On the complexity of clustering with relaxed size constraints in fixed dimension
We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Goldwurm, Massimiliano [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018transfer abstract |
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| Schlagwörter: |
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| Umfang: |
10 |
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| Übergeordnetes Werk: |
Enthalten in: Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries - Schweiss, Rüdiger ELSEVIER, 2015transfer abstract, the journal of the EATCS, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:717 ; year:2018 ; day:22 ; month:03 ; pages:37-46 ; extent:10 |
| Links: |
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| DOI / URN: |
10.1016/j.tcs.2017.04.017 |
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ELV042077559 |
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| 520 | |a We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. | ||
| 520 | |a We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. | ||
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10.1016/j.tcs.2017.04.017 doi GBV00000000000145A.pica (DE-627)ELV042077559 (ELSEVIER)S0304-3975(17)30461-9 DE-627 ger DE-627 rakwb eng 004 004 DE-600 620 VZ 690 VZ 50.92 bkl Goldwurm, Massimiliano verfasserin aut On the complexity of clustering with relaxed size constraints in fixed dimension 2018transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. Geometric clustering problems Elsevier Constrained k-Means Elsevier Computational complexity Elsevier Cluster size constraints Elsevier Lin, Jianyi oth Saccà, Francesco oth Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:717 year:2018 day:22 month:03 pages:37-46 extent:10 https://doi.org/10.1016/j.tcs.2017.04.017 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 717 2018 22 0322 37-46 10 045F 004 |
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10.1016/j.tcs.2017.04.017 doi GBV00000000000145A.pica (DE-627)ELV042077559 (ELSEVIER)S0304-3975(17)30461-9 DE-627 ger DE-627 rakwb eng 004 004 DE-600 620 VZ 690 VZ 50.92 bkl Goldwurm, Massimiliano verfasserin aut On the complexity of clustering with relaxed size constraints in fixed dimension 2018transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. Geometric clustering problems Elsevier Constrained k-Means Elsevier Computational complexity Elsevier Cluster size constraints Elsevier Lin, Jianyi oth Saccà, Francesco oth Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:717 year:2018 day:22 month:03 pages:37-46 extent:10 https://doi.org/10.1016/j.tcs.2017.04.017 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 717 2018 22 0322 37-46 10 045F 004 |
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10.1016/j.tcs.2017.04.017 doi GBV00000000000145A.pica (DE-627)ELV042077559 (ELSEVIER)S0304-3975(17)30461-9 DE-627 ger DE-627 rakwb eng 004 004 DE-600 620 VZ 690 VZ 50.92 bkl Goldwurm, Massimiliano verfasserin aut On the complexity of clustering with relaxed size constraints in fixed dimension 2018transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. Geometric clustering problems Elsevier Constrained k-Means Elsevier Computational complexity Elsevier Cluster size constraints Elsevier Lin, Jianyi oth Saccà, Francesco oth Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:717 year:2018 day:22 month:03 pages:37-46 extent:10 https://doi.org/10.1016/j.tcs.2017.04.017 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 717 2018 22 0322 37-46 10 045F 004 |
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10.1016/j.tcs.2017.04.017 doi GBV00000000000145A.pica (DE-627)ELV042077559 (ELSEVIER)S0304-3975(17)30461-9 DE-627 ger DE-627 rakwb eng 004 004 DE-600 620 VZ 690 VZ 50.92 bkl Goldwurm, Massimiliano verfasserin aut On the complexity of clustering with relaxed size constraints in fixed dimension 2018transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. Geometric clustering problems Elsevier Constrained k-Means Elsevier Computational complexity Elsevier Cluster size constraints Elsevier Lin, Jianyi oth Saccà, Francesco oth Enthalten in Elsevier Schweiss, Rüdiger ELSEVIER Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries 2015transfer abstract the journal of the EATCS Amsterdam [u.a.] (DE-627)ELV013125583 volume:717 year:2018 day:22 month:03 pages:37-46 extent:10 https://doi.org/10.1016/j.tcs.2017.04.017 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_40 50.92 Meerestechnik VZ AR 717 2018 22 0322 37-46 10 045F 004 |
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Enthalten in Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries Amsterdam [u.a.] volume:717 year:2018 day:22 month:03 pages:37-46 extent:10 |
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Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries |
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004 004 DE-600 620 VZ 690 VZ 50.92 bkl On the complexity of clustering with relaxed size constraints in fixed dimension Geometric clustering problems Elsevier Constrained k-Means Elsevier Computational complexity Elsevier Cluster size constraints Elsevier |
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Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries |
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Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries |
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On the complexity of clustering with relaxed size constraints in fixed dimension |
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Influence of bulk fibre properties of PAN-based carbon felts on their performance in vanadium redox flow batteries |
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on the complexity of clustering with relaxed size constraints in fixed dimension |
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On the complexity of clustering with relaxed size constraints in fixed dimension |
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We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. |
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We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. |
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We study the computational complexity of the problem of computing an optimal clustering { A 1 , A 2 , . . . , A k } of a set of points assuming that every cluster size | A i | belongs to a given set M of positive integers. We present a polynomial time algorithm for solving the problem in dimension 1, i.e. when the points are simply rational values, for an arbitrary set M of size constraints, which extends to the ℓ 1 -norm an analogous procedure known for the Euclidean norm. Moreover, we prove that in dimension 2, assuming Euclidean norm, the problem is (strongly) NP-hard with size constraints M = { 2 , 4 } . This result is extended also to the size constraints M = { 2 , 3 } both in the case of Euclidean and ℓ 1 -norm. |
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On the complexity of clustering with relaxed size constraints in fixed dimension |
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