Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Approximation algorithms for time constrained scheduling
Information and Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Complexity of Scheduling Incompatible Jobs with Unit-Times
MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
An Approximation Scheme for Bin Packing with Conflicts
SWAT '98 Proceedings of the 6th Scandinavian Workshop on Algorithm Theory
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For the classical minimum spanning tree problem we introduce disjunctive constraints for pairs of edges which can not be both included in the spanning tree at the same time. These constraints are represented by a conflict graph whose vertices correspond to the edges of the original graph. Edges in the conflict graph connect conflicting edges of the original graph. It is shown that the problem becomes strongly $\mathcal{NP}$-hard even if the connected components of the conflict graph consist only of paths of length two. On the other hand, for conflict graphs consisting of disjoint edges (i.e. paths of length one) the problem remains polynomially solvable.