相关论文: Combinatorial settlement planning

Most of the routing algorithms for unmanned vehicles, that arise in data gathering and monitoring applications in the literature, rely on the Global Positioning System (GPS) information for localization. However, disruption of GPS signals…

In 1962, Tutte provided a formula for the number of combinatorial triangulations, that is, maximal planar graphs with a fixed triangular face and $n$ additional vertices. In this note, we study how many ways a combinatorial triangulation…

With the increasing attention to the integrated satellite-terrestrial networks (ISTNs), the satellite gateway placement problem becomes of paramount importance. The resulting network performance may vary depending on the different design…

This article focuses on a combinatorial structure specific to triangulated plane graphs with quadrangular outer face and no separating triangle, which are called irreducible triangulations. The structure has been introduced by Xin He under…

The optimal placement of measurement devices in electrical power systems is commonly modeled through the power dominating set problem. However, in real-world applications, these devices have limited capacities, leading to a capacitated…

Advances in computational optimization allow for the organization of large combinatorial markets. We aim for allocations and competitive equilibrium prices, i.e. outcomes that are in the core. The research is motivated by the design of…

We present a computational methodology for obtaining rotationally symmetric sets of points satisfying discrete geometric constraints, and demonstrate its applicability by discovering new solutions to some well-known problems in…

The paper briefly describes a basic set of special combinatorial engineering frameworks for solving complex problems in the field of hierarchical modular systems. The frameworks consist of combinatorial problems (and corresponding models),…

Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…

In this paper we consider multidimensional mechanism design problem for selling discrete substitutable items to a group of buyers. Previous work on this problem mostly focus on stochastic description of valuations used by the seller.…

We give a complete conjectural formula for the number $e_r(d,m)$ of maximum possible ${\mathbb{F}}q$-rational points on a projective algebraic variety defined by $r$ linearly independent homogeneous polynomial equations of degree $d$ in…

Stochastic Model Predictive Control has proved to be an efficient method to plan trajectories in uncertain environments, e.g., for autonomous vehicles. Chance constraints ensure that the probability of collision is bounded by a predefined…

There are many papers studying properties of point sets in the Euclidean space $\mathbb{E}^m$ or on integer grids $\mathbb{Z}^m$, with pairwise integral or rational distances. In this article we consider the distances or coordinates of the…

A combinatorial trade is a pair of sets of blocks of elements that can be exchanged while preserving relevant subset intersection constraints. The class of balanced and swap-robust minimal trades was proposed in [1] for exchanging blocks of…

Spectral clustering is one of the most popular algorithms to group high dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successful applications, its theoretical properties have not been…

We show that finding orthogonal grid-embeddings of plane graphs (planar with fixed combinatorial embedding) with the minimum number of bends in the so-called Kandinsky model (which allows vertices of degree $> 4$) is NP-complete, thus…

In our paper, we apply additive-combinatorial methods to study the distribution of the set of squares $\mathcal{R}$ in the prime field. We obtain the best upper bound on the number of gaps in $\mathcal{R}$ at the moment and generalize this…

Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…

Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings $R_k$.…

This paper introduces a combinatorial optimization approach to register allocation and instruction scheduling, two central compiler problems. Combinatorial optimization has the potential to solve these problems optimally and to exploit…