9 citations · 9 across the 17 of their papers we have counts for
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Riesz Energy Subset Selection in the Euclidean Plane is NP-Hard: A Reduction from the Ising Model on Planar Cubic Graphs
Michael Emmerich
We prove that minimum Riesz -energy subset selection in the Euclidean plane is NP-complete already for the fixed exponent . To our knowledge, this is the first Euclidean ha…
Computing the Integral R2 Indicator by Perspective Mapping and Box Decomposition
Michael T. M. Emmerich
The continuous integral R2 indicator is a Pareto-compliant refinement of the classical finite-weight-vector R2 indicator, used in performance assessment, bounded archiving for a-po…
Exact and Fast Subset Selection Algorithms for the Bi-objective Integral R2 Indicator
Michael T. M. Emmerich
We study fixed-cardinality subset selection for the exact integral bi-objective indicator with a uniform continuum of weighted Tchebycheff scalarizing functions. The indicato…
Polynomial-Time Riesz-Energy Subset Selection for Ordered Point Sets on Lines and -Staircases
Michael T. M. Emmerich
We study efficient algorithms for one-dimensional fixed-cardinality minimum Riesz -energy subset selection on ordered real-line point sets and propose and test a polynomial-time…
On the Complexity of Minimum Riesz s-Energy Subset Selection in Euclidean and Ultrametric Spaces
Michael T. M. Emmerich, Ksenia Pereverdieva, André Deutz
We study the computational complexity of exact cardinality-constrained minimum Riesz -energy subset selection in finite metric spaces: given points, select points of m…
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…
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…