Approximation algorithms for solving the heterogeneous Chinese postman problem
Abstract In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph $$G=(V,E;w;r)$$ with length function $$w:E\rightarrow R^{+}$$ satisfying the triangle inequality, a fixed depot $$r\in V$$,...
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| Autor*in: |
Li, Jianping [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Journal of combinatorial optimization - Springer US, 1997, 45(2022), 1 vom: 25. Nov. |
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| Übergeordnetes Werk: |
volume:45 ; year:2022 ; number:1 ; day:25 ; month:11 |
| Links: |
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| DOI / URN: |
10.1007/s10878-022-00931-5 |
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OLC2080051970 |
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| 520 | |a Abstract In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph $$G=(V,E;w;r)$$ with length function $$w:E\rightarrow R^{+}$$ satisfying the triangle inequality, a fixed depot $$r\in V$$, and k vehicles having k nonuniform speeds $$\lambda _{1}, \lambda _{2}, \ldots ,\lambda _{k}$$, respectively, it is asked to find k tours in G for these k vehicles, each starting at the same depot r, and collectively traversing each edge in E at least once. The objective is to minimize the maximum completion time of vehicles, where the completion time of a vehicle is its total travel length divided by its speed. The main contribution of our paper is to show the following two results. (1) Given any small constant $$\delta >0$$, we design a $$20.8765(1+\delta )$$-approximation algorithm to solve the HCPP, where the running time required is bounded by a polynomial in the input size and $$\frac{1}{\delta }$$. (2) We present a $$(1+\varDelta -1/k)$$-approximation algorithm to solve the HCPP in cubic time, where $$\varDelta $$ is the ratio of the largest vehicle speed to the smallest one. | ||
| 650 | 4 | |a Combinatorial optimization | |
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| 650 | 4 | |a Heterogeneous Chinese postman tours | |
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| 700 | 1 | |a Lichen, Junran |4 aut | |
| 700 | 1 | |a Cai, Lijian |4 aut | |
| 700 | 1 | |a Wang, Wencheng |4 aut | |
| 700 | 1 | |a Liu, Suding |4 aut | |
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10.1007/s10878-022-00931-5 doi (DE-627)OLC2080051970 (DE-He213)s10878-022-00931-5-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Li, Jianping verfasserin (orcid)0000-0003-1508-1440 aut Approximation algorithms for solving the heterogeneous Chinese postman problem 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph $$G=(V,E;w;r)$$ with length function $$w:E\rightarrow R^{+}$$ satisfying the triangle inequality, a fixed depot $$r\in V$$, and k vehicles having k nonuniform speeds $$\lambda _{1}, \lambda _{2}, \ldots ,\lambda _{k}$$, respectively, it is asked to find k tours in G for these k vehicles, each starting at the same depot r, and collectively traversing each edge in E at least once. The objective is to minimize the maximum completion time of vehicles, where the completion time of a vehicle is its total travel length divided by its speed. The main contribution of our paper is to show the following two results. (1) Given any small constant $$\delta >0$$, we design a $$20.8765(1+\delta )$$-approximation algorithm to solve the HCPP, where the running time required is bounded by a polynomial in the input size and $$\frac{1}{\delta }$$. (2) We present a $$(1+\varDelta -1/k)$$-approximation algorithm to solve the HCPP in cubic time, where $$\varDelta $$ is the ratio of the largest vehicle speed to the smallest one. Combinatorial optimization Nonuniform speeds Heterogeneous Chinese postman tours Approximation algorithms Pan, Pengxiang aut Lichen, Junran aut Cai, Lijian aut Wang, Wencheng aut Liu, Suding aut Enthalten in Journal of combinatorial optimization Springer US, 1997 45(2022), 1 vom: 25. Nov. (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:45 year:2022 number:1 day:25 month:11 https://doi.org/10.1007/s10878-022-00931-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_2108 AR 45 2022 1 25 11 |
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10.1007/s10878-022-00931-5 doi (DE-627)OLC2080051970 (DE-He213)s10878-022-00931-5-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Li, Jianping verfasserin (orcid)0000-0003-1508-1440 aut Approximation algorithms for solving the heterogeneous Chinese postman problem 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph $$G=(V,E;w;r)$$ with length function $$w:E\rightarrow R^{+}$$ satisfying the triangle inequality, a fixed depot $$r\in V$$, and k vehicles having k nonuniform speeds $$\lambda _{1}, \lambda _{2}, \ldots ,\lambda _{k}$$, respectively, it is asked to find k tours in G for these k vehicles, each starting at the same depot r, and collectively traversing each edge in E at least once. The objective is to minimize the maximum completion time of vehicles, where the completion time of a vehicle is its total travel length divided by its speed. The main contribution of our paper is to show the following two results. (1) Given any small constant $$\delta >0$$, we design a $$20.8765(1+\delta )$$-approximation algorithm to solve the HCPP, where the running time required is bounded by a polynomial in the input size and $$\frac{1}{\delta }$$. (2) We present a $$(1+\varDelta -1/k)$$-approximation algorithm to solve the HCPP in cubic time, where $$\varDelta $$ is the ratio of the largest vehicle speed to the smallest one. Combinatorial optimization Nonuniform speeds Heterogeneous Chinese postman tours Approximation algorithms Pan, Pengxiang aut Lichen, Junran aut Cai, Lijian aut Wang, Wencheng aut Liu, Suding aut Enthalten in Journal of combinatorial optimization Springer US, 1997 45(2022), 1 vom: 25. Nov. (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:45 year:2022 number:1 day:25 month:11 https://doi.org/10.1007/s10878-022-00931-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_2108 AR 45 2022 1 25 11 |
