Article Per Year (5 Year)
p-Index From 2019 - 2024
0.444
P-Index
This Author published in this journals
All Journal Journal of Fundamental Mathematics and Applications
Marco Ripà
sPIqr Society, World Intelligence Network
Decision Sciences, Operations Research & Management

Published : 2 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 2 Documents
Search

 1 
SOLVING THE 106 YEARS OLD 3^k POINTS PROBLEM WITH THE CLOCKWISE-ALGORITHM Marco Ripà
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 2 (2020)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1907.297 KB) | DOI: 10.14710/jfma.v3i2.8551

Abstract

In this paper, we present the clockwise-algorithm that solves the extension in ????-dimensions of the infamous nine-dot problem, the well known two-dimensional thinking outside the box puzzle. We describe a general strategy that constructively produces minimum length covering trails, for any ???? ∈ N−{0}, solving the NP-complete (3×3×⋯×3)-points problem inside a 3×3×⋯×3 hypercube. In particular, using our algorithm, we explicitly draw different covering trails of minimal length h(????) = (3^???? − 1)/2, for ???? = 3, 4, 5. Furthermore, we conjecture that, for every ???? ≥ 1, it is possible to solve the 3^????-points problem with h(????) lines starting from any of the 3^???? nodes, except from the central one. Finally, we cover 3×3×3 points with a tree of size 12.
GENERAL UNCROSSING COVERING PATHS INSIDE THE AXIS-ALIGNED BOUNDING BOX Marco Ripà
Journal of Fundamental Mathematics and Applications (JFMA) Vol 4, No 2 (2021)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (3132.348 KB) | DOI: 10.14710/jfma.v4i2.12053

Abstract

Given the finite set of n_1⋅n_2⋅...⋅n_k points G(n_1,n_2,...,n_k) in R^???? such that n_k≥...≥n_2≥n_1∈Z+, we introduce a new algorithm, called MΛI, which returns an uncrossing covering path inside the minimum axis-aligned bounding box [0,n_1−1]×[0,n_2−1]×...×[0,n_k−1], consisting of 3⋅(n_1⋅n_2⋅...⋅n_k−1)−2 links of prescribed length n_k−1 units. Thus, for any n_k≥3, the link length of the covering path provided by our MΛI-algorithm is smaller than the cardinality of the set G(n_1,n_2,...,n_k). Furthermore, assuming k>2, we present an uncrossing covering path for G(3,3,...,3), comprising only 20*3^(k−3)−2 two units long edges, which is constrained by the axis-aligned bounding box [0,4−√3]×[0,4−√3]×[0,2]×...×[0,2].
Co-Authors