Total dual integrality of the linear complementarity problem View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03

AUTHORS

Hanna Sumita, Naonori Kakimura, Kazuhisa Makino

ABSTRACT

In this paper, we introduce total dual integrality of the linear complementarity problem (LCP) by analogy with the linear programming problem. The main idea of defining the notion is to propose the LCP with orientation, a variant of the LCP whose feasible complementary cones are specified by an additional input vector. Then we naturally define the dual problem of the LCP with orientation and total dual integrality of the LCP. We show that if the LCP is totally dual integral, then all basic solutions are integral. If the input matrix is sufficient or rank-symmetric, and the LCP is totally dual integral, then our result implies that the LCP always has an integral solution whenever it has a solution. We also introduce a class of matrices such that any LCP instance having the matrix as a coefficient matrix is totally dual integral. We investigate relationships between matrix classes in the LCP literature such as principally unimodular matrices. Principally unimodular matrices are known that all basic solutions to the LCP are integral for any integral input vector. In addition, we show that it is coNP-hard to decide whether a given LCP instance is totally dual integral. More... »

PAGES

531-553

References to SciGraph publications

  • 1989-03. NP-Completeness of the linear complementarity problem in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2008-08. The complexity of recognizing linear systems with certain integrality properties in MATHEMATICAL PROGRAMMING
  • 1997. Matrix Algebra From a Statistician’s Perspective in NONE
  • 2011-06. Recognizing conic TDI systems is hard in MATHEMATICAL PROGRAMMING
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10479-018-2926-8

    DOI

    http://dx.doi.org/10.1007/s10479-018-2926-8

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1104600624


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Tokyo Metropolitan University", 
              "id": "https://www.grid.ac/institutes/grid.265074.2", 
              "name": [
                "Faculty of Economics and Business Administration, Tokyo Metropolitan University, 192-0397, Tokyo, Japan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Sumita", 
            "givenName": "Hanna", 
            "id": "sg:person.014752603443.11", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014752603443.11"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Keio University", 
              "id": "https://www.grid.ac/institutes/grid.26091.3c", 
              "name": [
                "Department of Mathematics, Keio University, 223-8522, Yokohama, Japan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Kakimura", 
            "givenName": "Naonori", 
            "id": "sg:person.010332452701.72", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010332452701.72"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Kyoto University", 
              "id": "https://www.grid.ac/institutes/grid.258799.8", 
              "name": [
                "Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Kyoto, Japan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Makino", 
            "givenName": "Kazuhisa", 
            "id": "sg:person.07741653331.03", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07741653331.03"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/b978-0-12-566780-7.50011-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1002224980"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10107-009-0294-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003845206", 
              "https://doi.org/10.1007/s10107-009-0294-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00940344", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004533629", 
              "https://doi.org/10.1007/bf00940344"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00940344", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004533629", 
              "https://doi.org/10.1007/bf00940344"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/b98818", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019237040", 
              "https://doi.org/10.1007/b98818"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/b98818", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019237040", 
              "https://doi.org/10.1007/b98818"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0024-3795(68)90052-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021814305"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.cor.2012.10.017", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023166969"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10107-007-0103-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032883236", 
              "https://doi.org/10.1007/s10107-007-0103-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10107-007-0103-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032883236", 
              "https://doi.org/10.1007/s10107-007-0103-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0167-5060(08)70734-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034679832"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0095-8956(92)90005-i", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1035998694"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1080/00207169008803803", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047102876"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/0024-3795(89)90463-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051924824"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/tpwrs.2012.2184562", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1061778537"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1287/mnsc.11.7.681", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064715257"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1287/mnsc.18.5.312", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064716997"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1287/moor.23.1.61", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064724129"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1287/moor.23.2.390", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064724136"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.15807/jorsj.35.45", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1090375590"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-03", 
        "datePublishedReg": "2019-03-01", 
        "description": "In this paper, we introduce total dual integrality of the linear complementarity problem (LCP) by analogy with the linear programming problem. The main idea of defining the notion is to propose the LCP with orientation, a variant of the LCP whose feasible complementary cones are specified by an additional input vector. Then we naturally define the dual problem of the LCP with orientation and total dual integrality of the LCP. We show that if the LCP is totally dual integral, then all basic solutions are integral. If the input matrix is sufficient or rank-symmetric, and the LCP is totally dual integral, then our result implies that the LCP always has an integral solution whenever it has a solution. We also introduce a class of matrices such that any LCP instance having the matrix as a coefficient matrix is totally dual integral. We investigate relationships between matrix classes in the LCP literature such as principally unimodular matrices. Principally unimodular matrices are known that all basic solutions to the LCP are integral for any integral input vector. In addition, we show that it is coNP-hard to decide whether a given LCP instance is totally dual integral.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s10479-018-2926-8", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.5829252", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.6838068", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.6826099", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1048429", 
            "issn": [
              "0254-5330", 
              "1572-9338"
            ], 
            "name": "Annals of Operations Research", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1-2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "274"
          }
        ], 
        "name": "Total dual integrality of the linear complementarity problem", 
        "pagination": "531-553", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "724295e295d3270a16f39ba8197666df97efd618d88772cb3d9aa4f2addec8a6"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10479-018-2926-8"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1104600624"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10479-018-2926-8", 
          "https://app.dimensions.ai/details/publication/pub.1104600624"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T14:00", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000371_0000000371/records_130826_00000005.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs10479-018-2926-8"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10479-018-2926-8'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10479-018-2926-8'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10479-018-2926-8'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10479-018-2926-8'


     

    This table displays all metadata directly associated to this object as RDF triples.

