An algorithm for covering polygons with rectangles
Information and Control
A weighted min-max relation for intervals
Journal of Combinatorial Theory Series A
Covering polygons with rectangles via edge coverings of bipartite permutation graphs
Journal of Information Processing and Cybernetics
Minimal edge-coverings of pairs of sets
Journal of Combinatorial Theory Series B
On edge perfectness and classes of bipartite graphs
Discrete Mathematics
Journal of Experimental Algorithmics (JEA)
Communication complexity
Optimizing combinatorial library construction via split synthesis
RECOMB '99 Proceedings of the third annual international conference on Computational molecular biology
Graph classes: a survey
Finding minimum generators of path systems
Journal of Combinatorial Theory Series B
Computing a minimum biclique cover is polynomial for bipartite domino-free graphs
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
The Computation of the Jump Number of Convex Graphs
ORDAL '94 Proceedings of the International Workshop on Orders, Algorithms, and Applications
The Jump Number Problem for Biconvex Graphs and Rectangle Covers of Rectangular Regions
FCT '89 Proceedings of the International Conference on Fundamentals of Computation Theory
Pushdown-reduce: an algorithm for connectivity augmentation and poset covering problems
Discrete Applied Mathematics
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Discrete Applied Mathematics
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
Flows in Networks
An algorithm to increase the node-connectivity of a digraph by one
Discrete Optimization
Approximating minimum manhattan networks in higher dimensions
ESA'11 Proceedings of the 19th European conference on Algorithms
Approximating hitting sets of axis-parallel rectangles intersecting a monotone curve
Computational Geometry: Theory and Applications
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We model maximum cross-free matchings and minimum biclique covers of two-directional orthogonal ray graphs (2-dorgs) as maximum independent sets and minimum hitting sets of an associated family of rectangles in the plane, respectively. We then compute the corresponding maximum independent set using linear programming and uncrossing techniques. This procedure motivates an efficient combinatorial algorithm to find a cross-free matching and a biclique cover of the same cardinality, proving the corresponding min-max relation. We connect this min-max relation with the work of Györi [19], Lubiw[23], and Frank and Jordán [16] on seemingly unrelated problems. Our result can be seen as a non-trivial application of Frank and Jordán's Theorem. As a direct consequence, we obtain the first polynomial algorithm for the jump number problem on 2-dorgs. For the subclass of convex graphs, our approach is a vast improvement over previous algorithms. Additionally, we prove that the weighted maximum cross-free matching problem is NP-complete for 2-dorgs and give polynomial algorithms for some subclasses.