2,013 research outputs found
Preference diversity orderings
This paper surveys approaches to preference diversity measurement. Applying preference diversity axiomatics, a generalization of the Alcalde-Unzu and Vorsatz (2016) criterion, is developed. It is shown that all previously used indices violate this criterion. Two new indices (geometric mean based and leximaxbased)are developed that satisfy a new criterion. Leximax-based orders act as a polarization index and are compared with Can et al.’s (2015) polarization index. The paper concludes by formulating a new open question: the preference profile reconstruction conjecture
A theory of knockout tournament seedings
This paper provides nested sets and vector representations of knockout tournaments. The paper introduces classification of probability domain assumptions and a new set of axioms. Two new seeding methods are proposed: equal gap seeding and increasing competitive intensity seeding. Under different probability domain assumptions, several axiomatic justifications are obtained for equal gap seeding. A discrete optimization approach is developed. It is applied to justify equal gap seeding and increasing competitive intensity seeding. Some justification for standard seeding is obtained. Combinatorial properties of the seedings are studied
Parameterized Complexity of Secluded Connectivity Problems
The Secluded Path problem models a situation where a sensitive information
has to be transmitted between a pair of nodes along a path in a network. The
measure of the quality of a selected path is its exposure, which is the total
weight of vertices in its closed neighborhood. In order to minimize the risk of
intercepting the information, we are interested in selecting a secluded path,
i.e. a path with a small exposure. Similarly, the Secluded Steiner Tree problem
is to find a tree in a graph connecting a given set of terminals such that the
exposure of the tree is minimized. The problems were introduced by Chechik et
al. in [ESA 2013]. Among other results, Chechik et al. have shown that Secluded
Path is fixed-parameter tractable (FPT) on unweighted graphs being
parameterized by the maximum vertex degree of the graph and that Secluded
Steiner Tree is FPT parameterized by the treewidth of the graph. In this work,
we obtain the following results about parameterized complexity of secluded
connectivity problems.
We give FPT-algorithms deciding if a graph G with a given cost function
contains a secluded path and a secluded Steiner tree of exposure at most k with
the cost at most C.
We initiate the study of "above guarantee" parameterizations for secluded
problems, where the lower bound is given by the size of a Steiner tree.
We investigate Secluded Steiner Tree from kernelization perspective and
provide several lower and upper bounds when parameters are the treewidth, the
size of a vertex cover, maximum vertex degree and the solution size. Finally,
we refine the algorithmic result of Chechik et al. by improving the exponential
dependence from the treewidth of the input graph.Comment: Minor corrections are don
Diagnostic System in Electrical Impedance Mammography: Background
Electrical impedance mammography (EIM) belongs to nonlocal techniques of image creation. It is based on a number of data collection methods, including the cross-sectional approach, the back-projection method with the weight function applied horizontally and vertically, and the static image method. The analysis of data acquired by applying the above methods enabled to work out the EIM diagnostic system. It involves the following diagnostic categories: structural percentile limits and the mammary gland structure, age-related percentile limits and age-related electric conductivity, outlying values statistics and early diagnostics of breast cancer, D-statistics and distortion of the mammographic scheme in the presence of breast cancer, diagnostic table, and the assessment of the electrical impedance image
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