On Maximizing the Distance to a Given Point over an Intersection of Balls II
M Costandin - arXiv preprint arXiv:2307.13015, 2023 - arxiv.org
In this paper the problem of maximizing the distance to a given fixed point over an intersection
of balls is considered. It is known that this problem is NP complete in the general case, …
of balls is considered. It is known that this problem is NP complete in the general case, …
On a Geometric Interpretation Of the Subset Sum Problem
M Costandin - arXiv preprint arXiv:2410.19024, 2024 - arxiv.org
For $S \in \mathbb{N}^n$ and $T \in \mathbb{N}$, the Subset Sum Problem (SSP) $\exists^?
x \in \{0,1\}^n $ such that $S^T\cdot x = T$ can be interpreted as the problem of deciding …
x \in \{0,1\}^n $ such that $S^T\cdot x = T$ can be interpreted as the problem of deciding …
Fully Subexponential Time Approximation Scheme for Product Partition
M Costandin - arXiv preprint arXiv:2405.17692, 2024 - arxiv.org
In this paper we study the Product Partition Problem (PPP), ie we are given a set of $n$ natural
numbers represented on $m$ bits each and we are asked if a subset exists such that the …
numbers represented on $m$ bits each and we are asked if a subset exists such that the …
A Quasi-Polynomial Algorithm for Subset-Sum Problems with At Most One Solution
M Costandin, B Costandin - arXiv preprint arXiv:2308.15054, 2023 - arxiv.org
In this paper we study the problem of maximizing the distance to a given point over an
intersection of balls. It was already known that this problem can be solved in polynomial time and …
intersection of balls. It was already known that this problem can be solved in polynomial time and …
Tight Bounds for the Maximum Distance Over a Polytope to a Given Point
M Costandin, B Costandin - arXiv preprint arXiv:2310.06185, 2023 - arxiv.org
In this paper we study the problem of maximizing the distance to a given point $C_0$ over a
polytope $\mathcal{P}$. Assuming that the polytope is circumscribed by a known ball we …
polytope $\mathcal{P}$. Assuming that the polytope is circumscribed by a known ball we …
A Subexponential Reduction from Product Partition to Subset Sum
M Costandin - arXiv preprint arXiv:2405.12555, 2024 - arxiv.org
In this paper we study the Product Partition Problem (PPP), ie we are given a set of $n$ natural
numbers represented on $m$ bits each and we are asked if a subset exists such that the …
numbers represented on $m$ bits each and we are asked if a subset exists such that the …
[PDF][PDF] A Polynomial Algorithm for Some Relaxed Subset Sum Problems with Real Numbers
M Costandin - arXiv preprint arXiv:2207.12306, 2022 - researchgate.net
In this paper we study the subset sum problem with real numbers. Starting from the given
problem, we formulate a quadratic maximization problem over a polytope, P, which is …
problem, we formulate a quadratic maximization problem over a polytope, P, which is …
A Deterministic Algorithm of Quasi-Polynomial Complexity for Clipped Cubes Volume Approximation
M Costandin - arXiv preprint arXiv:2407.21365, 2024 - arxiv.org
We give a deterministic method of quasi-polynomial complexity to approximate the volume
of the intersection of the unit hypercube with two specific sets. The method can actually be …
of the intersection of the unit hypercube with two specific sets. The method can actually be …
An Algorithm for Global Minimization of Non-Convex Functions
M Costandin - Available at SSRN 4821892, 2024 - papers.ssrn.com
In this paper we present a novel global optimization algorithm. Given a function $ f $ to
minimize, our approach is to construct a derived functions from it, that we call" eroded function", …
minimize, our approach is to construct a derived functions from it, that we call" eroded function", …
Sustainable development disparities in the EU-27 based on R&D and innovation factors
Ever since it was adopted in 2015 by the United Nations, the 2030 Agenda for Sustainable
Development has acted as the main guideline for European Union Member States in regard …
Development has acted as the main guideline for European Union Member States in regard …