Medians of Binary Relations: computational complexity
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1992
|
| Schriftenreihe: | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC
1992,4 |
| Schlagwörter: | |
| Abstract: | Abstract: "Let R be the set of all binary relations on a finite set N and d be the symmetric difference distance defined on R. For a given profile II = (Rs, ..., R[subscript m]) [epsilon] R[superscript m], a relation R* [epsilon] R that minimizes the function [formula] is called a median relation of II. A number of problems occurring [sic] in the social sciences, in qualitative data analysis and in multicriteria decision making can be modelled as problems of finding medians of a profile of binary relations. In these contexts the profile II represents collected data (preferences, similarities, games) and the objective is that of finding a median relation of II with some special feature (representing e.g., consensus of preferences, clustering of similar objects, ranking of teams, etc.) In this paper we analyse the computational complexity of all such problems in which the median is required to satisfy one or more of the properties: reflexivity, symmetry, antisymmetry, transitivity and completeness. We prove that whenever transitivity is required (except when symmetry and completeness are also simultaneously required) then the corresponding median problem is NP-hard. In some cases we prove that they remain NP-hard when the profile II has a fixed number of binary relations. |
| Umfang: | 26 S. graph. Darst. |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV005877928 | ||
| 003 | DE-604 | ||
| 005 | 20120314 | ||
| 007 | t| | ||
| 008 | 921130s1992 xx d||| |||| 00||| engod | ||
| 035 | |a (OCoLC)28155328 | ||
| 035 | |a (DE-599)BVBBV005877928 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 | ||
| 100 | 1 | |a Wakabayashi, Yoshiko |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Medians of Binary Relations |b computational complexity |c Yoshiko Wakabayashi |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 1992 | |
| 300 | |a 26 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1992,4 | |
| 520 | 3 | |a Abstract: "Let R be the set of all binary relations on a finite set N and d be the symmetric difference distance defined on R. For a given profile II = (Rs, ..., R[subscript m]) [epsilon] R[superscript m], a relation R* [epsilon] R that minimizes the function [formula] is called a median relation of II. A number of problems occurring [sic] in the social sciences, in qualitative data analysis and in multicriteria decision making can be modelled as problems of finding medians of a profile of binary relations. In these contexts the profile II represents collected data (preferences, similarities, games) and the objective is that of finding a median relation of II with some special feature (representing e.g., consensus of preferences, clustering of similar objects, ranking of teams, etc.) | |
| 520 | 3 | |a In this paper we analyse the computational complexity of all such problems in which the median is required to satisfy one or more of the properties: reflexivity, symmetry, antisymmetry, transitivity and completeness. We prove that whenever transitivity is required (except when symmetry and completeness are also simultaneously required) then the corresponding median problem is NP-hard. In some cases we prove that they remain NP-hard when the profile II has a fixed number of binary relations. | |
| 650 | 4 | |a Computational complexity | |
| 830 | 0 | |a Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |v 1992,4 |w (DE-604)BV004801715 |9 1992,4 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-003680111 | |
Datensatz im Suchindex
| _version_ | 1818947980911181824 |
|---|---|
| any_adam_object | |
| author | Wakabayashi, Yoshiko |
| author_facet | Wakabayashi, Yoshiko |
| author_role | aut |
| author_sort | Wakabayashi, Yoshiko |
| author_variant | y w yw |
| building | Verbundindex |
| bvnumber | BV005877928 |
| ctrlnum | (OCoLC)28155328 (DE-599)BVBBV005877928 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02290nam a2200301 cb4500</leader><controlfield tag="001">BV005877928</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20120314 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">921130s1992 xx d||| |||| 00||| engod</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)28155328</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV005877928</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Wakabayashi, Yoshiko</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Medians of Binary Relations</subfield><subfield code="b">computational complexity</subfield><subfield code="c">Yoshiko Wakabayashi</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin</subfield><subfield code="b">Konrad-Zuse-Zentrum für Informationstechnik</subfield><subfield code="c">1992</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">26 