An algorithm for covering polygons with rectangles
Information and Control
Edge-connectivity augmentation problems
Journal of Computer and System Sciences
A weighted min-max relation for intervals
Journal of Combinatorial Theory Series A
Augmenting graphs to meet edge-connectivity requirements
SIAM Journal on Discrete Mathematics
Efficient splitting off algorithms for graphs
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On the optimal vertex-connectivity augmentation
Journal of Combinatorial Theory Series B
Minimal edge-coverings of pairs of sets
Journal of Combinatorial Theory Series B
Journal of Experimental Algorithmics (JEA)
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Finding maximum flows in undirected graphs seems easier than bipartite matching
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Finding minimum generators of path systems
Journal of Combinatorial Theory Series B
Augmenting undirected edge connectivity in Õ(n2) time
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Dilworth's Theorem and Its Application for Path Systems of a Cycle - Implementation and Analysis
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Primal-dual approach for directed vertex connectivity augmentation and generalizations
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Primal-dual approach for directed vertex connectivity augmentation and generalizations
ACM Transactions on Algorithms (TALG)
Jump number of two-directional orthogonal ray graphs
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
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In their seminal paper, Frank and Jordán show that a large class of optimization problems including certain directed edge augmentation ones fall into the class of covering supermodular functions over pairs of sets. They also give an algorithm for such problems, however, that relies on the ellipsoid method.Our main result is a combinatorial algorithm for the restricted covering problem when the supermodular function is 0-1 valued; the problem includes directed vertex or S-T connectivity augmentation by one. Our algorithm uses an approach completely different from that of an independent recent result of Frank. It finds covers of partially ordered sets that satisfy natural abstract properties slightly extending those in Frank and Jordán. The algorithm resembles primal-dual augmenting path algorithms: For an initial (possibly greedy) cover the algorithm searches for witnesses for the necessity of each element in the cover. If no two witness have a common cover, the solution is optimal. As long as this is not the case, the witnesses are gradually exchanged by smaller ones (PUSHDOWN step). Each witness change defines an appropriate change in the solution; these changes are finally unwound in a shortest path manner to obtain a solution of size one less (REDUCE step).