Search

A procedure for solving, suboptimally, the traveling salesman problem is presented. The set of points on the traveling salesman tour is distributed over a region having the shape of a circular or ring sector. The procedure is based on an optimal partition of the sector and reduces the tour construction to a sorting problem. Namely, the tour is constructed by visiting the points in radial or angular order depending on the part of the sector on which they are located. The optimal partition is derived by a continuous approximation of the set of points. It is defined by a single parameter and simple analytical expressions for it are obtained. A great number of numerical tests were carried out to evaluate the performance of the procedure. These tests allowed a measure of the difference from the optimum solution that could be obtained for problems up to a few hundred points. The results show that the euclidean length of the tours produced by the partition procedure grows, on average, like AN , where A is the region area and N the number of points. The initial tours are improved by means of the Or’s algorithm and the final tours obtained are nearly as good as those given by more intrincate improvement heuristics. The whole procedure, that is, the tour construction and improvement heuristics, is rather simple to implement on a computer, which makes it very appealing to use in routing software.

Percutaneous balloon mitral valvotomy (BMV) is an alternative therapeutic method for patients with mitral stenosis. We studied 62 patients (56 females, mean age 36.4 years) who underwent balloon mitral valvotomy. Five patients were pregnant and in New York Heart Association Functional Class IV. Doppler echocardiographic studies were performed prior to the procedure, and at 7 days, 6 months, 12 months, and 24 months after the procedure. We studied the following parameters: echo-score by the sum of valvular mobility, thickening, and calcification, and subvalvular disease, graded from 1 to 4; and mitral valve area (MVA) and mitral pressure gradient (MPG) by Doppler echocardiography. The patients were separated into two groups: group I with an echo-score less than or equal to 8 (40 patients), and group II with an echo-score greater than or equal to 9 (22 patients). Mitral valve area and MPG were compared with hemodynamics through the correlation coefficient and linear regression. Comparison between groups I and II was performed using the unpaired Student's t-test. Follow-up of MVA and MPG was analyzed by analysis of variance. The Student's t-test did not show any significant difference between MVA and MPG before balloon mitral valvotomy. There was significant decrease of MVA in group II (P less than 0.01) in the last three studies. There was significant increase in MPG in group II (P less than 0.01) in every postvalvotomy study. The analysis of variance of group I showed statistical increase of the MVA, and significant decrease of the MPG after BMV. The analysis of variance of group II showed significant increase in MVA and significant decrease in MPG between the pre- and the first postvalvotomy study. There was significant decrease (P less than 0.01) in MVA, and increase in MPG in the three postvalvotomy studies. Complications included mitral regurgitation, residual interatrial communication, pericardial effusion due to an atrial wall perforation, and peripheral embolization. Atrial fibrillation did not significantly alter the results of BMV. Results were considered positive when MVA was greater than 1.5 cm 2 and area increase was greater than 25%. Patients with an echo-score less than or equal to 8 (group I) benefit from BMV, with a positive predictive value greater than 78%. In pregnant patients the symptomatology was alleviated by BMV, without any signs of fetal compromise.