Sentence examples for hardness proof from inspiring English sources

It will be used in our hardness proof and also in our algorithms.

The NP hardness proof follows a reduction from the minimum set cover problem (See the Supplementary Materials for the detailed proof).

We study its parameterized complexity, and identify computationally easy and hard cases by providing hardness proofs as well as efficient (fixed-parameter tractable) algorithms.

We give a full complexity classification of all eleven 2-Π problems, observing that in the switch from one to two linear orders the complexity landscape changes quite abruptly and that hardness proofs become rather intricate.

We first present a strong NP-hardness proof for the case with two working crews.

The NP-hardness proof considers the service selection problem on a sequence of operations.

Next, we show NP-hardness proof and design a pseudo-polynomial time dynamic programming algorithm for the problem of minimizing the number of tardy jobs.

Though some evidence of the computational difficulty of such problems can be found in the literature, no formal NP-hardness proof was available up to now.

The (mathcal {NP} -hardness proof is based on a Karp reduction, the principle of which (proof by contradiction) is depicted in Fig. 9.

In our NP-hardness proof we use a very general instance which makes the proof applicable to a large set of special cases of the RDAP, including several important scheduling problems whose complexity was unresolved heretofore.

The (mathcal {NP} -hardness proof presented here makes use of a reduction from the perfect matching with conflict pair constraints (PMPC) problem, which is known to be strongly (mathcal {NP} -hardness, 32].