Outside the box

The Rectangular Spiral or the n_1 × n_2 × · · · × n_k Points Problem

  • Marco Ripà
    • Categories Bound-constrained Optimization, Combinatorial Optimization, Graphs and Matroids Tags , , , , , , ,

    A generalization of Ripà’s square spiral solution for the n × n × ··· × n Points Upper Bound Problem. Additionally, we provide a non-trivial lower bound for the k-dimensional n_1 × n_2 × ··· × n_k Points Problem. In this way, we can build a range in which, with certainty, all the best possible … Read more

    Solving the n_1 × n_2 × n_3 Points Problem for n_3 < 6

  • Marco Ripà
    • Categories Graphs and Matroids Tags , , , , , , , ,

    In this paper, we show enhanced upper bounds of the nontrivial \(n_1 \times n_2 \times n_3\) points problem for every \(n_1 \leq n_2 \leq n_3 < 6\). We present new patterns that significantly improve the previously known algorithms for finding minimum-link covering paths and trails. CitationAn old version of the present paper has been published … Read more