Complexity Analysis of Pipeline Mapping Problems in Distributed Heterogeneous Networks

Molecular computing has proved its possibility to solve weighted graph problem such as Hamiltonian Path Problem (HPP), Traveling Salesman Problem (TSP) and the Shortest Path Problem (SPP). Normally, in molecular computation, the DNA sequences used for the computation should be critically designed in order to reduce error that could occur during computation. In the previous paper, we have proposed a readout method tailored specifically to HPP in DNA Computing using real-time PCR for output visualization. Six nodes of HPP was considered. Based on the example instance, the method requires 11 oligonucleotides, where 6 oligonucleotides are for the nodes and 5 oligonucleotides are for the edges. Three TaqMan probes and five primers are required as well. In this study, a procedure for DNA sequence design is presented in order to obtain good sequences for those nodes, primers, and probes. The experiment is done based on the generated DNA sequences and the Hamiltonian Path can be determined successfully.

Supporting high-performance computing pipelines in wide-area networks is crucial to enabling large-scale distributed scientific applications that require minimizing end-to-end delay for fast user interaction or maximizing frame rate for smooth data flow. We formulate and categorize the linear pipeline configuration problems into six classes with two mapping objectives, i.e. minimum end-to-end delay and maximum frame rate, and three network constraints, i.e. no, contiguous, and arbitrary node reuse. We design a dynamic programming-based optimal solution to the configuration problem for minimum end-to-end delay with arbitrary node reuse and prove the NP-completeness of the rest five problems, for each of which, a heuristic algorithm based on a similar optimization procedure is proposed. Performance superiorities of these heuristics are illustrated by extensive experimental results in comparison with existing methods.

In this article we consider the Directed Steiner Path Cover problem on directed co-graphs. Given a directed graph G=(V,E) and a set T subseteq V of so-called terminal vertices, the problem is to find a minimum number of vertex-disjoint simple directed paths, which contain all terminal vertices and a minimum number of non-terminal vertices (Steiner vertices). The primary minimization criteria is the number of paths. We show how to compute in linear time a minimum Steiner path cover for directed co-graphs. This leads to a linear time computation of an optimal directed Steiner path on directed co-graphs, if it exists. Since the Steiner path problem generalizes the Hamiltonian path problem, our results imply the first linear time algorithm for the directed Hamiltonian path problem on directed co-graphs. We also give binary integer programs for the (directed) Hamiltonian path problem, for the (directed) Steiner path problem, and for the (directed) Steiner path cover problem. These integer programs can be used to minimize change-over times in pick-and-place machines used by companies in electronic industry.

The Hamiltonian cycle and path problems are fundamental in graph theory and useful in modelling real-life problems. Research in this area is directed toward designing better and better algorithms for general problems, but also toward defining new special cases for which exact polynomial-time algorithms exist. In the paper, such new classes of digraphs are proposed. The classes include, among others, quasi-adjoint graphs, which are a superclass of adjoints, directed line graphs, and graphs modelling a DNA sequencing problem.

Let G V , E be a simple undirected complete graph with vertex and edge sets V and E , respectively. In this paper, we consider the degree-constrained k -minimum spanning tree (DC k MST) problem which consists of finding a minimum cost subtree of G formed with at least k vertices of V where the degree of each vertex is less than or equal to an integer value d ≤ k − 2 . In particular, in this paper, we consider degree values of d ∈ 2,3 . Notice that DC k MST generalizes both the classical degree-constrained and k -minimum spanning tree problems simultaneously. In particular, when d = 2 , it reduces to a k -Hamiltonian path problem. Application domains where DC k MST can be adapted or directly utilized include backbone network structures in telecommunications, facility location, and transportation networks, to name a few. It is easy to see from the literature that the DC k MST problem has not been studied in depth so far. Thus, our main contributions in this paper can be highlighted as follows. We propose three mixed-integer linear programming (MILP) models for the DC k MST problem and derive for each one an equivalent counterpart by using the handshaking lemma. Then, we further propose ant colony optimization (ACO) and variable neighborhood search (VNS) algorithms. Each proposed ACO and VNS method is also compared with another variant of it which is obtained while embedding a Q-learning strategy. We also propose a pure Q-learning algorithm that is competitive with the ACO ones. Finally, we conduct substantial numerical experiments using benchmark input graph instances from TSPLIB and randomly generated ones with uniform and Euclidean distance costs with up to 400 nodes. Our numerical results indicate that the proposed models and algorithms allow obtaining optimal and near-optimal solutions, respectively. Moreover, we report better solutions than CPLEX for the large-size instances. Ultimately, the empirical evidence shows that the proposed Q-learning strategies can bring considerable improvements.

