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Robotic motion-planning problems, such as a UAV flying fast in a partially-known environment or a robot arm moving around cluttered objects, require finding collision-free paths quickly. Typically, this is solved by constructing a graph,…
In order to achieve speedup over conventional classical computing for finding solution of computationally hard problems, quantum computing was introduced. Quantum algorithms can be simulated in a pseudo quantum environment, but…
The computation of (i) $\varepsilon$-kernels, (ii) approximate diameter, and (iii) approximate bichromatic closest pair are fundamental problems in geometric approximation. In this paper, we describe new algorithms that offer significant…
We study the problem of path planning with soft homology constraints on a surface topologically equivalent to a disk with punctures. Specifically, we propose an algorithm, named $\Hstar$, for the efficient computation of a path homologous…
The classic problem of constrained pathfinding is a well-studied, yet challenging, topic in AI with a broad range of applications in various areas such as communication and transportation. The Weight Constrained Shortest Path Problem…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
We consider the $(1+\epsilon)$-approximate nearest neighbor search problem: given a set $X$ of $n$ points in a $d$-dimensional space, build a data structure that, given any query point $y$, finds a point $x \in X$ whose distance to $y$ is…
Shallow cuttings are a fundamental tool in computational geometry and spatial databases for solving offline and online range searching problems. For a set $P$ of $N$ points in 3-D, at SODA'14, Afshani and Tsakalidis designed an optimal…
We consider the problem of finding the set of architectural parameters for a chosen deep neural network which is optimal under three metrics: parameter size, inference speed, and error rate. In this paper we state the problem formally, and…
This paper addresses the problem of finding shortest paths homotopic to a given disjoint set of paths that wind amongst point obstacles in the plane. We present a faster algorithm than previously known.
We present a number of novel algorithms, based on mathematical optimization formulations, in order to solve a homogeneous multiprocessor scheduling problem, while minimizing the total energy consumption. In particular, for a system with a…
This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning…
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application…
The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…
The paper introduces an asymptotically optimal lifelong sampling-based path planning algorithm that combines the merits of lifelong planning algorithms and lazy search algorithms for rapid replanning in dynamic environments where edge…
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…
The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency…
We present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension. This data-structure is then applied to obtain improved algorithms for the following problems: Approximate…
The asymptotically optimal version of Rapidly-exploring Random Tree (RRT*) is often used to find optimal paths in a high-dimensional configuration space. The well-known issue of RRT* is its slow convergence towards the optimal solution. A…
Trained humans exhibit highly agile spatial skills, enabling them to operate vehicles with complex dynamics in demanding tasks and conditions. Prior work shows that humans achieve this performance by using strategies such as satisficing,…