.org/W2561675875","https://openalex.org/W2610179052","https://openalex.org/W2988480584","https://openalex.org/W4254807835"],"related_works":["https://openalex.org/W4232403550","https://openalex.org/W623607250","https://openalex.org/W4245429118","https://openalex.org/W4205110281","https://openalex.org/W2035485837","https://openalex.org/W2070875930","https://openalex.org/W2037870595","https://openalex.org/W3165916245","https://openalex.org/W2003676461","https://openalex.org/W2123652094"],"abstract_inverted_index":{"BACKGROUND:":[0],"Multi-assembly":[1],"problems":[2,132],"have":[3,15,114,146],"gathered":[4],"much":[5],"attention":[6],"in":[7,39,44,154,160,173,196,246],"the":[8,26,50,59,68,82,85,130,144,155,161,167,179,186,213,217,224,232,247],"last":[9],"years,":[10],"as":[11,23],"Next-Generation":[12],"Sequencing":[13],"technologies":[14],"started":[16],"being":[17],"applied":[18],"to":[19,147,178,201],"mixed":[20],"settings,":[21],"such":[22],"reads":[24,108,165,228,257,260],"from":[25,30,106],"transcriptome":[27],"(RNA-Seq),":[28],"or":[29,109,139],"viral":[31],"quasi-species.":[32],"One":[33],"classical":[34,180,218],"model":[35],"that":[36,65,159,191,240],"has":[37],"resurfaced":[38],"many":[40],"multi-assembly":[41,267],"methods":[42],"(e.g.":[43],"Cufflinks,":[45],"ShoRAH,":[46],"BRANCH,":[47],"CLASS)":[48],"is":[49,78,242,261],"Minimum":[51],"Path":[52],"Cover":[53],"(MPC)":[54],"Problem,":[55],"which":[56],"asks":[57],"for":[58],"minimum":[60,219],"number":[61,249],"of":[62,70,84,99,137,141,143,163,216,226,230,250],"directed":[63,72],"paths":[64],"cover":[66],"all":[67],"nodes":[69],"a":[71,135,176,199,202,207,263],"acyclic":[73],"graph.":[74],"The":[75],"MPC":[76,181,221],"Problem":[77],"highly":[79],"popular":[80],"because":[81],"acyclicity":[83],"graph":[86,145],"ensures":[87],"its":[88],"polynomial-time":[89,174,197],"solvability.":[90],"RESULTS:":[91],"In":[92,223],"this":[93],"paper,":[94],"we":[95,128,210,238],"consider":[96,185],"two":[97,119,131],"generalizations":[98],"it":[100,192,241],"dealing":[101],"with":[102],"integrating":[103],"constraints":[104],"arising":[105],"long":[107,164,256],"paired-end":[110,227,259],"reads;":[111],"these":[112],"extensions":[113],"also":[115,134,184,211,262],"been":[116],"considered":[117],"by":[118,151,175,198],"recent":[120],"methods,":[121],"but":[122,237],"not":[123],"fully":[124],"solved.":[125],"More":[126],"specifically,":[127],"study":[129],"where":[133],"set":[136],"subpaths,":[138,142],"pairs":[140],"be":[148,171,194],"entirely":[149],"covered":[150],"some":[152],"path":[153],"MPC.":[156],"We":[157,183],"show":[158,190,239],"case":[162,225],"(subpaths),":[166],"generalized":[168,233],"problem":[169,234],"can":[170,193],"solved":[172,195],"reduction":[177,200],"Problem.":[182,222],"weighted":[187],"case,":[188],"and":[189,258],"min-cost":[203],"circulation":[204],"problem.":[205],"As":[206],"side":[208],"result,":[209],"improve":[212],"time":[214],"complexity":[215],"weight":[220],"(pairs":[229],"subpaths),":[231],"becomes":[235],"NP-hard,":[236],"fixed-parameter":[243],"tractable":[244],"(FPT)":[245],"total":[248],"constraints.":[251],"This":[252],"computational":[253],"dichotomy":[254],"between":[255],"general":[264],"insight":[265],"into":[266],"problems.":[268]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}