Informatica

We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a random objective function distributed according to the Wiener measure.

The result of simulation of an idealized thin wet film connecting fixed points in the Euclidean plane is a length-minimizing curve. Gradually increasing the exterior pressure we are able to achieve the film configuration near to the Steiner minimal tree. This film evolution may be an interesting tool for solving the Euclidean Steiner problem, but several dead-point situations may occur for a certain location of fixed points. A continuous evolution of the film is impossible by increasing the pressure in these situations. The investigation of dead-point situations gives the ways of overcoming the difficulties of dead-point situations and continuing the film evolution by temporarily decreasing pressure.

The Steiner problem asks for the shortest network that spans a given set of fixed points in the Euclidean plane. The problem is NP hard.

We consider finite population slotted ALOHA where each of n terminals has its own transmission probability pi. Given the overall traffic load λ, the probabilities pi are determined in such a way as to maximize throughput. This is achieved by solving a constrained optimization problem. The results of Abramson (1970) are obtained as a special case. Our recent results are improved (Mathar and Žilinskas, 1993).

The aggregate approach to the formal description, verification and simulation of computer network protocols is considered in the paper. With this approach, the offered design stages can be performed using a single mathematical scheme. The reachability analysis method and the program proof technique are viewed as methods for correctness analysis. The proposed approach for correctness analysis and model construction was used in creating the protocol analysis system PRANAS.