The Hamiltonian path problem is one of the famous hard combinatorial problems. We provide the first molecular-scale autonomous solution of the decision Hamiltonian path problem. It is based on the formation of secondary structures of DNA molecules.

We obtain new polynomial kernels and compression algorithms for Path Cover and Cycle Cover, the well-known generalizations of the classical Hamiltonian Path and Hamiltonian Cycle problems. Our choice of parameterization is strongly influenced by the work of Bir\\'o, Hujter, and Tuza, who in 1992 introduced H-graphs, intersection graphs of connected subgraphs of a subdivision of a fixed (multi-)graph H. In this work, we turn to proper H-graphs, where the containment relationship between the representations of the vertices is forbidden. As the treewidth of a graph measures how similar the graph is to a tree, the size of graph H is the parameter measuring the closeness of the graph to a proper interval graph. We prove the following results. Path Cover admits a kernel of size O (parallel to H parallel to(8)), where parallel to H parallel to is the size of graph H. In other words, we design an algorithm that for an n-vertex graph G and integer k \\geq 1, in time polynomial in n and parallel to H parallel to, outputs a graph G\\prime of size \\scrO (parallel to H parallel to(8)) and k\\prime \\leq | V (G' such that the vertex set of G is coverable by k vertex-disjoint paths if and only if the vertex set of G' is coverable by k' vertex-disjoint paths. Hamiltonian Cycle admits a kernel of size O (parallel to H parallel to(8)). Cycle Cover admits a polynomial kernel. We prove it by providing a compression of size O (parallel to H parallel to(10)) into another NP-complete problem, namely, Prize Collecting Cycle Cover, that is, we design an algorithm that, in time polynomial in n and parallel to H parallel to, outputs an equivalent instance of Prize Collecting Cycle Cover of sizeO (parallel to H parallel to(10)). In all our algorithms we assume that a proper H-decomposition is given as a part of the input.

This dissertation is to illustrate the current state of the art of DNA computing achievements, especially of new approaches to solve theoretical 3-SAT problems and the hitting-set problem. Beginning with Adleman’s breakthrough which is an molecular algorithm for the solution of a NP-complete, combinatorial problem, the directed Hamiltonian path problem (HPP). Today, many researchers all over the world concentrate on proposing new methods to solve engineering or application problems with a DNA computing approach. Satisfiability problem is given a Boolean formula, and decide if a satisfying truth assignment exists. ( ) ( ) … ( ) ( ) is an example of Boolean formula. k-SAT problem means that each clause has exactly k literals. Not-All-Equal (NAE) 3-SAT problem and One-In-Three (1IN3) 3-SAT problem are both NP-complete problems. In this dissertation, we present molecular solutions to find all true assignments (3-SAT problem) and furthermore find Not-All-Equal (NAE) solutions and One-In-Three (1IN3) solutions in DNA-based Supercomputing. Hitting-set problem assume that there exists a collection C of subsets of a finite set S, and a positive integer K  |S|, and we need to know if there is a subset  S with | |  K such that contains at least one element of each subset in C. In other words, is the subset that intersects every subset in C and is called the hitting-set. In this dissertation, a DNA-based algorithm is proposed to solve the small hitting-set problem. A small hitting-set is a hitting-set with the smallest K value, i.e., the hitting-set with the smallest number of elements. Furthermore, an algorithm is introduced to find the number of ones from 2n combinations and minimum numbers of ones represents the small hitting-set since K is expected to be as small as possible. The complexity of all the presented DNA-based algorithms is also discussed. We describe time complexity and volume complexity of three Algorithms, numbers of test tube used and the longest library strand in solution space of all three Algorithms. Finally, the simulated experiment is applied to verify correctness of the proposed DNA-based algorithm for solving the One-In-Three (1IN3) 3-SAT problem, and simulation of Not-All-Equal (NAE) 3-SAT problem is similar. Also, another simulated experiment is applied to our proposed DNA-based algorithm 6-2, in order to solve the well-known hitting-set problem. This research has been motivated by the benefit and the application of DNA computing and gives new methods to solve two 3-SAT problems and the hitting-set problem which are NP-complete.

