A DNA sequence design for molecular computation of HPP with output visualization based on real-time PCR

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.

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.

A digraph is semicomplete if it has no pair of non-adjacent vertices. It is complete if every pair of distinct vertices induces a 2-cycle. A digraph is semicomplete multipartite if it can be obtained from a semicomplete digraph D by choosing a collection of vertex-disjoint subsets X₁,…,X_c of V(D) and then deleting all arcs both of whose end-vertices lie inside some X_i. We can also think of a semicomplete digraph as being obtained from a semicomplete multipartite digraph on the same vertex set and partite sets V₁,…,V_c by adding the arcs of a semicomplete digraph D_i on V_i for each partite set V_i. It is well known that both the hamiltonian path and the hamiltonian cycle problem can be solved in polynomial time for semicomplete multipartite digraphs. In this paper we study the complexity of finding a hamiltonian path or cycle in a semicomplete digraph S which is obtained as above from a semicomplete multipartite digraph D and semicomplete digraphs D_i=(V_i,A_i), i∈[c] such that the path or cycle uses as few arcs of A₁∪…A_c as possible. We obtain a number of results for the case when each D_i is a complete digraph. Already this case is highly nontrivial in the cycle case and the complexity is still open. We show how to find a Hamiltonian path which uses as few arcs from the D_i’s as possible in polynomial time and obtain a number of results, both structural and algorithmic on hamiltonian cycles that use the minimum or close to the minimum number of arcs from the D_i’s. Our results imply the polynomial solvability of some special cases of the NP-complete {0,1}-TSP problem. Finally we show that two natural questions about properties of quasi-hamiltonian cycles, that is, cycles meeting all partite sets in semicomplete multipartite digraphs are NP-complete.

The Hamiltonian cycle problem is a well-known NP-complete problem in graph theory. This problem relates to lots of practical problems such as designing very large scale integration (VLSI) and travel-ling salesman problem (TSP). Since it is NP-complete, there is no efficient algorithm to solve the Hamiltonian cycle problem, and hence, its solution is valuable. In this paper, we propose new physical zero-knowledge proof protocols for the Hamiltonian cycle problem, whereby an entity can prove its knowledge of a solution to another entity without leaking any information about the valuable solution. Our protocols are more efficient than the previous protocols. We also propose a physical zero-knowledge proof protocol for TSP, one of whose building blocks is a new representation of an integer commitment with a secure addition protocol.

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.

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 process of designing a set of good DNA sequences is an essential problem and one of the most practical and important research topics in DNA-based computing. In this field of research, a DNA sequence design problem is defined as a multi-objective problem, and it is evaluated using four objective functions, which are h-measure, similarity, continuity, and hairpin. In addition, two constraints, GC content and melting temperature, are used to maintain uniform chemical characteristics of the sequences. In the authors' previous research, ant colony system (ACS) was proposed to solve the DNA sequence design problem and the Watson-Crick base pair ÄGo37 was used as the distance between nodes in the computational model of DNA sequence design. In the current study, the use of other parameters, namely, unified near estneighbour thermodynamic parameters, are investigated and the result is compared with the previous work.

The process of designing a set of good DNA sequences is an essential problem and one of the most practical and important research topics in DNA-based computing. In this field of research, a DNA sequence design problem is defined as a multi-objective problem, and it is evaluated using four objective functions, which are h-measure, similarity, continuity, and hairpin. In addition, two constraints, GC content and melting temperature, are used to maintain uniform chemical characteristics of the sequences. In the authors' previous research, ant colony system (ACS) was proposed to solve the DNA sequence design problem and the Watson-Crick base pair ΔGo37 was used as the distance between nodes in the computational model of DNA sequence design. In the current study, the use of other parameters, namely, Breslauer nearest-neighbour thermodynamic parameters are investigated and the result is compared with the previous work.

Since the quantity and quality of DNA sequence directly affect the accuracy and efficiency of computation, the design of DNA sequence is critical to DNA computing. In order to improve the reliability of DNA computing, there is a rich literature targeting at making DNA sequences specifically hybridize at a lower melting temperature, no non-complementary bases pairs or mismatch hybridization in the reformed double helix. However, most of them are not good enough to control the melting temperature, because DNA sequence design problem under the constraints of hamming distance, secondary structure, molecular thermodynamic is known to be NP-hard. For the sake of achieving the lower and similar melting temperature for each DNA sequence, we proposed a DNA sequence coding method based on Bacterial Foraging Algorithm (BFA). An evaluation criterion is particularly proposed to assess the quality of DNA sequence in the optimization process. With BFA, high-quality DNA strands are replicated to avoid the participation of inferior strands in the operation. Experiments show our proposed approach significantly outperforms existing methods in terms of continuity and melting temperature.

