5 papers
Exact Dynamic Programming for Solow--Polasky Diversity Subset Selection on Lines and Staircases
Michael T. M. Emmerich
This paper studies exact fixed-cardinality Solow--Polasky diversity subset selection on ordered finite point sets, with monotone biobjective Pareto fronts and their higher…
Maximum Solow--Polasky Diversity Subset Selection Is NP-hard Even in the Euclidean Plane
Michael T. M. Emmerich, Ksenia Pereverdieva, André H. Deutz
We prove that, for every fixed , selecting a subset of prescribed cardinality that maximizes the Solow--Polasky diversity indicator is NP-hard for finite point sets in $\mat…
The Magnitude of Dominated Sets: A Pareto Compliant Indicator Grounded in Metric Geometry
Michael T. M. Emmerich
We investigate \emph{magnitude} as a new unary and strictly Pareto-compliant quality indicator for finite approximation sets to the Pareto front in multiobjective optimization. Mag…
Critical phase transitions in minimum-energy configurations for the exponential kernel family on the unit interval
Michael T. M. Emmerich
We study the optimal placement of ordered points on the unit interval for the bounded pair potential \[ K_q(d)=e^{-d^q}, \qquad q>0. \] The family interpolates between strongly…
Selecting a Maximum Solow-Polasky Diversity Subset in General Metric Spaces Is NP-hard
Michael T. M. Emmerich, Ksenia Pereverdieva, André H. Deutz
The Solow--Polasky diversity indicator (or magnitude) is a classical measure of diversity based on pairwise distances. It has applications in ecology, conservation planning, and, m…