Welcome to the 6th International Workshop on Challenges of Large Applications in Distributed Environments (CLADE 2008) and to Boston, Massachusetts. Distributed cyberinfrastructure for the realization of e-Science and e-Business continues to be developed at a rapid pace and across diverse disciplines. This development reinforces the need for effective distributed applications. From sensor data to online data collections to remote visualization, the most challenging problems will be solved by applications that can make effective use of such distributed, heterogeneous resources. This workshop will highlight the successful development, deployment, management and evaluation of large scale applications and scientific workflows in science, engineering, medicine, business, economics, education, and other disciplines, on Grids and other distributed heterogeneous and dynamic computing environments. In addition, the program includes invited talks by stellar researchers of international reputation from research institutes such as Arizona, Chicago, Minnesota, MIT, Rutgers, and SDSC, and industry such as Intel and Microsoft. CLADE 2008 also features a keynote on autonomic computing paradigms to enable self-* applications. These invited talks cover a wide spectrum of the-state-of-the-art technologies in large-scale computing and applications, including autonomic computing engines for Internet-scale applications, high-productivity computing for datacenters, multicore programming, and scalable computing on open distributed systems. A special talk will investigate "Lessons Learnt from CLADE" for retrospections on the past CLADE experiences and ushering in new era of large-scale applications and environments.

In this chapter we will consider the hamiltonian path and cycle problems for digraphs as well as some related problems such as the longest path and cycle problems and the minimum path factor problem. We describe and prove a number of results in the area as well as formulate several open questions.

A graph is called Hamiltonian connected if it contains a Hamiltonian path between any two distinct vertices. In the past, we proved the Hamiltonian path and cycle problems for general supergrid graphs to be NP-complete. However, they are still open for solid supergrid graphs. In this paper, first we will verify the Hamiltonian cycle property of C-shaped supergrid graphs, which are a special case of solid supergrid graphs. Next, we show that C-shaped supergrid graphs are Hamiltonian connected except in a few conditions. For these excluding conditions of Hamiltonian connectivity, we compute their longest paths. Then, we design a linear-time algorithm to solve the longest path problem in these graphs. The Hamiltonian connectivity of C-shaped supergrid graphs can be applied to compute the optimal stitching trace of computer embroidery machines, and construct the minimum printing trace of 3D printers with a C-like component being printed.

DNA algorithms have solved some NP-complete problems such as Hamilton path and Chinese postman problem; however there are only some suggestions for the shortest path problem. Weight encoding is a very important and challenge aspect in DNA computing. In this paper a computing method which based on incomplete Molecule Commixed Encoding (IMCE) is proposed. In this method, the vertex of the graph is encoded as single-strand, weight is encoded as double-strands and the edge is incomplete encoded. This method is used to solve the shortest path problem.

MediaWare: A distributed multimedia environment with interoperability

Hamiltonian problems in directed graphs with simple row patterns

Grid computing infrastructures embody a cost-effective computing paradigm that virtualises heterogeneous system resources to meet the dynamic needs of critical business and scientific applications. These applications range from batch processes and long-running tasks to more real-time and even transactional applications. Grid schedulers aim to make efficient use of grid resources in a cost-effective way, while satisfying the quality-of-service requirements of the applications. Scheduling in such a large-scale, dynamic and distributed environment is a complex undertaking. In this paper, we propose an approach to grid scheduling which abstracts over the details of individual applications and aims to provide a globally optimal schedule, while having the ability to dynamically adjust to varying workload demands using various capacity planning techniques. Our model places particular emphasis on the stochastic and unpredictable nature of the grid, leading to a more accurate reflection of the state of the grid and hence more efficient and accurate scheduling decisions