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC</subfield><subfield code="v">1992,4</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">Abstract: "Let R be the set of all binary relations on a finite set N and d be the symmetric difference distance defined on R. For a given profile II = (Rs, ..., R[subscript m]) [epsilon] R[superscript m], a relation R* [epsilon] R that minimizes the function [formula] is called a median relation of II. A number of problems occurring [sic] in the social sciences, in qualitative data analysis and in multicriteria decision making can be modelled as problems of finding medians of a profile of binary relations. In these contexts the profile II represents collected data (preferences, similarities, games) and the objective is that of finding a median relation of II with some special feature (representing e.g., consensus of preferences, clustering of similar objects, ranking of teams, etc.)</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">In this paper we analyse the computational complexity of all such problems in which the median is required to satisfy one or more of the properties: reflexivity, symmetry, antisymmetry, transitivity and completeness. We prove that whenever transitivity is required (except when symmetry and completeness are also simultaneously required) then the corresponding median problem is NP-hard. In some cases we prove that they remain NP-hard when the profile II has a fixed number of binary relations.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computational complexity</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC</subfield><subfield code="v">1992,4</subfield><subfield code="w">(DE-604)BV004801715</subfield><subfield code="9">1992,4</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-003680111</subfield></datafield></record></collection> |
| id | DE-604.BV005877928 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T08:39:32Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003680111 |
| oclc_num | 28155328 |
| open_access_boolean | |
| owner | DE-12 |
| owner_facet | DE-12 |
| physical | 26 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| series2 | Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC |
| spelling | Wakabayashi, Yoshiko Verfasser aut Medians of Binary Relations computational complexity Yoshiko Wakabayashi Berlin Konrad-Zuse-Zentrum für Informationstechnik 1992 26 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1992,4 Abstract: "Let R be the set of all binary relations on a finite set N and d be the symmetric difference distance defined on R. For a given profile II = (Rs, ..., R[subscript m]) [epsilon] R[superscript m], a relation R* [epsilon] R that minimizes the function [formula] is called a median relation of II. A number of problems occurring [sic] in the social sciences, in qualitative data analysis and in multicriteria decision making can be modelled as problems of finding medians of a profile of binary relations. In these contexts the profile II represents collected data (preferences, similarities, games) and the objective is that of finding a median relation of II with some special feature (representing e.g., consensus of preferences, clustering of similar objects, ranking of teams, etc.) In this paper we analyse the computational complexity of all such problems in which the median is required to satisfy one or more of the properties: reflexivity, symmetry, antisymmetry, transitivity and completeness. We prove that whenever transitivity is required (except when symmetry and completeness are also simultaneously required) then the corresponding median problem is NP-hard. In some cases we prove that they remain NP-hard when the profile II has a fixed number of binary relations. Computational complexity Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC 1992,4 (DE-604)BV004801715 1992,4 |
| spellingShingle | Wakabayashi, Yoshiko Medians of Binary Relations computational complexity Konrad-Zuse-Zentrum für Informationstechnik <Berlin>: Preprint SC Computational complexity |
| title | Medians of Binary Relations computational complexity |
| title_auth | Medians of Binary Relations computational complexity |
| title_exact_search | Medians of Binary Relations computational complexity |
| title_full | Medians of Binary Relations computational complexity Yoshiko Wakabayashi |
| title_fullStr | Medians of Binary Relations computational complexity Yoshiko Wakabayashi |
| title_full_unstemmed | Medians of Binary Relations computational complexity Yoshiko Wakabayashi |
| title_short | Medians of Binary Relations |
| title_sort | medians of binary relations computational complexity |
| title_sub | computational complexity |
| topic | Computational complexity |
| topic_facet | Computational complexity |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT wakabayashiyoshiko mediansofbinaryrelationscomputationalcomplexity |