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10.1007/s10878-022-00931-5 doi (DE-627)OLC2080051970 (DE-He213)s10878-022-00931-5-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Li, Jianping verfasserin (orcid)0000-0003-1508-1440 aut Approximation algorithms for solving the heterogeneous Chinese postman problem 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph $$G=(V,E;w;r)$$ with length function $$w:E\rightarrow R^{+}$$ satisfying the triangle inequality, a fixed depot $$r\in V$$, and k vehicles having k nonuniform speeds $$\lambda _{1}, \lambda _{2}, \ldots ,\lambda _{k}$$, respectively, it is asked to find k tours in G for these k vehicles, each starting at the same depot r, and collectively traversing each edge in E at least once. The objective is to minimize the maximum completion time of vehicles, where the completion time of a vehicle is its total travel length divided by its speed. The main contribution of our paper is to show the following two results. (1) Given any small constant $$\delta >0$$, we design a $$20.8765(1+\delta )$$-approximation algorithm to solve the HCPP, where the running time required is bounded by a polynomial in the input size and $$\frac{1}{\delta }$$. (2) We present a $$(1+\varDelta -1/k)$$-approximation algorithm to solve the HCPP in cubic time, where $$\varDelta $$ is the ratio of the largest vehicle speed to the smallest one. Combinatorial optimization Nonuniform speeds Heterogeneous Chinese postman tours Approximation algorithms Pan, Pengxiang aut Lichen, Junran aut Cai, Lijian aut Wang, Wencheng aut Liu, Suding aut Enthalten in Journal of combinatorial optimization Springer US, 1997 45(2022), 1 vom: 25. Nov. (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:45 year:2022 number:1 day:25 month:11 https://doi.org/10.1007/s10878-022-00931-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_2108 AR 45 2022 1 25 11 |
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10.1007/s10878-022-00931-5 doi (DE-627)OLC2080051970 (DE-He213)s10878-022-00931-5-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Li, Jianping verfasserin (orcid)0000-0003-1508-1440 aut Approximation algorithms for solving the heterogeneous Chinese postman problem 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph $$G=(V,E;w;r)$$ with length function $$w:E\rightarrow R^{+}$$ satisfying the triangle inequality, a fixed depot $$r\in V$$, and k vehicles having k nonuniform speeds $$\lambda _{1}, \lambda _{2}, \ldots ,\lambda _{k}$$, respectively, it is asked to find k tours in G for these k vehicles, each starting at the same depot r, and collectively traversing each edge in E at least once. The objective is to minimize the maximum completion time of vehicles, where the completion time of a vehicle is its total travel length divided by its speed. The main contribution of our paper is to show the following two results. (1) Given any small constant $$\delta >0$$, we design a $$20.8765(1+\delta )$$-approximation algorithm to solve the HCPP, where the running time required is bounded by a polynomial in the input size and $$\frac{1}{\delta }$$. (2) We present a $$(1+\varDelta -1/k)$$-approximation algorithm to solve the HCPP in cubic time, where $$\varDelta $$ is the ratio of the largest vehicle speed to the smallest one. Combinatorial optimization Nonuniform speeds Heterogeneous Chinese postman tours Approximation algorithms Pan, Pengxiang aut Lichen, Junran aut Cai, Lijian aut Wang, Wencheng aut Liu, Suding aut Enthalten in Journal of combinatorial optimization Springer US, 1997 45(2022), 1 vom: 25. Nov. (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:45 year:2022 number:1 day:25 month:11 https://doi.org/10.1007/s10878-022-00931-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_2108 AR 45 2022 1 25 11 |
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10.1007/s10878-022-00931-5 doi (DE-627)OLC2080051970 (DE-He213)s10878-022-00931-5-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 ssgn Li, Jianping verfasserin (orcid)0000-0003-1508-1440 aut Approximation algorithms for solving the heterogeneous Chinese postman problem 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph $$G=(V,E;w;r)$$ with length function $$w:E\rightarrow R^{+}$$ satisfying the triangle inequality, a fixed depot $$r\in V$$, and k vehicles having k nonuniform speeds $$\lambda _{1}, \lambda _{2}, \ldots ,\lambda _{k}$$, respectively, it is asked to find k tours in G for these k vehicles, each starting at the same depot r, and collectively traversing each edge in E at least once. The objective is to minimize the maximum completion time of vehicles, where the completion time of a vehicle is its total travel length divided by its speed. The main contribution of our paper is to show the following two results. (1) Given any small constant $$\delta >0$$, we design a $$20.8765(1+\delta )$$-approximation algorithm to solve the HCPP, where the running time required is bounded by a polynomial in the input size and $$\frac{1}{\delta }$$. (2) We present a $$(1+\varDelta -1/k)$$-approximation algorithm to solve the HCPP in cubic time, where $$\varDelta $$ is the ratio of the largest vehicle speed to the smallest one. Combinatorial optimization Nonuniform speeds Heterogeneous Chinese postman tours Approximation algorithms Pan, Pengxiang aut Lichen, Junran aut Cai, Lijian aut Wang, Wencheng aut Liu, Suding aut Enthalten in Journal of combinatorial optimization Springer US, 1997 45(2022), 1 vom: 25. Nov. (DE-627)216539323 (DE-600)1339574-9 (DE-576)094421935 1382-6905 nnns volume:45 year:2022 number:1 day:25 month:11 https://doi.org/10.1007/s10878-022-00931-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OLC-WIW SSG-OPC-MAT GBV_ILN_2108 AR 45 2022 1 25 11 |
