NP-complete

Problem 2. (a). Here in the given problem we have scheduling problem, which we call multiple interval scheduling. Here the change is job require a process for more than one set of intervals. (b). This problem belongs to NP-complete, because we have k set of times and we can check that it overlaps or not. (c). Suppose we have Algorithm A to solve this problem we have k collection of interval. And we will take the instance of the 3 dimension that is, set of 3 intervals. So

for permutation based encoding is described \cite{Chira-2012}. The proposed operator is using not only genetic information from the two parents, but from the best individual obtained up to the current generation too. Some of the most widely studied NP-hard optimization problems with many applications in domains such as logistics, planning, routing, and scheduling are considered to test the efficiency of the proposed operator. A comparative analysis of several recombination operators is presented

Complexity and Tractability The area of tractability explores problems and algorithms that can take an impossible amount of computation to solve. Tractable problems can be roughly defined as problems that can be solved in a reasonable amount of time, while intractable problems are those which take too long to solve to be useful. Finding solutions to these problems is a key problem in computer science today and has been for many years. It is also important for a computer scientist to recognise intractable

Personal Statement I have majored in Industrial and Systems Engineering (ISE) for one and a half years at Virginia Tech. My passion for ISE originated from my undergraduate studies. I achieved GPA 91/100 and ranked 1/66 when I graduated from Nanjing University of Aeronautics and Astronautics (NUAA), one of China 's top 3 universities offering the Industrial Engineering program. When I got into NUAA, I entered an Honors Program, which offers students a chance to choose their majors according to academic

No one has come up with the efficient way of coming up with the solution to large size problems as the NP-complete problems are much intractable. The exact methods provide an exact optimal solution to the problem. One of the ways of solving the Travelling Salesman Problem is simply taking all the available and feasible solutions and evaluating their function

A Novel Study of Bee Colony Optimization Algorithms for their Applications into Various Domains INTRODUCTION The Bee Colony Optimization (BCO) is a technique based on the mutual understanding of the natural bees in food foraging process. It is a population based search algorithm for optimizing numerical problems. Bees are classic example of teamwork experience, coordination and synchronization. The way they work is remarkable. They carry out a kind of neighborhood search combined with global search

returns the result for Vertex Cover problem. Hence, we can conclude that Interval Scheduling ≤p Vertex Cover. Question 1 (b): Is it the case that Independent Set ≤p Interval Scheduling? Unknown, because it would resolve the question of whether P = NP. Let’s suppose Y ≤p X. If X requires polynomial time to be constructed, then Y can be also be constructed in similar time. Now, Interval Scheduling can

Background study and Related Works: In this chapter, we present a detailed discussion of the research on exam timetabling in the last 20 years. In the first decade there has been significant attention of researchers in this area and there has been a significant contribution in both theoretical and practical sector. Our aim is to discuss about the achievement made in this area. We have discussed about the barriers and challenges overcame by the researchers. First, we defined some constraint from

these physical machines. With a large number of datacenters and each datacenter having a large number of physical machines. The VM allocation becomes an NP-Hard problem. Thus, the VM allocation, the VM migration becomes a trivial task. In this article, a survey is carried out on cloud computing in energy cloud, based on scalable algorithms. To solve NP-Hard problems, there are two ways to either give an exact solution or to provide an approximation.

solution based on the behaviour of ants searching for food. This paper list out various techniques used to solve such problems and their advantages, disadvantages. Through this review we identify some suggestion for solving NP hard problem. Keywords :Ant colony optimization, NP hard, stigmergy, Pheromone, optimal , heuristics 1. Introduction 1.1 Swarm Intelligence Swarm intelligence was been proposed and induced in the Artificial Intelligence by Beni and Wang [10] in 1989. It was been applied in the