The inapproximability of non NP-hard optimization problems is investigated. Techniques are given to show that problems Log Dominating Set and Log Hypergraph Vertex Cover cannot be approximated to a constant ratio in polynomial time unless the corresponding NP-hard versions are also approximable in deterministic subexponential time. A direct connection is established between non NP-hard problems...

We consider the classical minimum makespan scheduling problem, where the processing time of job j on machine i is pij , and the matrix P = (pij)m×n is of a low rank. It is proved in [1] that rank 7 scheduling is NP-hard to approximate to a factor of 3/2− ǫ, and rank 4 scheduling is APX-hard (NP-hard to approximate within a factor of 1.03− ǫ). We improve this result by showing that rank 4 schedu...

The consequences of the existence of sparse hard sets for NP have been investigated for nearly 20 years. Many surprising results have been found, e.g. the result of Ogihara and Watanabe that P = NP is implied by the existence of sparse pbtt -hard sets for NP. It is clear that the existence of sparse hard sets for a weak reduction (e.g. pm) implies stronger results than the existence of sparse h...

In last decades, mobile factories have been used due to their high production capability, carrying their equipment and covering rough and uneven routes. Nowadays, more companies use mobile factories with the aim of reducing the transportation and manufacturing costs. The mobile factory must travel between the suppliers, visit all of them in each time period and return to the initial location of...

Tractability is the study of computational tasks with the goal of identifying which problem classes are tractable or, in other words, efficiently solvable. The class of tractable problems is traditionally assumed to be solvable in polynomial time by a deterministic Turing machine and is denoted by P. The class contains many natural tasks such as sorting a set of numbers, linear programming (the...

Recall that the approximation ratio for an approximation algorithm is a measure to evaluate the approximation performance of the algorithm. The closer the ratio to 1 the better the approximation performance of the algorithm. It is notable that there is a class of NP-hard optimization problems, most originating from scheduling problems, for which there are polynomial time approximation algorithm...

the allocation of human resources to project activities in order to schedule them is one of the closest states to the actual conditions of scheduling problems. but regarding the fact that this problem belongs to the class of np-hard problems; so far the exact methods have only been able to solve the small size problems. in this study, the renewable resources are humans in a way that every staff...

In this paper, we first introduce a generalized version of open shop scheduling (OSS), called generalized cyclic open shop scheduling (GCOSS) and then develop a hybrid method of metaheuristic to solve this problem. Open shop scheduling is concerned with processing n jobs on m machines, where each job has exactly m operations and operation i of each job has to be processed on machine i . However...

It was proved by [Garey and Johnson, 1983] that computing the crossing number of a graph is an NP -hard problem. Their reduction, however, used parallel edges and vertices of very high degrees. We prove here that it is NP -hard to determine the crossing number of a simple cubic graph. In particular, this implies that the minor-monotone version of crossing number is also NP -hard, which has been...

Weighted independent domination is an NP-hard graph problem, which remains computationally intractable in many restricted graph classes. In particular, the problem is NP-hard in the classes of sat-graphs and chordal graphs. We strengthen these results by showing that the problem is NP-hard in a proper subclass of the intersection of sat-graphs and chordal graphs. On the other hand, we identify ...