{"id":"https://openalex.org/W7220378806","doi":"https://doi.org/10.48550/arxiv.2610.03336","title":"Optimal allocation in combat models with multiple battlefields","display_name":"Optimal allocation in combat models with multiple battlefields","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220378806","doi":"https://doi.org/10.48550/arxiv.2610.03336"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03336","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03336","pdf_url":"https://arxiv.org/pdf/2610.03336","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.03336","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080936602","display_name":"Anton\u00edn Slav\u00edk","orcid":"https://orcid.org/0000-0003-3941-7375","observed_orcids":["https://orcid.org/0000-0003-3941-7375"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Slav\u00edk, Anton\u00edn","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071166642","display_name":"Vladim\u00edr \u0160v\u00edgler","orcid":"https://orcid.org/0000-0003-0063-3564","observed_orcids":["https://orcid.org/0000-0003-0063-3564"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"\u0160v\u00edgler, Vladim\u00edr","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":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/T13371","display_name":"Military Defense Systems Analysis","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13371","display_name":"Military Defense Systems Analysis","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.0044999998062849045,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T11031","display_name":"Game Theory and Applications","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/force-allocation","display_name":"force allocation","score":0.7369999885559082},{"id":"https://openalex.org/keywords/combat-models","display_name":"combat models","score":0.7900000214576721},{"id":"https://openalex.org/keywords/loss-functions","display_name":"loss functions","score":0.5559999942779541},{"id":"https://openalex.org/keywords/survival-function","display_name":"survival function","score":0.7799999713897705},{"id":"https://openalex.org/keywords/convex-loss-functions","display_name":"convex loss functions","score":0.6769999861717224},{"id":"https://openalex.org/keywords/np-hardness","display_name":"NP-hardness","score":0.9490000009536743},{"id":"https://openalex.org/keywords/pseudo-polynomial-time-algorithm","display_name":"pseudo-polynomial time algorithm","score":0.984000027179718},{"id":"https://openalex.org/keywords/lanchester-combat-model","display_name":"Lanchester combat model","score":0.7950000166893005},{"id":"https://openalex.org/keywords/optimal-allocation","display_name":"optimal allocation","score":0.3700000047683716}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6098999977111816},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5855000019073486},{"id":"https://openalex.org/C41065033","wikidata":"https://www.wikidata.org/wiki/Q2825412","display_name":"Adversary","level":2,"score":0.5638999938964844},{"id":"https://openalex.org/C3020013979","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Optimal allocation","level":2,"score":0.5530999898910522},{"id":"https://openalex.org/C2779669469","wikidata":"https://www.wikidata.org/wiki/Q4895508","display_name":"Battlefield","level":2,"score":0.541100025177002},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46389999985694885},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.37700000405311584},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35120001435279846},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.3314000070095062},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.32280001044273376},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.2628999948501587}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03336","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03336","pdf_url":"https://arxiv.org/pdf/2610.03336","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,"listed_in":[],"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.2610.03336","doi":"https://doi.org/10.48550/arxiv.2610.03336","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03336","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,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.03336","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03336","pdf_url":"https://arxiv.org/pdf/2610.03336","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,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220378806.pdf","grobid_xml":"https://content.openalex.org/works/W7220378806.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2148867127","https://openalex.org/W2142069996","https://openalex.org/W2039358176","https://openalex.org/W2137072708","https://openalex.org/W1994899936","https://openalex.org/W3148149388","https://openalex.org/W2020114909","https://openalex.org/W3092166802","https://openalex.org/W2075110736","https://openalex.org/W4382401921"],"abstract_inverted_index":{"We":[0,59,97],"study":[1],"the":[2,84,88,111,125],"allocation":[3,33,50,100],"of":[4,7,18,40,66,113],"a":[5,8,15,37,121],"force":[6,90],"fixed":[9],"size":[10,91],"across":[11],"independent":[12],"battlefields":[13],"against":[14],"known":[16],"distribution":[17],"opposing":[19],"forces.":[20],"Formulating":[21],"battlefield":[22],"outcomes":[23],"through":[24],"loss":[25,46,71],"and":[26,77,92,109,129],"survival":[27],"functions":[28,72],"allows":[29],"us":[30],"to":[31,116],"establish":[32],"results":[34],"without":[35],"assuming":[36],"specific":[38],"system":[39],"combat":[41,131],"equations.":[42],"For":[43],"convex":[44],"enemy":[45,114],"functions,":[47],"an":[48,74,79],"optimal":[49],"exists":[51],"with":[52,137],"at":[53],"most":[54],"one":[55],"partially":[56],"saturated":[57],"battlefield.":[58],"prove":[60],"NP-hardness":[61],"for":[62,83,102],"every":[63],"prescribed":[64],"family":[65,123],"strictly":[67,69],"convex,":[68],"increasing":[70],"satisfying":[73],"endpoint":[75],"normalization,":[76],"give":[78],"exact":[80],"pseudopolynomial":[81],"algorithm":[82],"special":[85],"case":[86],"when":[87],"total":[89],"saturation":[93],"thresholds":[94],"are":[95],"integers.":[96],"also":[98],"derive":[99],"rules":[101],"maximizing":[103,106,110],"successful":[104],"engagements,":[105],"own":[107,117],"survivors,":[108],"ratio":[112],"losses":[115],"losses.":[118],"Applications":[119],"include":[120],"power-law":[122],"containing":[124],"classical":[126],"Lanchester,":[127],"guerrilla,":[128],"mixed":[130],"models,":[132],"as":[133,135],"well":[134],"models":[136],"implicitly":[138],"defined":[139],"outcomes.":[140]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-06T00:00:00"}