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 …
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, …
A Geometric Algorithm for Maximizing the Distance over an Intersection of Balls to a Given Point
M Costandin, B Costandin - arXiv preprint arXiv:2308.15054, 2023 - arxiv.org
In this paper the authors propose a polynomial algorithm which allows the computation of
the farthest in an intersection of balls to a given point under three additional hypothesis: the …
the farthest in an intersection of balls to a given point under three additional hypothesis: the …
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 …
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 Polynomial Algorithm for Some Relaxed Subset Sum Problems with Real Numbers
M Costandin - arXiv preprint arXiv:2207.12306, 2022 - arxiv.org
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 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 …
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", …
Deliver smart, not more! Building economically sustainable competitiveness on the ground of high agri-food trade specialization in the EU
Competitiveness has always been a multifaceted illusive concept, which has made it a real
challenge for scholars and practitioners to find the most suitable measurement tools to …
challenge for scholars and practitioners to find the most suitable measurement tools to …