Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2014
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/1410.3408 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909870164279296 |
|---|---|
| author | Rajabi-Alni, Fatemeh Minaei-Bidgoli, Behrouz |
| author_facet | Rajabi-Alni, Fatemeh Minaei-Bidgoli, Behrouz |
| contents | Given an undirected bipartite graph $G=(A \cup B, E)$, a many-to-many matching (MM) in $G$ matches each vertex $v$ in $A$ (resp. $B$) to at least one vertex in $B$ (resp. $A$). In this paper, we consider the limited-capacity many-to-many matching (LCMM) in $G$, where each vertex $v\in A\cup B$ is matched to at least one and at most $Cap(v)$ vertices; the function $Cap : A\cup B \rightarrow \mathbb{Z}> 0$ denotes the capacity of $v$ (an upper bound on its degree in the LCMM). We give an $O(n^3)$ time algorithm for finding a maximum (respectively minimum) weight LCMM in $G$ with non-positive real (respectively non-negative real) edge weights, where $\lvert A \rvert+\lvert B \rvert=n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1410_3408 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | An $O(n^3)$ time algorithm for the maximum-weight limited-capacity many-to-many matching Rajabi-Alni, Fatemeh Minaei-Bidgoli, Behrouz Data Structures and Algorithms Given an undirected bipartite graph $G=(A \cup B, E)$, a many-to-many matching (MM) in $G$ matches each vertex $v$ in $A$ (resp. $B$) to at least one vertex in $B$ (resp. $A$). In this paper, we consider the limited-capacity many-to-many matching (LCMM) in $G$, where each vertex $v\in A\cup B$ is matched to at least one and at most $Cap(v)$ vertices; the function $Cap : A\cup B \rightarrow \mathbb{Z}> 0$ denotes the capacity of $v$ (an upper bound on its degree in the LCMM). We give an $O(n^3)$ time algorithm for finding a maximum (respectively minimum) weight LCMM in $G$ with non-positive real (respectively non-negative real) edge weights, where $\lvert A \rvert+\lvert B \rvert=n$. |
| title | An $O(n^3)$ time algorithm for the maximum-weight limited-capacity many-to-many matching |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/1410.3408 |