
Planar Bichromatic Bottleneck Spanning Trees
Given a set P of n red and blue points in the plane, a planar bichromati...
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Degree Bounded Bottleneck Spanning Trees in Three Dimensions
The geometric δminimum spanning tree problem (δMST) is the problem of ...
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Deleting to Structured Trees
We consider a natural variant of the wellknown Feedback Vertex Set prob...
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On the minimum spanning tree problem in imprecise setup
In this article, we study the Euclidean minimum spanning tree problem in...
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The stochastic bilevel continuous knapsack problem with uncertain follower's objective
We consider a bilevel continuous knapsack problem where the leader contr...
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Cutting an alignment with Ockham's razor
In this article, we investigate different parsimonybased approaches tow...
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Biobjective Optimization Problems on Matroids with Binary Costs
Like most multiobjective combinatorial optimization problems, biobjectiv...
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On the Complexity of the Bilevel Minimum Spanning Tree Problem
We consider the bilevel minimum spanning tree (BMST) problem where the leader and the follower choose a spanning tree together, according to different objective functions. By showing that this problem is NPhard in general, we answer an open question stated by Shi et al. We prove that BMST remains hard even in the special case where the follower only controls a matching. Moreover, by a polynomial reduction from the vertexdisjoint Steiner trees problem, we give some evidence that BMST might even remain hard in case the follower controls only few edges. On the positive side, we present a polynomialtime (n1)approximation algorithm for BMST, where n is the number of vertices in the input graph. Moreover, considering the number of edges controlled by the follower as parameter, we show that 2approximating BMST is fixedparameter tractable and that, in case of uniform costs on leader's edges, even solving BMST exactly is fixedparameter tractable. We finally consider bottleneck variants of BMST and settle the complexity landscape of all combinations of sum or bottleneck objective functions for the leader and follower, for the optimistic as well as the pessimistic setting.
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