NP-completeness of minimum spanner problems

Restrictions of Minimum Spanner Problems

A t-spanner of a graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times their distance in G. Spanners arise in the context of approximating the original graph with a sparse subgraph (Peleg, D., and Scha ffer, A. A. (1989), J. Graph. Theory 13 (1), 99 116). The MINIMUM t-SPANNER problem seeks to find a t-spanner with the minimum number of edges f...

NP-Completeness of Minimum Rule Sets

Rule induction systems seek to generate rule sets which are optimal in the complexity of the rule set. This paper develops a formal proof of the NP-Completeness of the problem of generating the simplest rule set (MIN RS) which accurately predicts examples in the training set for a particular type of generalization algorithm algorithm and complexity measure. The proof is then informally extended...

Minimum weight Euclidean t-spanner is NP-hard

Given a set P of points in the plane, an Euclidean t-spanner for P is a geometric graph that preserves the Euclidean distances between every pair of points in P up to a constant factor t. The weight of a geometric graph refers to the total length of its edges. In this paper we show that the problem of deciding whether there exists an Euclidean t-spanner, for a given set of points in the plane, ...

NP-Completeness of Stage Illumination Problems

On Strong NP-Completeness of Rational Problems

The computational complexity of the partition, 0-1 subset sum, unbounded subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple variants were studied in numerous papers in the past where all the weights and profits were assumed to be integers. We re-examine here the computational complexity of all these problems in the setting where the weights and profits are allowed to be...