Fundamenta Informaticae - Volume 184, issue 3

Authors: Adamson, Duncan | Deligkas, Argyrios | Gusev, Vladimir | Potapov, Igor

Article Type: Research Article

Abstract: Crystal Structure Prediction (CSP) is one of the central and most challenging problems in materials science and computational chemistry. In CSP, the goal is to find a configuration of ions in 3D space that yields the lowest potential energy. Finding an efficient procedure to solve this complex optimisation question is a well known open problem. Due to the exponentially large search space, the problem has been referred in several materials-science papers as “NP-Hard and very challenging” without a formal proof. This paper fills a gap in the literature providing the first set of formally proven NP-Hardness results for a variant …of CSP with various realistic constraints. In particular, we focus on the problem of removal : the goal is to find a substructure with minimal potential energy, by removing a subset of the ions. Our main contributions are NP-Hardness results for the CSP removal problem, new embeddings of combinatorial graph problems into geometrical settings, and a more systematic exploration of the energy function to reveal the complexity of CSP. In a wider context, our results contribute to the analysis of computational problems for weighted graphs embedded into the three-dimensional Euclidean space. Show more

Keywords: Energy Minimisation, Graph theory, Euclidean Graphs, NP-Hard Problems, Crystal Structure Prediction

DOI: 10.3233/FI-2021-2096

Citation: Fundamenta Informaticae, vol. 184, no. 3, pp. 181-203, 2021

Authors: Keikha, Vahideh | Aghamolaei, Sepideh | Mohades, Ali | Ghodsi, Mohammad

Article Type: Research Article

Abstract: The k -center problem is to choose a subset of size k from a set of n points such that the maximum distance from each point to its nearest center is minimized. Let Q = {Q 1 , . . . , Q n } be a set of polygons or segments in the region-based uncertainty model, in which each Q i is an uncertain point, where the exact locations of the points in Q i are unknown. The geometric objects such as segments and polygons can be models of a point set. We define …the uncertain version of the k -center problem as a generalization in which the objective is to find k points from Q to cover the remaining regions of Q with minimum or maximum radius of the cluster to cover at least one or all exact instances of each Q i , respectively. We modify the region-based model to allow multiple points to be chosen from a region, and call the resulting model the aggregated uncertainty model . All these problems contain the point version as a special case, so they are all NP-hard with a lower bound 1.822 for the approximation factor. We give approximation algorithms for uncertain k -center of a set of segments and polygons. We also have implemented some of our algorithms on a data-set to show our theoretical performance guarantees can be achieved in practice. Show more

Keywords: k-center Uncertain data Approximation algorithms

DOI: 10.3233/FI-2021-2097

Citation: Fundamenta Informaticae, vol. 184, no. 3, pp. 205-231, 2021

Authors: Mitrović, Melanija | Hounkonnou, Mahouton Norbert | Baroni, Marian Alexandru

Article Type: Research Article

Abstract: This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also draw attention to its possible applications in other (constructive) mathematics disciplines, in computer science, social sciences, economics, etc. Another important goal of this paper is to provide a clear, understandable picture of constructive semigroups with apartness in Bishop’s style both to (classical) algebraists and the ones who apply algebraic knowledge.

Keywords: Semigroup with apartness, set with apartness, co-quasiorder, co-equivalence, co-congruence

DOI: 10.3233/FI-2021-2098

Citation: Fundamenta Informaticae, vol. 184, no. 3, pp. 233-271, 2021