    142 TRIPLES      21 PREDICATES      44 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10479-018-2926-8 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Ne05df4e0556744a288388bd6d02044bd
    4 schema:citation sg:pub.10.1007/b98818
    5 sg:pub.10.1007/bf00940344
    6 sg:pub.10.1007/s10107-007-0103-y
    7 sg:pub.10.1007/s10107-009-0294-5
    8 https://doi.org/10.1016/0024-3795(68)90052-9
    9 https://doi.org/10.1016/0024-3795(89)90463-1
    10 https://doi.org/10.1016/0095-8956(92)90005-i
    11 https://doi.org/10.1016/b978-0-12-566780-7.50011-8
    12 https://doi.org/10.1016/j.cor.2012.10.017
    13 https://doi.org/10.1016/s0167-5060(08)70734-9
    14 https://doi.org/10.1080/00207169008803803
    15 https://doi.org/10.1109/tpwrs.2012.2184562
    16 https://doi.org/10.1287/mnsc.11.7.681
    17 https://doi.org/10.1287/mnsc.18.5.312
    18 https://doi.org/10.1287/moor.23.1.61
    19 https://doi.org/10.1287/moor.23.2.390
    20 https://doi.org/10.15807/jorsj.35.45
    21 schema:datePublished 2019-03
    22 schema:datePublishedReg 2019-03-01
    23 schema:description In this paper, we introduce total dual integrality of the linear complementarity problem (LCP) by analogy with the linear programming problem. The main idea of defining the notion is to propose the LCP with orientation, a variant of the LCP whose feasible complementary cones are specified by an additional input vector. Then we naturally define the dual problem of the LCP with orientation and total dual integrality of the LCP. We show that if the LCP is totally dual integral, then all basic solutions are integral. If the input matrix is sufficient or rank-symmetric, and the LCP is totally dual integral, then our result implies that the LCP always has an integral solution whenever it has a solution. We also introduce a class of matrices such that any LCP instance having the matrix as a coefficient matrix is totally dual integral. We investigate relationships between matrix classes in the LCP literature such as principally unimodular matrices. Principally unimodular matrices are known that all basic solutions to the LCP are integral for any integral input vector. In addition, we show that it is coNP-hard to decide whether a given LCP instance is totally dual integral.
    24 schema:genre research_article
    25 schema:inLanguage en
    26 schema:isAccessibleForFree false
    27 schema:isPartOf N7cbe899db4ff4ad7ad2c3e479a640689
    28 Nfcf378f8901042de912925820c63f38f
    29 sg:journal.1048429
    30 schema:name Total dual integrality of the linear complementarity problem
    31 schema:pagination 531-553
    32 schema:productId N16a1bf350d494335a2b464a74e425ca1
    33 N5718ca2a57404a5fa4b126367c5107b8
    34 N5f9d505534f64410a1c82a4d32d3b35c
    35 schema:sameAs https://app.dimensions.ai/details/publication/pub.1104600624
    36 https://doi.org/10.1007/s10479-018-2926-8
    37 schema:sdDatePublished 2019-04-11T14:00
    38 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    39 schema:sdPublisher N7ae79214f2084ebfb7663bb73d7cc79c
    40 schema:url https://link.springer.com/10.1007%2Fs10479-018-2926-8
    41 sgo:license sg:explorer/license/
    42 sgo:sdDataset articles
    43 rdf:type schema:ScholarlyArticle
    44 N0a5eab58d2fe475aadf93a633d3b5f4d rdf:first sg:person.07741653331.03
    45 rdf:rest rdf:nil
    46 N16a1bf350d494335a2b464a74e425ca1 schema:name readcube_id
    47 schema:value 724295e295d3270a16f39ba8197666df97efd618d88772cb3d9aa4f2addec8a6
    48 rdf:type schema:PropertyValue
    49 N5718ca2a57404a5fa4b126367c5107b8 schema:name doi
    50 schema:value 10.1007/s10479-018-2926-8
    51 rdf:type schema:PropertyValue
    52 N5f9d505534f64410a1c82a4d32d3b35c schema:name dimensions_id
    53 schema:value pub.1104600624
    54 rdf:type schema:PropertyValue
    55 N7ae79214f2084ebfb7663bb73d7cc79c schema:name Springer Nature - SN SciGraph project
    56 rdf:type schema:Organization
    57 N7cbe899db4ff4ad7ad2c3e479a640689 schema:volumeNumber 274
    58 rdf:type schema:PublicationVolume
    59 Nba600356cd484f719653e0af72f28493 rdf:first sg:person.010332452701.72
    60 rdf:rest N0a5eab58d2fe475aadf93a633d3b5f4d
    61 Ne05df4e0556744a288388bd6d02044bd rdf:first sg:person.014752603443.11
    62 rdf:rest Nba600356cd484f719653e0af72f28493
    63 Nfcf378f8901042de912925820c63f38f schema:issueNumber 1-2
    64 rdf:type schema:PublicationIssue
    65 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    66 schema:name Mathematical Sciences
    67 rdf:type schema:DefinedTerm
    68 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    69 schema:name Pure Mathematics
    70 rdf:type schema:DefinedTerm
    71 sg:grant.5829252 http://pending.schema.org/fundedItem sg:pub.10.1007/s10479-018-2926-8
