NP Hard Research Articles

An ant colony optimization technique for solving min–max Multi-Depot Vehicle Routing Problem

The Multi-Depot Vehicle Routing Problem (MDVRP) involves minimizing the total distance traveled by vehicles originating from multiple depots so that the vehicles together visit the specified customer locations (or cities) exactly once. This problem belongs to a class of Nondeterministic Polynomial Hard (NP Hard) problems and has been used in literature as a benchmark for development of optimization schemes. This article deals with a variant of MDVRP, called min–max MDVRP, where the objective is to minimize the tour-length of the vehicle traveling the longest distance in MDVRP. Markedly different from the traditional MDVRP, min–max MDVRP is of specific significance for time-critical applications such as emergency response, where one wants to minimize the time taken to attend any customer. This article presents an extension of an existing ant-colony technique for solving the Single Depot Vehicle Routing Problem (SDVRP) to solve the multiple depots and min–max variants of the problem. First, the article presents the algorithm that solves the min–max version of SDVRP. Then, the article extends the algorithm for min–max MDVRP using an equitable region partitioning approach aimed at assigning customer locations to depots so that MDVRP is reduced to multiple SDVRPs. The proposed method has been implemented in MATLAB for obtaining the solution for the min–max MDVRP with any number of vehicles and customer locations. A comparative study is carried out to evaluate the proposed algorithm's performance with respect to a currently available Linear Programming (LP) based algorithm in literature in terms of the optimality of solution. Based on simulation studies and statistical evaluations, it has been demonstrated that the ant colony optimization technique proposed in this article leads to more optimal results as compared to the existing LP based method.

Security Driven Scheduling Model for Computational Grid Using NSGA-II

Number of software applications demands various levels of security at the time of scheduling in Computational Grid. Grid may offer these securities but may result in the performance degradation due to overhead in offering the desired security. Scheduling performance in a Grid is affected by the heterogeneities of security and computational power of resources. Customized Genetic Algorithms have been effectively used for solving complex optimization problems (NP Hard) and various heuristics have been suggested for solving Multi-objective optimization problems. In this paper a security driven, elitist non-dominated sorting genetic algorithm, Optimal Security with Optimal Overhead Scheduling (OSO2S), based on NSGA-II, is proposed. The model considers dual objectives of minimizing the security overhead and maximizing the total security achieved. Simulation results exhibit that the proposed algorithm delivers improved makespan and lesser security overhead in comparison to other such algorithms viz. MinMin, MaxMin, SPMinMin, SPMaxMin and SDSG.

A Parallel Scalable Multi-Core Short Read Assembler

Bioinformatics and computational biology are rooted in life sciences as well as computer and information sciences and technologies. Bioinformatics applies principles of information sciences and technologies to make the vast, diverse, and complex life sciences data more understandable and useful. Computational biology uses mathematical and computational approaches to address theoretical and experimental questions in biology. Short read sequence assembly is one of the most important steps in the analysis of biological data. There are many open source software’s available for short read sequence assembly where MAQ is one such popularly used software by the research community. In general, biological data sets generated by next generation sequencers are very huge and massive which requires tremendous amount of computational resources. The algorithm used for the short read sequence assembly is NP Hard which is computationally expensive and time consuming. Also MAQ is single threaded software which doesn't use the power of multi core and distributed computing and it doesn't scale. In this paper we report HPC-MAQ which addresses the NP-Hard related challenges of genome reference assembly and enables MAQ parallel and scalable through Hadoop which is a software framework for distributed computing. In this paper we try to perform thread level parallelism using openMP .and it can reduce computational time.

Extracting Dynamical Equations from Experimental Data is NP Hard

The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this Letter, we show that, remarkably, identifying the underlying dynamical equation from any amount of experimental data, however precise, is a provably computationally hard problem (it is NP hard), both for classical and quantum mechanical systems. As a by-product of this work, we give complexity-theoretic answers to both the quantum and classical embedding problems, two long-standing open problems in mathematics (the classical problem, in particular, dating back over 70years).

Efficient multi-objective genetic algorithm for hardware-software partitioning in embedded system design: ENGA

This paper presents a novel multi-objective evolutionary algorithm for hardware software partitioning of embedded systems. Customised genetic algorithms have been effectively used for solving complex optimisation problems (NP Hard) but are mainly applied to optimise a particular solution with respect to a single objective. Many real world problems in embedded systems have multiple objective functions like area, performance, power, latency, etc., which are to be maximised or minimised at the early stage of the design process. Hence multi-objective formulations are realistic models for many complex engineering optimisation problems. A multi-objective optimisation problem usually has a set of Pareto-optimal solutions, instead of one single optimal solution. A method is put forward for generating Pareto solutions using elitist non-dominated sorting genetic algorithm (ENGA) whose complexity is only O(MN²), where M is the number of objectives and N is the population size. The algorithm is implemented using Visual C++ and the performance metrics for weighted-sum genetic algorithm (WSGA) and ENGA are compared. The results of extensive hardware/software partitioning technique on numerous benchmarks are also presented which can be used practically at the early stage of the design process. From the simulation results ENGA (NSGA-II) was found to perform better than WSGA.

