相关论文: Combinatorial settlement planning

Using the recently proposed model of combinatorial landscapes: local optima networks, we study the distribution of local optima in two classes of instances of the quadratic assignment problem. Our results indicate that the two problem…

As the share of renewable sources is increasing the need for multiple storage units appropriately sized and located is essential to achieve better inertial response. This work focuses on the question of "how to distribute constant number of…

Given a set of $m$ points and a set of $n$ lines in the plane, we consider the problem of computing the faces of the arrangement of the lines that contain at least one point. In this paper, we present an $O(m^{2/3}n^{2/3}+(n+m)\log n)$ time…

We use computational experiments to find the rectangles of minimum perimeter into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. In many of the packings…

We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a…

Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…

The optimization of the light scattered by photonic cluster made of small particles is studied with the help of the local perturbation method and special optimization algorithm. It was shown that photonic cluster can be optimized in a such…

The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging…

We propose a method for redistricting, decomposing a geographical area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are compact and contiguous. Each district is the…

By modeling the uncertainty of spinning reserves provided by energy storage with probabilistic constraints, a new optimal scheduling mode is proposed for minimizing the operating costs of an isolated microgrid (MG) by using…

A family $\mathcal{F}$ on ground set $\{1,2,\ldots, n\}$ is maximal $k$-wise intersecting if every collection of $k$ sets in $\mathcal{F}$ has non-empty intersection, and no other set can be added to $\mathcal{F}$ while maintaining this…

We are interested in embedding trees T with maximum degree at most four in a rectangular grid, such that the vertices of T correspond to grid points, while edges of T correspond to non-intersecting straight segments of the grid lines. Such…

We study the combinatorics of hyperplane arrangements over arbitrary fields. Specifically, we determine in which situation an arrangement and its reduction modulo a prime number have isomorphic lattices via the use of minimal strong…

The installation and operation distributed energy resources (DER) and the electrification of the heat supply significantly changes the interaction of the residential building stock with the grid infrastructure. Evaluating the mass…

This article addresses the residential energy cost optimization problem in smart grid. To date, most of the previous research only consider a partial aspect of the cost optimization problem. As a result, they fail to analyze scenarios when…

This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive generalized anticode construction.…

We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively…

We deal with the asymptotic enumeration of combinatorial structures on planar maps. Prominent instances of such problems are the enumeration of spanning trees, bipartite perfect matchings, and ice models. The notion of orientations with…

Despite the rich existing literature about minimax optimization in continuous settings, only very partial results of this kind have been obtained for combinatorial settings. In this paper, we fill this gap by providing a characterization of…

In this work, we study a triangular variant of the Lights Out game, proposed in the 2025 Capixaba Mathematics Olympiad. We present a combinatorial description of the game, formally characterize its operations, and introduce the notion of a…