Paper Info
Title
Dynamic matchings in convex bipartite graphs
Abstract
We consider the problem of maintaining a maximum matching in a convex bipartite graph G = (V,E) under a set of update operations which includes insertions and deletions of vertices and edges. It is not hard to show that it is impossible to maintain an explicit representation of a maximum matching in sub-linear time per operation, even in the amortized sense. Despite this difficulty, we develop a data structure which maintains the set of vertices that participate in a maximum matching in O(log2 |V|) amortized time per update and reports the status of a vertex (matched or unmatched) in constant worst-case time. Our structure can report the mate of a matched vertex in the maximum matching in worst-case O(min{k log2 |V |+log |V|, |V| log |V|}) time, where k is the number of update operations since the last query for the same pair of vertices was made. In addition, we give an O(√|V| log2 |V|)-time amortized bound for this pair query.
Year
DOI
Venue
2007
10.1007/978-3-540-74456-6_37
MFCS
Keywords
Field
DocType
sub-linear time,amortized time,dynamic matchings,convex bipartite graph,worst-case o,maximum matching,constant worst-case time,amortized sense,k log2,last query,data structure,update operation,bipartite graph,linear time
Discrete mathematics,Combinatorics,Vertex (geometry),Amortized analysis,Bipartite graph,Convex bipartite graph,Neighbourhood (graph theory),Matching (graph theory),3-dimensional matching,Mathematics,Blossom algorithm
Conference
Volume
ISSN
ISBN
4708
0302-9743
3-540-74455-X
Citations 
PageRank 
References 
8
0.59
15
Authors
4
Name
Order
Citations
PageRank
Gerth Stølting Brodal1139986.30
Loukas Georgiadis225022.75
Kristoffer Arnsfelt Hansen317621.40
Irit Katriel417613.72