### 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 | Theory and Applications of Models of Computation - 10th International Conference, TAMC 2013, Proceedings |

Publisher | Springer Verlag |

Pages | 62-71 |

Number of pages | 10 |

ISBN (Print) | 9783642382352 |

DOIs | |

Publication status | Published - Jan 1 2013 |

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) |
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Volume | 7876 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### 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

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theory and Applications of Models of Computation - 10th International Conference, TAMC 2013, Proceedings*(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