    72 rdf:type schema:MonetaryGrant
    73 sg:grant.6826099 http://pending.schema.org/fundedItem sg:pub.10.1007/s10479-018-2926-8
    74 rdf:type schema:MonetaryGrant
    75 sg:grant.6838068 http://pending.schema.org/fundedItem sg:pub.10.1007/s10479-018-2926-8
    76 rdf:type schema:MonetaryGrant
    77 sg:journal.1048429 schema:issn 0254-5330
    78 1572-9338
    79 schema:name Annals of Operations Research
    80 rdf:type schema:Periodical
    81 sg:person.010332452701.72 schema:affiliation https://www.grid.ac/institutes/grid.26091.3c
    82 schema:familyName Kakimura
    83 schema:givenName Naonori
    84 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010332452701.72
    85 rdf:type schema:Person
    86 sg:person.014752603443.11 schema:affiliation https://www.grid.ac/institutes/grid.265074.2
    87 schema:familyName Sumita
    88 schema:givenName Hanna
    89 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014752603443.11
    90 rdf:type schema:Person
    91 sg:person.07741653331.03 schema:affiliation https://www.grid.ac/institutes/grid.258799.8
    92 schema:familyName Makino
    93 schema:givenName Kazuhisa
    94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07741653331.03
    95 rdf:type schema:Person
    96 sg:pub.10.1007/b98818 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019237040
    97 https://doi.org/10.1007/b98818
    98 rdf:type schema:CreativeWork
    99 sg:pub.10.1007/bf00940344 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004533629
    100 https://doi.org/10.1007/bf00940344
    101 rdf:type schema:CreativeWork
    102 sg:pub.10.1007/s10107-007-0103-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1032883236
    103 https://doi.org/10.1007/s10107-007-0103-y
    104 rdf:type schema:CreativeWork
    105 sg:pub.10.1007/s10107-009-0294-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003845206
    106 https://doi.org/10.1007/s10107-009-0294-5
    107 rdf:type schema:CreativeWork
    108 https://doi.org/10.1016/0024-3795(68)90052-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021814305
    109 rdf:type schema:CreativeWork
    110 https://doi.org/10.1016/0024-3795(89)90463-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051924824
    111 rdf:type schema:CreativeWork
    112 https://doi.org/10.1016/0095-8956(92)90005-i schema:sameAs https://app.dimensions.ai/details/publication/pub.1035998694
    113 rdf:type schema:CreativeWork
    114 https://doi.org/10.1016/b978-0-12-566780-7.50011-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002224980
    115 rdf:type schema:CreativeWork
    116 https://doi.org/10.1016/j.cor.2012.10.017 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023166969
    117 rdf:type schema:CreativeWork
    118 https://doi.org/10.1016/s0167-5060(08)70734-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034679832
    119 rdf:type schema:CreativeWork
    120 https://doi.org/10.1080/00207169008803803 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047102876
    121 rdf:type schema:CreativeWork
    122 https://doi.org/10.1109/tpwrs.2012.2184562 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061778537
    123 rdf:type schema:CreativeWork
    124 https://doi.org/10.1287/mnsc.11.7.681 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064715257
    125 rdf:type schema:CreativeWork
    126 https://doi.org/10.1287/mnsc.18.5.312 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064716997
    127 rdf:type schema:CreativeWork
    128 https://doi.org/10.1287/moor.23.1.61 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064724129
    129 rdf:type schema:CreativeWork
    130 https://doi.org/10.1287/moor.23.2.390 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064724136
    131 rdf:type schema:CreativeWork
    132 https://doi.org/10.15807/jorsj.35.45 schema:sameAs https://app.dimensions.ai/details/publication/pub.1090375590
    133 rdf:type schema:CreativeWork
    134 https://www.grid.ac/institutes/grid.258799.8 schema:alternateName Kyoto University
    135 schema:name Research Institute for Mathematical Sciences, Kyoto University, 606-8502, Kyoto, Japan
    136 rdf:type schema:Organization
    137 https://www.grid.ac/institutes/grid.26091.3c schema:alternateName Keio University
    138 schema:name Department of Mathematics, Keio University, 223-8522, Yokohama, Japan
    139 rdf:type schema:Organization
    140 https://www.grid.ac/institutes/grid.265074.2 schema:alternateName Tokyo Metropolitan University
    141 schema:name Faculty of Economics and Business Administration, Tokyo Metropolitan University, 192-0397, Tokyo, Japan
    142 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...