We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list here includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor possesses a given eigenvalue, singular value, or spectral norm; approximating an eigenvalue, eigenvector, singular vector, or the spectral norm; and determi...

String problems arise in various applications ranging from text mining to biological sequence analysis. Many string problems are NP-hard. This motivates the search for (fixed-parameter) tractable special cases of these problems. We survey parameterized and multivariate algorithmics results for NP-hard string problems and identify challenges for future research.

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 chapter, we discuss approximation algorithms for optimization problems. An optimization problem consists in finding the best (cheapest, heaviest, etc.) element in a large set P, called the feasible region and usually specified implicitly, where the quality of elements of the set are evaluated using a function f(x), the objective function, usually something fairly simple. The element tha...

We study the effects of faulty data on NP-hard sets. We consider hard sets for several polynomial time reductions, add corrupt data and then analyze whether the resulting sets are still hard for NP. We explain that our results are related to a weakened deterministic variant of the notion of program self-correction by Blum, Luby, and Rubinfeld. Among other results, we use the Left-Set technique ...

Two subproblems that arise when routing channels with interchangeable terminals are shown to be NP-hard. These problems are: P1: Is there a net to terminal assignment that results in an acyclic vertical constraint graph? P2: For instances with acyclic vertical constraint graphs, obtain net to terminal assignments for which the length of the longest path in the vertical constraint graph is minimum.

The discrete gate sizing problem has been studied by several researchers recently. Some Complexity results have been obtained, ana' a number of heuristic algorithms have been proposed. For circuit networks that are restricted to the set of trees, or series-parallel graphs pseudo-polynomial time algorithms to obtain the exact solution have also been proposed, though none can be extended to arbit...

There exist a number of problem classes for which obtaining the exact solution becomes exponentially expensive with increasing problem size. The quadratic assignment problem (QAP) or the travelling salesman problem (TSP) are just two examples of such NP-hard problems. In practice, approximate algorithms are employed to obtain a suboptimal solution, where one must face a trade-off between comput...

assigning facilities to locations is one of the important problems, which significantly is influence in transportation cost reduction. in this study, we solve quadratic assignment problem (qap), using a meta-heuristic algorithm with deterministic tasks and equality in facilities and location number. it should be noted that any facility must be assign to only one location. in this paper, first o...