On the completability of mutually orthogonal Latin rectangles

This thesis examines the completability of an incomplete set of m-row orthogonal Latin rectangles (MOLRm) from a set theoretical viewpoint. We focus on the case of two rows, i.e. MOLR2, and define its independence system (IS) and the associated clutter of bases, which is the collection of all MOLR2. Any such clutter gives rise to a unique clutter of circuits which is the collection of all minimal dependent sets. To decide whether an incomplete set of MOLR2 is completable, it suffices to show that it does not contain a circuit therefore full knowledge of the clutter of circuits is needed. For the IS associated with 2-row orthogonal Latin rectangles (OLR2) we establish a methodology based on the notion of an availability matrix to fully characterise the corresponding clutter of circuits. We prove that..

Approximating the multi-level bottleneck assignment problem.

We consider the multi-level bottleneck assignment problem (MBA). This problem is described in the recent book 'Assignment Problems' by Burkard et al. (2009) on pages 188-189. One of the applications described there concerns bus driver scheduling.We view the problem as a special case of a bottleneck m-dimensional multi-index assignment problem. We give approximation algorithms and inapproximability results, depending upon the completeness of the underlying graph. Keywords: bottleneck problem; multidimensional assignment; approximation; computational complexity; efficient algorithm.Bottleneck problem; Multidimensional assignment; Approximation; Computational complexity; Efficient algorithm;

On the completability of incomplete orthogonal Latin rectangles

We address the problem of completability for 2-row orthogonal Latin rectangles (OLR2). Our approach is to identify all pairs of incomplete 2-row Latin rectangles that are not com- pletable to an OLR2 and are minimal with respect to this property; i.e., we characterize all circuits of the independence system associated with OLR2. Since there can be no poly- time algorithm generating the clutter of circuits of an arbitrary independence system, our work adds to the few independence systems for which that clutter is fully described. The result has a direct polyhedral implication; it gives rise to inequalities that are valid for the polytope associated with orthogonal Latin squares and thus planar multi-dimensional assign- ment. A complexity result is also at hand: completing a set of (n - 1) incomplete MOLR2 is NP-complete

Approximating the multi-level bottleneck assignment problem

We consider the multi-level bottleneck assignment problem (MBA). This problem is described in the recent book "Assignment Problems" by Burkard et al. (2009) on pages 188 - 189. One of the applications described there concerns bus driver scheduling. We view the problem as a special case of a bottleneck m-dimensional multi-index assignment problem. We give approximation algorithms and inapproximability results, depending upon the completeness of the underlying graph

On the recognition of 2-row orthogonal latin rectangle circuits

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On the completability of orthogonal Latin rectangles

International audienceWe address the problem of completability for 2-row orthogonal Latin rectangles (OLR2). The approach is to identify all incomplete pairs of 2-row Latin rectangles that are not completable to an OLR2 and are minimal with respect to this property; i.e., we characterize all circuits of the independence system associated with OLR2. Since there can be no polytime algorithm generating the clutter of circuits of an arbitrary independence system, our work adds to the few such cases for which that clutter is fully described. The result has a direct polyhedral implication; it gives rise to inequalities that are valid for the polytope associated with orthogonal Latin squares and thus planar multi-dimensional assignment. A complexity result is also at hand: completing an incomplete set of (n-1) MOLR2 is NP-complete

There are only 42 Types of 10x10 Latin Squares (LS) to Consider in the Search for a Mutually Orthogonal Triple

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Lessons for finding Mutually Orthogonal Latin Squares (MOLS) for n=10 from new and old proofs for infeasibility of n=6

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The Role of Metoprolol and Enalapril in the Prevention of Doxorubicin-induced Cardiotoxicity in Lymphoma Patients

Background/Aim: Anthracyclines, such as doxorubicin, though widely used in anticancer therapy, they are associated with cardiotoxic side-effects. The aim of this trial was to investigate long-term follow-up cardiotoxicity findings in patients treated with doxorubicin and concomitant metoprolol or enalapril 10 years earlier. Patients and Methods: Overall, 147 patients were randomized into the treatment arms. A total of 125 patients treated with doxorubicin without evidence of heart disease at the start of chemotherapy were analyzed. They were followed-up for up to 10 years after treatment start. Results and Conclusion: A total of 47 patients completed the follow-up and 21 patients died, none due to cardiotoxicity events. Clinical signs of heart failure were not seen in any patients and no statistically significant differences between baseline and 10-year findings were seen for echocardiographic variables. No evidence of long-term cardiotoxicity was seen and nor metoprolol or enalapril offered an additional benefit