In this article we study DNA computing, a method which is based on working with DNA molecules in a laboratory. That approach is implemented in solving one of the most popular combinatorial problem — the Hamiltonian path problem. Related to recent improvements in the biophysics methods, which are needed for DNA computing, we propose to change some steps in the classical algorithm to increase accuracy of this method. The branch-and-bound method, the most popular method which is realized on a computer, is also shown in this paper to compare its performance with the time consumption of DNA computing. The results of that comparison prove that it becomes inefficient to use the branch-and-bound method from the counted number of vertices because of its exponentially growing complexity, while DNA computing works parallel and has linearly growing time consumption.

In this article different approaches to one of the most popular combinatorial problem — the Hamiltonian path problem – are illustrated and compared between each other. It is shown that it becomes inefficient to use branch-and-bound method, the most popular method which is realized on a computer, from the counted number of vertices because of its exponentially growing complexity, one more algorithm which is based on working with deoxyribonucleic acid (DNA) molecules in a laboratory is analysed. That method works parallel and has linearly growing time consumption. Due to the improvements in the biophysics methods, which are needed for DNA computing, that algorithm became much faster than it was several years ago and it is now possible to add some new stages in DNA computing, which are shown in this paper.

The problem of sensor selection arises in various applications. In multi-target tracking, the main challenge is to select sensors for each target in such a way as to minimize the estimation error, taking into account the limitations of the computation and communication resources of the sensors. In this paper, we deal with two problems arising in sensor selection. First, we try to reduce the situations, in which selected sensors might be loaded more than the rest of the nodes. Secondly, we discard the assumption, requiring the measurement noise to have the Gaussian distribution. Instead of that, we consider the measurements corrupted by the unknown but bounded noise. We present a sensor selection strategy based on linear matrix inequalities and show its performance.

We consider a dynamic network system of multiple heterogeneous sensors collaborating among themselves to estimate an unknown signal of interest. That communication capability is essential because individual senors cannot fulfill the task due to the lack of necessary information. This paper considers the distributed estimation or tracking problem and focuses on combining two algorithms: Simultaneous Perturbation Stochastic Approximation (SPSA) and consensus Local Voting Protocol (LVP). The new distributed algorithm is proposed for network systems under wide range of uncertainties including unknown-but-bounded drift of parameters and noise in observations. The suggested approach is illustrated by an application of the proposed algorithm to the solving the multisensor-multitarget problem.