We consider the problem of finding a fundamental cycle basis with minimum total cost in an undirected graph. This problem is NP-hard and has several interesting applications. Since fundamental cycle bases correspond to spanning trees, we propose a local search algorithm, a tabu search and...

We demonstrate that two key theorems of Amaldi et al. (Math Methods Oper Res 69:205–223, 2009 ), which they presented with rather complicated proofs, can be more easily and cleanly established using a simple and classical property of binary matroids. Besides a simpler proof, we see that both...

We consider the problem of finding a fundamental cycle basis with minimum total cost in an undirected graph. This problem is NP-hard and has several interesting applications. Since fundamental cycle bases correspond to spanning trees, we propose a local search algorithm, a tabu search and...

The Molecular Distance Geometry Problem (MDGP) consists in finding an embedding in R3 of a nonnegatively weighted simple undirected graph with the property that the Euclidean distances between embedded adjacent vertices must be the same as the corresponding edge weights. The Discretizable...

We demonstrate that two key theorems of Amaldi et al. (Math Methods Oper Res 69:205–223, <CitationRef CitationID="CR1">2009</CitationRef>), which they presented with rather complicated proofs, can be more easily and cleanly established using a simple and classical property of binary matroids. Besides a simpler proof, we see that both...</citationref>

The Distance Geometry Problem in three dimensions consists in finding an embedding in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathbb{R}^3}$$</EquationSource> </InlineEquation> of a given nonnegatively weighted simple undirected graph such that edge weights are equal to the corresponding Euclidean distances in the embedding. This is a continuous search problem...</equationsource></inlineequation>

In the bottleneck hyperplane clustering problem, given n points in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathbb{R}^{d}$</EquationSource> </InlineEquation> and an integer k with 1≤k≤n, we wish to determine k hyperplanes and assign each point to a hyperplane so as to minimize the maximum Euclidean distance between each point and its assigned hyperplane. This...</equationsource></inlineequation>