Abstract
We consider the problem which is dynamically maintaining a maximum weight matching in a left weighted convex bipartite graph G = (V,E), V = X ∪ Y, in which each x ∈ X has an associated weight, and neighbors of each x ∈ X form an interval in the ordered Y set. The maintenance includes update operations (vertices and edges insertions and deletions) and query operations (inquiries of a vertex matching information). We reduce this problem to the corresponding unweighted problem and design an algorithm that maintains the update operations in O(log3|V|) amortized time per update. In addition, we develop a data structure to 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.
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Zu, Q., Zhang, M., Yu, B. (2014). Dynamic Matchings in Left Weighted Convex Bipartite Graphs. In: Chen, J., Hopcroft, J.E., Wang, J. (eds) Frontiers in Algorithmics. FAW 2014. Lecture Notes in Computer Science, vol 8497. Springer, Cham. https://doi.org/10.1007/978-3-319-08016-1_30
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DOI: https://doi.org/10.1007/978-3-319-08016-1_30
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