Related papers: Optimizing Symbol Visibility through Displacement
Binary embedding is the problem of mapping points from a high-dimensional space to a Hamming cube in lower dimension while preserving pairwise distances. An efficient way to accomplish this is to make use of fast embedding techniques…
Our research deals with the optimization version of the set partition problem, where the objective is to minimize the absolute difference between the sums of the two disjoint partitions. Although this problem is known to be NP-hard and…
Visual localization is a fundamental task for a wide range of applications in the field of robotics. Yet, it is still a complex problem with no universal solution, and the existing approaches are difficult to scale: most state-of-the-art…
Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…
An upward drawing of a tree is a drawing such that no parents are below their children. It is order-preserving if the edges to children appear in prescribed order around each node. Chan showed that any tree has an upward order-preserving…
Given a collection of red and blue mobile agents located on two grid rows, we seek to move all the blue agents to the far left side and all the red agents to the far right side, thus \textit{physically sorting} them according to color. The…
Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
In this paper, we study planar drawings of maximal outerplanar graphs with the objective of achieving small height. A recent paper gave an algorithm for such drawings that is within a factor of 4 of the optimum height. In this paper, we…
In this paper, using an optimal partition approach, we study the parametric analysis of a second-order conic optimization problem, where the objective function is perturbed along a fixed direction. We characterize the notions of so-called…
Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
We propose a novel optimization-based approach to embedding heterogeneous high-dimensional data characterized by a graph. The goal is to create a two-dimensional visualization of the graph structure such that edge-crossings are minimized…
In the Strip Packing problem, we are given a vertical strip of fixed width and unbounded height, along with a set of axis-parallel rectangles. The task is to place all rectangles within the strip, without overlaps, while minimizing the…
Motivated by automated junction recognition in tracking data, we study a problem of placing a square or disc of fixed size in an arrangement of lines or line segments in the plane. We let distances among the intersection points of the lines…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
The list-labeling problem captures the basic task of storing a dynamically changing set of up to $n$ elements in sorted order in an array of size $m = (1 + \Theta(1))n$. The goal is to support insertions and deletions while moving around…
Nowadays, Non-Linear Least-Squares embodies the foundation of many Robotics and Computer Vision systems. The research community deeply investigated this topic in the last years, and this resulted in the development of several open-source…