The edge versus path incidence matrix of series-parallel graphs and greedy packing
| Autor: | Alan J. Hoffman, Baruch Schieber |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Discrete mathematics
Series parallel graphs Applied Mathematics Incidence matrix Graph theory Packing problems Greedy algorithms Combinatorics Series-parallel graph Matrix (mathematics) Permutation Edge versus path incidence matrix Path (graph theory) Discrete Mathematics and Combinatorics Greedy algorithm Mathematics |
| Zdroj: | Discrete Applied Mathematics. 113:275-284 |
| ISSN: | 0166-218X |
| DOI: | 10.1016/s0166-218x(00)00294-8 |
| Popis: | We characterize the edge versus path incidence matrix of a series-parallel graph. One characterization is algorithmic while the second is structural. The structural characterization implies that the greedy algorithm solves the max flow problem in series-parallel graphs, as shown by Bein et al. (Discrete Appl. Math. 10 (1985) 117–124). The algorithmic characterization gives an efficient way to identify such matrices. Hoffman and Tucker (J. Combin. Theory Ser. A 47 (1988) 6–5). proved that a packing problem defined by a (0,1) matrix in which no column contains another column can be solved optimally using a greedy algorithm with any permutation on the variables if and only if the (0,1) matrix is the edge versus path incidence matrix of a series parallel graph. Thus, our algorithm can be applied to check whether such a packing problem is solvable greedily. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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