Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Fast algorithms for shortest paths in planar graphs, with applications
SIAM Journal on Computing
A faster approximation algorithm for the Steiner problem in graphs
Information Processing Letters
Faster shortest-path algorithms for planar graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Undirected single-source shortest paths with positive integer weights in linear time
Journal of the ACM (JACM)
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation Hardness of the Steiner Tree Problem on Graphs
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Improved Shortest Paths on the Word RAM
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
A Simple Shortest Path Algorithm with Linear Average Time
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
A Shortest Path Algorithm for Real-Weighted Undirected Graphs
SIAM Journal on Computing
| Hi-index | 0.00 |
We generalize the linear-time shortest-paths algorithm for planar graphs with nonnegative edge-weights of Henzinger et al. (1994) to work for any proper minor-closed class of graphs. We argue that their algorithm can not be adapted by standard methods to all proper minor-closed classes. By using recent deep results in graph minor theory, we show how to construct an appropriate recursive division in linear time for any graph excluding a fixed minor and how to transform the graph and its division afterwards, so that it has maximum degree three. Based on such a division, the original framework of Henzinger et al. can be applied. Afterwards, we show that using this algorithm, one can implement Mehlhorn's (1988) 2-approximation algorithm for the Steiner tree problem in linear time on these graph classes.