A note on the NP–hardness of the consecutive block minimization problem

We show that consecutive block minimization problem is NP–hard even when restricted to binary matrices that have two ones per row.

Topological design of centralized computer networks

Topological design of centralized computer-communication networks is an important issue that has been investigated by a large number of researchers. Such networks typically involve a large number of terminals connected by low or medium speed lines to concentrators, which are then connected to a central computing site by high speed lines. This problem is known to be a very difficult one. In general, the design problem involves determining the following: (a) the numbers and locations of concentrators that are to be opened; (b) the topology of connecting user nodes to concentrations sites; and (c) determining the links between open concentrators and the central node. Since the overall design problem belongs to the class of problems that are NP Hard, most prior research has investigated ways in which to disaggregate the problem into several simpler problems that can be solved iteratively until a satisfactory solution is reached. The problem we solve is this research involves multipoint lines between terminals and concentrators, and dedicated lines between concentrators and the central node. This problem therefore combines features of concentrator location problems as well as local access network design problems. We utilize a Lagrangian heuristic designed to efficiently solve this problem with gaps ranging from 2.7 to 10.4% of the lower bound.

Topological Design of Centralized Computer Networks

Topological design of centralized computer‐communication networks is an important issue that has been investigated by a large number of researchers. Such networks typically involve a large number of terminals connected by low or medium speed lines to concentrators, which are then connected to a central computing site by high speed lines. This problem is known to be a very difficult one. In general, the design problem involves determining the following: (a) the numbers and locations of concentrators that are to be opened; (b) the topology of connecting user nodes to concentrations sites; and (c) determining the links between open concentrators and the central node. Since the overall design problem belongs to the class of problems that are NP Hard, most prior research has investigated ways in which to disaggregate the problem into several simpler problems that can be solved iteratively until a satisfactory solution is reached. The problem we solve is this research involves multipoint lines between terminals and concentrators, and dedicated lines between concentrators and the central node. This problem therefore combines features of concentrator location problems as well as local access network design problems. We utilize a Lagrangian heuristic designed to efficiently solve this problem with gap ranging from 2.7 to 10.4% of the lower bound.

A Quasi-mechanical Method for Solving the Rectangle Covering Problem-An Approach to Tackling NP Hard Problems

An approximate algorithm is proposed for solving the Rectangle Covering Problem based on the quasi-mechanical concept. The phenomenon due to universal gravitation and screen has been simulated. It is pointed out that valuable approximate algorithms can be obtained for large numbers of NP hard problems by following the quasi-mechanical procedure. Behind the quasi-mechanical procedure are the strategies in the priority method in modern recursive theory.

A Quasi-mechanical Method for Solving the Rectangle Covering Problem An Approach to Tackling NP Hard Problems

An approximate algorithm is proposed for solving the Rectangle Covering Problem based on the quasi-mechanical concept. The phenomenon due to universal gravitation and screen has been simulated. It is pointed out that valuable approximate algorithms can be obtained for large numbers of NP hard problems by following the quasi-mechanical procedure. Behind the quasi-mechanical procedure are the strategies in the priority method in modern recursive theory.

Design of Performance Constrained Optic Fiber Multidrop Access Networks

Propagation delay may not be negligible in comparison to transmission times in high speed networks. As a consequence, design procedures for high speed networks, such as optic fiber based networks, must take propagation delay into account. The design problem for multidrop access networks that includes transmission and propagation delay times is modeled as a mixed integer program. The problem is shown to be NP Hard and a solution procedure is proposed. Experimentation reveals the effect of poll cycle time limits on topology and cost. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

On the Distributed Database Union Operation

In a distributed relational database, an operation that produces the union of fragments stored at different sites at a specified site is called a distributed union operation. In implementing the distributed union operation, operations other than the union operation, such as intersection and difference, may be used to facilitate the union. Optimization of the distributed union operation when the fragments are not disjoint requires the ability to predict the size of the result of set operations. A minimal basis of the result of multiple non-disjoint horizontal fragments of a relation is derived. This is used to develop a model for the optimization of the distributed union operation. As the problem is NP Hard, heuristic and lower bounding procedures are developed for a special case.Request access from your librarian to read this article's full text.