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510 VZ 3,2 ssgn Approximation algorithms for solving the heterogeneous Chinese postman problem Combinatorial optimization Nonuniform speeds Heterogeneous Chinese postman tours Approximation algorithms |
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ddc 510 ssgn 3,2 misc Combinatorial optimization misc Nonuniform speeds misc Heterogeneous Chinese postman tours misc Approximation algorithms |
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ddc 510 ssgn 3,2 misc Combinatorial optimization misc Nonuniform speeds misc Heterogeneous Chinese postman tours misc Approximation algorithms |
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Approximation algorithms for solving the heterogeneous Chinese postman problem |
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Approximation algorithms for solving the heterogeneous Chinese postman problem |
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Li, Jianping |
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Journal of combinatorial optimization |
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Li, Jianping Pan, Pengxiang Lichen, Junran Cai, Lijian Wang, Wencheng Liu, Suding |
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approximation algorithms for solving the heterogeneous chinese postman problem |
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Approximation algorithms for solving the heterogeneous Chinese postman problem |
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Abstract In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph $$G=(V,E;w;r)$$ with length function $$w:E\rightarrow R^{+}$$ satisfying the triangle inequality, a fixed depot $$r\in V$$, and k vehicles having k nonuniform speeds $$\lambda _{1}, \lambda _{2}, \ldots ,\lambda _{k}$$, respectively, it is asked to find k tours in G for these k vehicles, each starting at the same depot r, and collectively traversing each edge in E at least once. The objective is to minimize the maximum completion time of vehicles, where the completion time of a vehicle is its total travel length divided by its speed. The main contribution of our paper is to show the following two results. (1) Given any small constant $$\delta >0$$, we design a $$20.8765(1+\delta )$$-approximation algorithm to solve the HCPP, where the running time required is bounded by a polynomial in the input size and $$\frac{1}{\delta }$$. (2) We present a $$(1+\varDelta -1/k)$$-approximation algorithm to solve the HCPP in cubic time, where $$\varDelta $$ is the ratio of the largest vehicle speed to the smallest one. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Abstract In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph $$G=(V,E;w;r)$$ with length function $$w:E\rightarrow R^{+}$$ satisfying the triangle inequality, a fixed depot $$r\in V$$, and k vehicles having k nonuniform speeds $$\lambda _{1}, \lambda _{2}, \ldots ,\lambda _{k}$$, respectively, it is asked to find k tours in G for these k vehicles, each starting at the same depot r, and collectively traversing each edge in E at least once. The objective is to minimize the maximum completion time of vehicles, where the completion time of a vehicle is its total travel length divided by its speed. The main contribution of our paper is to show the following two results. (1) Given any small constant $$\delta >0$$, we design a $$20.8765(1+\delta )$$-approximation algorithm to solve the HCPP, where the running time required is bounded by a polynomial in the input size and $$\frac{1}{\delta }$$. (2) We present a $$(1+\varDelta -1/k)$$-approximation algorithm to solve the HCPP in cubic time, where $$\varDelta $$ is the ratio of the largest vehicle speed to the smallest one. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Abstract In this paper, we consider the heterogeneous Chinese postman problem (the HCPP), which generalizes the k-Chinese postman problem. Specifically, given a weighted graph $$G=(V,E;w;r)$$ with length function $$w:E\rightarrow R^{+}$$ satisfying the triangle inequality, a fixed depot $$r\in V$$, and k vehicles having k nonuniform speeds $$\lambda _{1}, \lambda _{2}, \ldots ,\lambda _{k}$$, respectively, it is asked to find k tours in G for these k vehicles, each starting at the same depot r, and collectively traversing each edge in E at least once. The objective is to minimize the maximum completion time of vehicles, where the completion time of a vehicle is its total travel length divided by its speed. The main contribution of our paper is to show the following two results. (1) Given any small constant $$\delta >0$$, we design a $$20.8765(1+\delta )$$-approximation algorithm to solve the HCPP, where the running time required is bounded by a polynomial in the input size and $$\frac{1}{\delta }$$. (2) We present a $$(1+\varDelta -1/k)$$-approximation algorithm to solve the HCPP in cubic time, where $$\varDelta $$ is the ratio of the largest vehicle speed to the smallest one. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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