相关论文: An exact algorithm for higher-dimensional orthogon…

As the development of distributed systems progresses, more and more challenges arise and the need for developing optimized systems and for optimizing existing systems from multiple perspectives becomes more stringent. In this paper I…

The problem of {\em efficiently} finding the best match for a query in a given set with respect to the Euclidean distance or the cosine similarity has been extensively studied in literature. However, a closely related problem of efficiently…

In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…

The present work surveys problems in $n$-dimensional space with $n$ large. Early development in the study of packing and covering in high dimensions was motivated by the geometry of numbers. Subsequent results, such as the discovery of the…

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…

This paper tackles the problem of finding optimal variable-height transport packaging. The goal is to reduce the empty space left in a box when shipping goods to customers, thereby saving on filler and reducing waste. We cast this problem…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…

In this article we propose a heuristic algorithm to explore search space trees associated with instances of combinatorial optimization problems. The algorithm is based on Monte Carlo tree search, a popular algorithm in game playing that is…

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…

At present, high-dimensional global optimization problems with time-series models have received much attention from engineering fields. Since it was proposed, Bayesian optimization has quickly become a popular and promising approach for…

We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…

Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…

Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…

We consider algorithmic approaches to the D-optimality problem for cases where the input design matrix is large and highly structured, in particular implicitly specified as a full quadratic or linear response-surface model in several levels…

Algorithms are given for determining $L_\infty$ isotonic regression of weighted data. For a linear order, grid in multidimensional space, or tree, of $n$ vertices, optimal algorithms are given, taking $\Theta(n)$ time. These improve upon…

In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…

In this paper I present several novel, efficient, algorithmic techniques for solving some multidimensional geometric data management and analysis problems. The techniques are based on several data structures from computational geometry…

The article proposes a heuristic approximation approach to the bin packing problem under multiple objectives. In addition to the traditional objective of minimizing the number of bins, the heterogeneousness of the elements in each bin is…

We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…