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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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 32; no. 1; pp. 25 - 50
Main Authors: Zu, Quan, Zhang, Miaomiao, Yu, Bin
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2016
Subjects:
Combinatorics
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Dynamic matching
BST
Alternating path
Implicit representation
Matroid
Weighted convex bipartite graph
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary: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