
Threedimensional matching is NPHard
The standard proof of NPHardness of 3DM provides a power4 reduction of...
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Embeddability in R^3 is NPhard
We prove that the problem of deciding whether a 2 or 3dimensional simp...
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A polynomialtime algorithm for the routing flow shop problem with two machines: an asymmetric network with a fixed number of nodes
We consider the routing flow shop problem with two machines on an asymme...
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Upward Planar Drawings with Three Slopes
We study upward planar straightline drawings that use only three differ...
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On the complexity of open shop scheduling with time lags
The minimization of makespan in open shop with time lags has been shown ...
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Degrees and Gaps: Tight Complexity Results of General Factor Problems Parameterized by Treewidth and Cutwidth
For the General Factor problem we are given an undirected graph G and fo...
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Multistage Committee Election
Electing a single committee of a small size is a classical and wellunde...
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Twomachine routing open shop on a tree: instance reduction and efficiently solvable subclass
The routing open shop problem is a natural combination of the metric traveling salesman problem and the classical open shop scheduling problem. Both counterparts generally are NPhard, being however polynomially solvable in special cases considered: TSP is trivial on a tree, and open shop is solvable in linear time in case of two machines by a wellknown GonzalezSahni algorithm (while being NPhard for three and more machines). Surprisingly, the combination of those problem becomes NPhard even in a simplest case of a twomachine routing open shop on a link. We describe an instance reduction procedure for the twomachine problem on arbitrary tree. The procedure preserves the standard lower bound on the makespan and allows to describe wide polynomially solvable subclasses of the problem. Conditions, describing these classes, allow building an optimal schedule in linear time. For any instance from those classes optimal makespan coincides with the standard lower bound.
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