We show that solving linear programming (LP) relaxations of many classical NP-hard combinatorial optimization problems is as hard as solving the general LP problem. Precisely, the general LP can be reduced in linear time to the LP relaxation of each of these problems. This result poses a fundamental limitation for designing efficient algorithms to solve the LP relaxations, because finding such ...

evolutionary algorithms are some of the most crucial random approaches tosolve the problems, but sometimes generate low quality solutions. on the otherhand, learning automata are adaptive decision-making devices, operating onunknown random environments, so it seems that if evolutionary and learningautomaton based algorithms are operated simultaneously, the quality of results willincrease sharpl...

We formally study two methods for data sanitation that have been used extensively in the database community: k-anonymity and l-diversity. We settle several open problems concerning the difficulty of applying these methods optimally, proving both positive and negative results: – 2-anonymity is in P. – The problem of partitioning the edges of a triangle-free graph into 4-stars (degree-three verti...

This work deals with a class of problems under interval data uncertainty, namely interval robusthard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible so...

Solving some mathematical problems such as NP-complete problems by conventional silicon-based computers is problematic and takes so long time. DNA computing is an alternative method of computing which uses DNA molecules for computing purposes. DNA computers have massive degrees of parallel processing capability. The massive parallel processing characteristic of DNA computers is of particular in...

  In this paper, a single machine sequencing problem is considered in order to find the sequence of jobs minimizing the sum of the maximum earliness and tardiness with idle times (n/1/I/ETmax). Due to the time complexity function, this sequencing problem belongs to a class of NP-hard ones. Thus, a special design of a simulated annealing (SA) method is applied to solve such a hard problem. To co...

The problem of (approximately) counting the independent sets of a bipartite graph (#BIS) is the canonical approximate counting problem that is complete in the intermediate complexity class #RHΠ1. It is believed that #BIS does not have an efficient approximation algorithm but also that it is not NP-hard. We study the robustness of the intermediate complexity of #BIS by considering variants of th...

Copositive programming has become a useful tool in dealing with all sorts of optimisation problems. It has however been shown by Murty and Kabadi [K.G. Murty and S.N. Kabadi, Some NP-complete problems in quadratic and nonlinear programming, Mathematical Programming, 39, no.2:117–129, 1987] that the strong membership problem for the copositive cone, that is deciding whether or not a given matrix...

Flow shop sequencing problem is included in NP-hard problems and a number of heuristic methods have been developed to solve it. Most of these methods are offered for the crisp processing time. However fuzzy algorithm is appropriate for the problems with fuzzy processing time. This paper presents a method in which an algorithm is used to minimize make span of flow shop with fuzzy processing time...