A note on approximation algorithms of the clustered traveling salesman problem
In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Bao, Xiaoguang [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017transfer abstract |
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| Schlagwörter: |
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| Umfang: |
4 |
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| Übergeordnetes Werk: |
Enthalten in: Galectin-3 in Atrial Fibrillation: A Novel Marker of Atrial Remodeling or Just Bystander? - Kornej, Jelena ELSEVIER, 2015, devoted to the rapid publication of short contributions to information processing, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:127 ; year:2017 ; pages:54-57 ; extent:4 |
| Links: |
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| DOI / URN: |
10.1016/j.ipl.2017.07.003 |
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ELV040599930 |
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| 520 | |a In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . | ||
| 520 | |a In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . | ||
| 650 | 7 | |a Traveling salesman problem |2 Elsevier | |
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| 700 | 1 | |a Li, Ganggang |4 oth | |
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10.1016/j.ipl.2017.07.003 doi GBV00000000000310_01.pica (DE-627)ELV040599930 (ELSEVIER)S0020-0190(17)30125-4 DE-627 ger DE-627 rakwb eng 610 VZ 510 VZ 31.80 bkl Bao, Xiaoguang verfasserin aut A note on approximation algorithms of the clustered traveling salesman problem 2017transfer abstract 4 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . Traveling salesman problem Elsevier Approximation algorithms Elsevier Clustered traveling salesman problem Elsevier Liu, Zhaohui oth Yu, Wei oth Li, Ganggang oth Enthalten in Elsevier Kornej, Jelena ELSEVIER Galectin-3 in Atrial Fibrillation: A Novel Marker of Atrial Remodeling or Just Bystander? 2015 devoted to the rapid publication of short contributions to information processing Amsterdam [u.a.] (DE-627)ELV023909307 volume:127 year:2017 pages:54-57 extent:4 https://doi.org/10.1016/j.ipl.2017.07.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_30 GBV_ILN_62 GBV_ILN_70 GBV_ILN_72 GBV_ILN_77 GBV_ILN_110 GBV_ILN_120 GBV_ILN_176 31.80 Angewandte Mathematik VZ AR 127 2017 54-57 4 |
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10.1016/j.ipl.2017.07.003 doi GBV00000000000310_01.pica (DE-627)ELV040599930 (ELSEVIER)S0020-0190(17)30125-4 DE-627 ger DE-627 rakwb eng 610 VZ 510 VZ 31.80 bkl Bao, Xiaoguang verfasserin aut A note on approximation algorithms of the clustered traveling salesman problem 2017transfer abstract 4 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . Traveling salesman problem Elsevier Approximation algorithms Elsevier Clustered traveling salesman problem Elsevier Liu, Zhaohui oth Yu, Wei oth Li, Ganggang oth Enthalten in Elsevier Kornej, Jelena ELSEVIER Galectin-3 in Atrial Fibrillation: A Novel Marker of Atrial Remodeling or Just Bystander? 2015 devoted to the rapid publication of short contributions to information processing Amsterdam [u.a.] (DE-627)ELV023909307 volume:127 year:2017 pages:54-57 extent:4 https://doi.org/10.1016/j.ipl.2017.07.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_30 GBV_ILN_62 GBV_ILN_70 GBV_ILN_72 GBV_ILN_77 GBV_ILN_110 GBV_ILN_120 GBV_ILN_176 31.80 Angewandte Mathematik VZ AR 127 2017 54-57 4 |
