Dynamic matchings in left vertex weighted convex bipartite graphs
A left vertex weighted convex bipartite graph (LWCBG) is a bipartite graph G = ( X , Y , E ) in which the neighbors of each x ∈ X form an interval in Y where Y is linearly ordered, and each x ∈ X has an associated weight. This paper considers the problem of maintaining a maximum weight matching in a...
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| Vydáno v: | Journal of combinatorial optimization Ročník 32; číslo 1; s. 25 - 50 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.07.2016
|
| Témata: | |
| ISSN: | 1382-6905, 1573-2886 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | A left vertex weighted convex bipartite graph (LWCBG) is a bipartite graph
G
=
(
X
,
Y
,
E
)
in which the neighbors of each
x
∈
X
form an interval in
Y
where
Y
is linearly ordered, and each
x
∈
X
has an associated weight. This paper considers the problem of maintaining a maximum weight matching in a dynamic LWCBG. The graph is subject to the updates of vertex and edge insertions and deletions. Our dynamic algorithms maintain the update operations in
O
(
log
2
|
V
|
)
amortized time per update, obtain the matching status of a vertex (whether it is matched) in constant worst-case time, and find the pair of a matched vertex (with which it is matched) in worst-case
O
(
k
)
time, where
k
is not greater than the cardinality of the maximum weight matching. That achieves the same time bound as the best known solution for the problem of the unweighted version. |
|---|---|
| ISSN: | 1382-6905 1573-2886 |
| DOI: | 10.1007/s10878-015-9890-x |