### Abstract

In this paper we study a problem named graph partitioning with supply and demand (GPSD), motivated by applications in energy transmission. The input consists of an undirected graph G with the nodes partitioned into two sets: suppliers and consumers. Each supply node has associated a capacity and each consumer node has associated a demand. The goal is to find a subgraph of G and to partition it into trees, such that in each tree: (i) there is precisely one supplier and (ii) the total demand of the consumers is less than or equal to the capacity of the supplier. Moreover, we want to maximize the demand of all the consumers in such a partition. We also study a variation of the GPSD, termed energy delivery (ED). In this paper we show the following results: 1. A 2k-approximation algorithm for the GPSD problem, where k is the number of suppliers. This is the first approximation algorithm proposed for the general case. 2. A 2-approximation for the GPSD in the case of two suppliers implies a polynomial time algorithm for the famous minimum sum 2-disjoint paths problem, which is not known if it is in P or NP-hard. 3. The ED problem in the case of two or more suppliers is hard to approximate within any factor, assuming P ≠ NP.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 62-71 |

Number of pages | 10 |

Volume | 7876 LNCS |

ISBN (Print) | 9783642382352 |

DOIs | |

Publication status | Published - 2013 |

Externally published | Yes |

Event | 10th International Conference on Theory and Applications of Models of Computation, TAMC 2013 - Hong Kong, China Duration: May 20 2013 → May 22 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 7876 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 10th International Conference on Theory and Applications of Models of Computation, TAMC 2013 |
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Country | China |

City | Hong Kong |

Period | 5/20/13 → 5/22/13 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 7876 LNCS, pp. 62-71). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7876 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-642-38236-9_7

**Modelling the power supply network - Hardness and approximation.** / Popa, Alexandru.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 7876 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7876 LNCS, Springer Verlag, pp. 62-71, 10th International Conference on Theory and Applications of Models of Computation, TAMC 2013, Hong Kong, China, 5/20/13. https://doi.org/10.1007/978-3-642-38236-9_7

}

TY - GEN

T1 - Modelling the power supply network - Hardness and approximation

AU - Popa, Alexandru

PY - 2013

Y1 - 2013

N2 - In this paper we study a problem named graph partitioning with supply and demand (GPSD), motivated by applications in energy transmission. The input consists of an undirected graph G with the nodes partitioned into two sets: suppliers and consumers. Each supply node has associated a capacity and each consumer node has associated a demand. The goal is to find a subgraph of G and to partition it into trees, such that in each tree: (i) there is precisely one supplier and (ii) the total demand of the consumers is less than or equal to the capacity of the supplier. Moreover, we want to maximize the demand of all the consumers in such a partition. We also study a variation of the GPSD, termed energy delivery (ED). In this paper we show the following results: 1. A 2k-approximation algorithm for the GPSD problem, where k is the number of suppliers. This is the first approximation algorithm proposed for the general case. 2. A 2-approximation for the GPSD in the case of two suppliers implies a polynomial time algorithm for the famous minimum sum 2-disjoint paths problem, which is not known if it is in P or NP-hard. 3. The ED problem in the case of two or more suppliers is hard to approximate within any factor, assuming P ≠ NP.

AB - In this paper we study a problem named graph partitioning with supply and demand (GPSD), motivated by applications in energy transmission. The input consists of an undirected graph G with the nodes partitioned into two sets: suppliers and consumers. Each supply node has associated a capacity and each consumer node has associated a demand. The goal is to find a subgraph of G and to partition it into trees, such that in each tree: (i) there is precisely one supplier and (ii) the total demand of the consumers is less than or equal to the capacity of the supplier. Moreover, we want to maximize the demand of all the consumers in such a partition. We also study a variation of the GPSD, termed energy delivery (ED). In this paper we show the following results: 1. A 2k-approximation algorithm for the GPSD problem, where k is the number of suppliers. This is the first approximation algorithm proposed for the general case. 2. A 2-approximation for the GPSD in the case of two suppliers implies a polynomial time algorithm for the famous minimum sum 2-disjoint paths problem, which is not known if it is in P or NP-hard. 3. The ED problem in the case of two or more suppliers is hard to approximate within any factor, assuming P ≠ NP.

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U2 - 10.1007/978-3-642-38236-9_7

DO - 10.1007/978-3-642-38236-9_7

M3 - Conference contribution

SN - 9783642382352

VL - 7876 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 62

EP - 71

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -