A PTAS for single machine scheduling with controllable processing times

We deal with a single machine scheduling problem in which each job has a release date, a delivery time and a controllable processing time. The fact that the jobs have a controllable processing time means that it is allowed to compress (a part of) the processing time of the job, in return for compression cost. The objective is to find a schedule that minimizes the total cost, that is, the latest delivery time of any job plus the total compression cost. In this note we discuss how the techniques of Hall and Shmoys [3] and Hall [1] can directly be applied to design a polynomial time approximation scheme for this problem

Increase in perceived case suspiciousness due to local contrast optimisation in digital screening mammography

Item does not contain fulltextOBJECTIVES: To determine the influence of local contrast optimisation on diagnostic accuracy and perceived suspiciousness of digital screening mammograms. METHODS: Data were collected from a screening region in the Netherlands and consisted of 263 digital screening cases (153 recalled,110 normal). Each case was available twice, once processed with a tissue equalisation (TE) algorithm and once with local contrast optimisation (PV). All cases had digitised previous mammograms. For both algorithms, the probability of malignancy of each finding was scored independently by six screening radiologists. Perceived case suspiciousness was defined as the highest probability of malignancy of all findings of a radiologist within a case. Differences in diagnostic accuracy of the processing algorithms were analysed by comparing the areas under the receiver operating characteristic curves (A(z)). Differences in perceived case suspiciousness were analysed using sign tests. RESULTS: There was no significant difference in A(z) (TE: 0.909, PV 0.917, P = 0.46). For all radiologists, perceived case suspiciousness using PV was higher than using TE more often than vice versa (ratio: 1.14-2.12). This was significant (P <0.0083) for four radiologists. CONCLUSIONS: Optimisation of local contrast by image processing may increase perceived case suspiciousness, while diagnostic accuracy may remain similar. KEY POINTS: Variations among different image processing algorithms for digital screening mammography are large. Current algorithms still aim for optimal local contrast with a low dynamic range. Although optimisation of contrast may increase sensitivity, diagnostic accuracy is probably unchanged. Increased local contrast may render both normal and abnormal structures more conspicuous.1 april 201