| Presentation | 1995/9/22 Generalized k-edge-partition problem with specified bases Hiroshi NAGAMOCHI, Toshimasa ISHII, Toshihide IBARAKI, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Given an undirected graph G=(V, E) with k distinct edges e_i∈E(i=1,…,k), and natural numbers m_i(i=1,…,k) such that m_1+…+m_k=|E|, the k-edge-partition problem with specified bases asks to find a partition E_1…∪E_k of E such that (1)e_i∈E_i, and |E_i|=m_i(i=1,…,k), (2)each E_i induces a connected subgraph. It has been shown that there exists such a partition E_1∪…∪E_k if G is k-edge-connected. If the input graph is k-edge-connected, polynomial time algorithms for solving this problem are known for k=2,3, but no polynomial time algorithm is known for k≥4. In this paper, we generalize the probrem as follows. Given an undirected graph G=(V,E), where each vertex has some labels chosen from a label set {1,…,k}, and natural numbers m_i(i=1,…,k) such that m_1+…+m_k=|E|, the k-edge-partition problem with specified labels asks to find a partition E_1∪…∪E_k of E such that (i)|E_i|= m_i, and (ii) each connected component induced by E_i contains a vertex which has label i. We present a sufficient condition for this problem with k=2,3 to have such a partition, and construct O(|E|) and O(|E|+|V|^2) time algorithms for finding a partition under the condition for k=2 and 3, respectively. And we show that this problem can be solved in O(|E|)(k=2), O(|E|+|V|^2)(k=3) time. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | k-edge-connected graph / k-edge-partition problem with specified bases / graph with specified labels / k-edge-partition problem with specified labels |
| Paper # | COMP95-46 |
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| Conference Information | |
| Committee | COMP |
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| Conference Date | 1995/9/22(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Theoretical Foundations of Computing (COMP) |
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| Language | ENG |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Generalized k-edge-partition problem with specified bases |
| Sub Title (in English) | |
| Keyword(1) | k-edge-connected graph |
| Keyword(2) | k-edge-partition problem with specified bases |
| Keyword(3) | graph with specified labels |
| Keyword(4) | k-edge-partition problem with specified labels |
| 1st Author's Name | Hiroshi NAGAMOCHI |
| 1st Author's Affiliation | Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University() |
| 2nd Author's Name | Toshimasa ISHII |
| 2nd Author's Affiliation | Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University |
| 3rd Author's Name | Toshihide IBARAKI |
| 3rd Author's Affiliation | Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University |
| Date | 1995/9/22 |
| Paper # | COMP95-46 |
| Volume (vol) | vol.95 |
| Number (no) | 259 |
| Page | pp.pp.- |
| #Pages | 10 |
| Date of Issue | |