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10.1016/j.ipl.2017.07.003 doi GBV00000000000310_01.pica (DE-627)ELV040599930 (ELSEVIER)S0020-0190(17)30125-4 DE-627 ger DE-627 rakwb eng 610 VZ 510 VZ 31.80 bkl Bao, Xiaoguang verfasserin aut A note on approximation algorithms of the clustered traveling salesman problem 2017transfer abstract 4 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . Traveling salesman problem Elsevier Approximation algorithms Elsevier Clustered traveling salesman problem Elsevier Liu, Zhaohui oth Yu, Wei oth Li, Ganggang oth Enthalten in Elsevier Kornej, Jelena ELSEVIER Galectin-3 in Atrial Fibrillation: A Novel Marker of Atrial Remodeling or Just Bystander? 2015 devoted to the rapid publication of short contributions to information processing Amsterdam [u.a.] (DE-627)ELV023909307 volume:127 year:2017 pages:54-57 extent:4 https://doi.org/10.1016/j.ipl.2017.07.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_30 GBV_ILN_62 GBV_ILN_70 GBV_ILN_72 GBV_ILN_77 GBV_ILN_110 GBV_ILN_120 GBV_ILN_176 31.80 Angewandte Mathematik VZ AR 127 2017 54-57 4 |
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10.1016/j.ipl.2017.07.003 doi GBV00000000000310_01.pica (DE-627)ELV040599930 (ELSEVIER)S0020-0190(17)30125-4 DE-627 ger DE-627 rakwb eng 610 VZ 510 VZ 31.80 bkl Bao, Xiaoguang verfasserin aut A note on approximation algorithms of the clustered traveling salesman problem 2017transfer abstract 4 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . Traveling salesman problem Elsevier Approximation algorithms Elsevier Clustered traveling salesman problem Elsevier Liu, Zhaohui oth Yu, Wei oth Li, Ganggang oth Enthalten in Elsevier Kornej, Jelena ELSEVIER Galectin-3 in Atrial Fibrillation: A Novel Marker of Atrial Remodeling or Just Bystander? 2015 devoted to the rapid publication of short contributions to information processing Amsterdam [u.a.] (DE-627)ELV023909307 volume:127 year:2017 pages:54-57 extent:4 https://doi.org/10.1016/j.ipl.2017.07.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_30 GBV_ILN_62 GBV_ILN_70 GBV_ILN_72 GBV_ILN_77 GBV_ILN_110 GBV_ILN_120 GBV_ILN_176 31.80 Angewandte Mathematik VZ AR 127 2017 54-57 4 |
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10.1016/j.ipl.2017.07.003 doi GBV00000000000310_01.pica (DE-627)ELV040599930 (ELSEVIER)S0020-0190(17)30125-4 DE-627 ger DE-627 rakwb eng 610 VZ 510 VZ 31.80 bkl Bao, Xiaoguang verfasserin aut A note on approximation algorithms of the clustered traveling salesman problem 2017transfer abstract 4 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . Traveling salesman problem Elsevier Approximation algorithms Elsevier Clustered traveling salesman problem Elsevier Liu, Zhaohui oth Yu, Wei oth Li, Ganggang oth Enthalten in Elsevier Kornej, Jelena ELSEVIER Galectin-3 in Atrial Fibrillation: A Novel Marker of Atrial Remodeling or Just Bystander? 2015 devoted to the rapid publication of short contributions to information processing Amsterdam [u.a.] (DE-627)ELV023909307 volume:127 year:2017 pages:54-57 extent:4 https://doi.org/10.1016/j.ipl.2017.07.003 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_30 GBV_ILN_62 GBV_ILN_70 GBV_ILN_72 GBV_ILN_77 GBV_ILN_110 GBV_ILN_120 GBV_ILN_176 31.80 Angewandte Mathematik VZ AR 127 2017 54-57 4 |
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Enthalten in Galectin-3 in Atrial Fibrillation: A Novel Marker of Atrial Remodeling or Just Bystander? Amsterdam [u.a.] volume:127 year:2017 pages:54-57 extent:4 |
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Enthalten in Galectin-3 in Atrial Fibrillation: A Novel Marker of Atrial Remodeling or Just Bystander? Amsterdam [u.a.] volume:127 year:2017 pages:54-57 extent:4 |
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Galectin-3 in Atrial Fibrillation: A Novel Marker of Atrial Remodeling or Just Bystander? |
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In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . |
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In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . |
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In an earlier paper (Bao and Liu ), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter-node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu . Based on the above method, we then provide a 2.5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. . |
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