Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Fully dynamic planarity testing with applications
Journal of the ACM (JACM)
Hierarchical vertical decompositions, ray shooting, and circular arc queries in simple polygons
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Improved labeling scheme for ancestor queries
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Maintaining Center and Median in Dynamic Trees
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Short path queries in planar graphs in constant time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
JANUS: towards robust and malicious resilient routing in hybrid wireless networks
Proceedings of the 3rd ACM workshop on Wireless security
Multiple-source shortest paths in planar graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Maintaining information in fully dynamic trees with top trees
ACM Transactions on Algorithms (TALG)
A subset spanner for Planar graphs,: with application to subset TSP
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Oracles for bounded-length shortest paths in planar graphs
ACM Transactions on Algorithms (TALG)
On-line maintenance of simplified weighted graphs for efficient distance queries
GIS '06 Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems
Dynamic purity analysis for java programs
PASTE '07 Proceedings of the 7th ACM SIGPLAN-SIGSOFT workshop on Program analysis for software tools and engineering
Faster Regular Expression Matching
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Journal of Experimental Algorithmics (JEA)
Maintaining dynamic minimum spanning trees: An experimental study
Discrete Applied Mathematics
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Algorithms and theory of computation handbook
The tree inclusion problem: In linear space and faster
ACM Transactions on Algorithms (TALG)
Research paper: The saga of minimum spanning trees
Computer Science Review
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Ambivalent data structures are presented for several problems on undirected graphs. These data structures are used in finding the $k$ smallest spanning trees of a weighted undirected graph in $O(m \log \beta (m,n) + \min \{ k^{3/2}, km^{1/2} \} )$ time, where $m$ is the number of edges and $n$ the number of vertices in the graph. The techniques are extended to find the $k$ smallest spanning trees in an embedded planar graph in $O(n + k (\log n)^3 )$ time. Ambivalent data structures are also used to dynamically maintain 2-edge-connectivity information. Edges and vertices can be inserted or deleted in $O(m^{1/2})$ time, and a query as to whether two vertices are in the same 2-edge-connected component can be answered in $O(\log n)$ time, where $m$ and $n$ are understood to be the current number of edges and vertices, respectively.