In the past few years since Adleman’s pioneering work on solving the HPP(Hamiltonian Path Problem) with a DNA-based computer [1], many algorithms have been designed on solving NP problems. Most of them are in the solution bases and need some error correction or tolerance technique in order to get good and correct results [3] [7] [9] [11] [21] [22]. The advantage of surface-based DNA computing technique, with very low error rate, has been shown many times [12] [18] [17] [20] over the solution based DNA computing, but this technique has not been widely used in the DNA computer algorithms design. This is mainly due to the restriction of the surface-based technique comparing with those methods using the DNA strands in solutions. In this paper, we introduce a surface-based DNA computing algorithm for solving a hard computation problem: expansion of symbolic determinants given their patterns of zero entries. This problem is well-known for its exponential difficulty. It is even more difficult than evaluating determinants whose entries are merely numerical [15]. We will show how this problem can be solved with the low error rate surface-based DNA computer using our naive algorithm.

In this work, particle swarm optimization (PSO) is applied to automate the DNA computing readout method based on a real-time polymerase chain reaction (PCR). Moreover, real-time amplification was performed and the TaqMan detection approach was used for the plan and the readout approach development. The most important part of the readout method is identifying two different reactions in the real-time PCR, which involve in vitro and in silico processes in order to inspect the placement of pairs of nodes in the Hamiltonian path problem. In addition, the real-time PCR experiment is implemented on the LightCycler System. Previously, manual method was exploited to classify two different output reactions of real-time PCR that was a time consuming process. In this study, by exploiting MATLAB the PSO has been implemented for clustering output reactions of real-time PCR and experimental results depict that the amplification response for “YES” and “NO” reactions can be clustered correctly.

Not being (super)thin or solid is hard: A study of grid Hamiltonicity

Largescale scientific applications require using various system resources to execute complex computing pipelines in distributed networks to support collaborative research. System resources are typically shared in the Internet or over dedicated connections based on their location, availability, capability, and capacity. Optimizing the network performance of computing pipelines in such distributed environments is critical to the success of these applications. We consider two types of largescale distributed applications: (i) interactive applications where a single dataset is sequentially processed along a pipeline; and (ii) streaming applications where a series of datasets continuously flow through a pipeline. The computing pipelines of these applications consist of a number of modules executed in a linear order in network environments with heterogeneous resources under different constraints. Our goal is to find an efficient mapping scheme that allocates the modules of a pipeline to network nodes for minimum endtoend delay or maximum frame rate. We formulate the pipeline mappings in distributed environments as optimization problems and categorize them into six classes with different optimization goals and mapping constraints: (i) Minimum Endtoend Delay with No Node Reuse (MEDNNR), (ii) Minimum Endtoend Delay with Contiguous Node Reuse (MEDCNR), (iii) Minimum Endtoend Delay with Arbitrary Node Reuse (MEDANR), (iv) Maximum Frame Rate with No Node Reuse or Share (MFRNNRS), (v) Maximum Frame Rate with Contiguous Node Reuse and Share (MFRCNRS), and (vi) Maximum Frame Rate with Arbitrary Node Reuse and Share (MFRANRS). Here, “contiguous node reuse” means that multiple contiguous modules along the pipeline may run on the same node and “arbitrary node reuse” imposes no restriction on node reuse. Note that in interactive applications, a node can be reused but its resource is not shared. We prove that MEDANR is polynomially solvable and the rest are NP-complete. MEDANR, where either contiguous or noncontiguous modules in the pipeline can be mapped onto the same node, is essentially the Maximum n-hop Shortest Path problem, and can be solved using a dynamic programming method. In MEDNNR and MFRNNRS, any network node can be used only once, which requires selecting the same number of nodes for onetoone onto mapping. We show its NP-completeness by reducing from the Hamiltonian Path problem. Node reuse is allowed in MEDCNR, MFRCNRS and MFRANRS, which are similar to the Maximum n-hop Shortest Path problem that considers resource sharing. We prove their NP-completeness by reducing from the Disjoint-Connecting-Path Problem and Widest path with the Linear Capacity Constraints problem, respectively.

DNA computing relies on biochemical reactions of DNA molecules and may result in incorrect or undesirable computations. Therefore, much work has focused on designing the DNA sequences to make the molecular computation more reliable. Sequence design involves with a number of heterogeneous and conflicting design criteria and traditional optimization methods may face difficulties. In this paper, we formulate the DNA sequence design as a multiobjective optimization problem and solve it using a constrained multiobjective evolutionary algorithm (EA). The method is implemented into the DNA sequence design system, NACST/Seq, with a suite of sequence-analysis tools to help choose the best solutions among many alternatives. The performance of NACST/Seq is compared with other sequence design methods, and analyzed on a traveling salesman problem solved by bio-lab experiments. Our experimental results show that the evolutionary sequence design by NACST/Seq outperforms in its reliability the existing sequence design techniques such as conventional EAs, simulated annealing, and specialized heuristic methods.

Kombinatorische entscheidungsprobleme: Methoden und anwendungen; fortbildungskurs des instituts für operations research der ETH Zürich: Thomas M. Liebling, Max Rössler (Eds.) Springer, Berlin, 1978, 206 pages, Dfl. 32.75 Soft cover