arXiv subjects

José-Manuel Higes-López

Publications and source records attributed to José-Manuel Higes-López.

3 recordsLinked to original sources

arXiv2025

The Euclidean $k$-Matching Problem is NP-hard

Let $G$ be a complete edge-weighted graph on $n$ vertices. To each subset of vertices of $G$ assign the cost of the minimum spanning tree of the subset as its weight. Suppose that $n$ is a multiple of some fixed positive integer $k$. The $k$-matching problem is the problem of finding a partition of the vertices of $G$ into $k$-sets, that minimizes the sum of the weights of the $k$-sets. The case $k=3$ has been shown to be NP-hard [Johnsson et al.,1998]. In the Euclidean version, the vertices of $G$ are points in the plane and the weight of an edge is the Euclidean distance between its endpoints. We call this problem the Euclidean $k$-matching problem. We show that, for every fixed $k \ge 3$, the Euclidean $k$-matching is NP-hard. This resolves an open problem in the literature and provides the first theoretical justification for the use of known heuristic methods in the case $k=3$. We also show that the problem remains NP-hard if the trees are required to be paths.

cs.CG↗

arXiv2025

Modeling energy collection with shortest paths in rectangular grids: an efficient algorithm for energy harvesting

Parabolic Trough solar fields are among the most prominent methods for harnessing solar energy. However, continuous sun-tracking movements leads to wear and degradation of the tracking system, raising the question of whether the rotations can be minimized without compromising energy capture. In this paper, we address this question by exploring two problems: (1) minimizing the number of SCA rotational movements while maintaining energy production within a specified range, and (2) maximizing energy capture when the number of rotations is limited. Unlike prior work, we develop a general framework that considers variable conditions. By transforming the problem into grid-based path optimization, we design polynomial-time algorithms that can operate independently of the weather throughout the day. Through realistic simulations and experiments using real-world data, our methods show that rotational movements of solar trackers can be reduced by at least 10% while maintaining over 95% energy collection efficiency. These results offer a scalable solution for improving the operational lifespan of the solar field. Furthermore, our methods can be integrated with solar irradiance forecasting, enhancing their robustness and suitability for real-world deployment.

cs.DM↗

arXiv2025

Optimal covering of rectangular grid graphs with tours of constrained length

Given a rectangular grid graph with a special vertex at a corner called base station, we study the problem of covering the vertices of the entire graph with tours that start and end at the base station and whose lengths do not exceed a given threshold, while minimizing a quality measure. We consider two objective functions: minimizing the number of tours and minimizing the sum of their lengths. We present an algorithm that computes the optimal solution for both objectives in linear time with respect to the grid size.

cs.DM↗