The x-and-y-axes travelling salesman problem forms a special case of the Euclidean TSP, where all cities are situated on the x-axis and on the y-axis of an orthogonal coordinate system of the Euclidean plane. By carefully analyzing the underlying combinatorial and geometric structures, we show...

In this paper, we develop a fast algorithm for a smoothing spline estimator in multivariate regression. To accomplish this, we employ general concepts associated with roughness penalty methods in conjunction with the theory of radial basis functions and reproducing kernel Hilbert spaces. It is...

The paper concerns two scheduling problems with job values and losses of job values (costs) dependent on job completion times. In the first problem, we consider scheduling jobs with stepwise values in parallel processor environment. In the stepwise value, there is given a number of moments at...

A set of n nonpreemptive tasks are to be scheduled on m parallel dedicated machines with a regular criterion. Chain precedence constraints among the tasks, deterministic processing times and processing machine of each task are given.