1. On ▫$L^2$▫ approximation by planar Pythagorean-hodograph curvesRida T. Farouki, Marjetka Knez, Vito Vitrih, Emil Žagar, 2025, original scientific article Abstract: The ▫$L^2$▫ approximation of planar curves by Pythagorean-hodograph (PH) polynomial curves is addressed, based on the distance defined by a metric for planar curves represented as complex valued functions of a real parameter. Because of the nonlinear nature of polynomial PH curves, constructing ▫$L^2$▫ approximants involves solving a nonlinear optimization problem. However, a simplified method that requires only the solution of a linear system may be developed by formulating the ▫$L^2$▫ approximation in the preimage space. The extension of the methodology to approximation by PH B-spline curves is also addressed, and several examples are provided to illustrate its implementation and potential.
Keywords: ▫$L^2$▫ approximation, complex polynomial, Pythagorean-hodograph curve, Pythagorean-hodograph spline, preimage
Published in RUP: 30.05.2025; Views: 184; Downloads: 4
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3. Scaffolding problems revisited : complexity, approximation and fixed parameter tractable algorithms, and some special casesMathias Weller, Annie Chateau, Clément Jean Dallard, Rodolphe Giroudeau, 2018, original scientific article Keywords: complexity, approximation, lower bound, kernel, scaffolding, {ISK4, wheel}-free graph
Published in RUP: 11.02.2020; Views: 2374; Downloads: 64
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6. Perfect phylogenies via branchings in acyclic digraphs and a generalization of Dilworth's theoremAdemir Hujdurović, Martin Milanič, Edin Husić, Romeo Rizzi, Alexandru I. Tomescu, 2017, published scientific conference contribution abstract Keywords: perfect phylogeny, NP-hard problem, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic
Published in RUP: 17.09.2018; Views: 3022; Downloads: 123
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7. Reconstructing perfect phylogenies via binary matrices, branchings in DAGs, and a generalization of Dilworth's theoremAdemir Hujdurović, Martin Milanič, Edin Husić, Romeo Rizzi, Alexandru I. Tomescu, 2018, published scientific conference contribution abstract Keywords: perfect phylogeny, NP-hard problem, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic
Published in RUP: 17.09.2018; Views: 2954; Downloads: 87
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8. Reconstructing perfect phylogenies via binary matrices, branchings in DAGs, and a generalization of Dilworth's theoremMartin Milanič, 2018, published scientific conference contribution abstract (invited lecture) Keywords: perfect phylogeny, NP-hard problem, graph coloring, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, heuristic
Published in RUP: 17.09.2018; Views: 2840; Downloads: 22
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9. Perfect phylogenies via branchings in acyclic digraphs and a generalization of Dilworth's theoremAdemir Hujdurović, Edin Husić, Martin Milanič, Romeo Rizzi, Alexandru I. Tomescu, 2018, original scientific article Keywords: perfect phylogeny, minimum conflict-free row split problem, branching, acyclic digraph, chain partition, Dilworth's theorem, min-max theorem, approximation algorithm, APXhardness
Published in RUP: 08.05.2018; Views: 3412; Downloads: 160
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10. The minimum conflict-free row split problem revisitedAdemir Hujdurović, Edin Husić, Martin Milanič, Romeo Rizzi, Alexandru I. Tomescu, 2016, published scientific conference contribution Keywords: #the #minimum conflict-free row split problem, branching, Dilworth's theorem, min-max theorem, approximation algorithm, APX-hardness
Published in RUP: 14.11.2017; Views: 4112; Downloads: 283
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