Minimum perfect bipartite matchings and spanning trees under categorization
Discrete Applied Mathematics
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
The complexity of bottleneck labeled graph problems
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
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We consider rooted minimum spanning tree problems subject to allowed ancestor relations which follow from network security constraints. In one problem nodes are associated with security labels that impose father-child relations. We prove that the feasible solutions define a matroid. In the other problem, there are permission constraints which impose descendant-ancestor relations. We show that even simple special cases of this problem are not approximable within a sub-logarithmic factor, and describe a square root approximation when the edge weights satisfy the triangle inequality.