Data Structures for On-Line Updating of Minimum Spanning Trees, With Applications. Frederickson, G. N. SIAM Journal on Computing, 14(4):781--798, 1985.
Paper doi abstract bibtex Data structures are presented for the problem of maintaining a minimum spanning tree on-line under the operation of updating the cost of some edge in the graph. For the case of a general graph, maintaining the data structure and updating the tree are shown to take \$O(\backslash sqrt m )\$ time, where m is the number of edges in the graph. For the case of a planar graph, a data structure is presented which supports an update time of \$O((\backslash log m)^2 )\$. These structures contribute to improved solutions for the on-line connected components problem and the problem of generating the K smallest spanning trees.
@article{ Frederickson1985,
abstract = {Data structures are presented for the problem of maintaining a minimum spanning tree on-line under the operation of updating the cost of some edge in the graph. For the case of a general graph, maintaining the data structure and updating the tree are shown to take \$O(\backslash sqrt m )\$ time, where m is the number of edges in the graph. For the case of a planar graph, a data structure is presented which supports an update time of \$O((\backslash log m)^2 )\$. These structures contribute to improved solutions for the on-line connected components problem and the problem of generating the K smallest spanning trees.},
author = {Frederickson, Greg N.},
doi = {10.1137/0214055},
file = {:Users/KunihiroWASA/Dropbox/paper/1985/Frederickson, Data Structures for On-Line Updating of Minimum Spanning Trees, With Applications, 1985.pdf:pdf},
isbn = {0897910990},
issn = {0097-5397},
journal = {SIAM Journal on Computing},
keywords = {1,a minimum,be maintained for an,connected components,consider the following on-line,data structures,edge insertion and deletion,introduction,k smallest spanning,minimum spanning tree,on-line computation,planar graphs,spanning tree is to,trees,underlying graph,update problem,which is modified repeatedly},
number = {4},
pages = {781--798},
title = {{Data Structures for On-Line Updating of Minimum Spanning Trees, With Applications}},
url = {http://epubs.siam.org/doi/abs/10.1137/0214055},
volume = {14},
year = {1985}
}
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