Related papers: Approximately Optimal Search on a Higher-dimension…
A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown…
Hough transform (HT) has been the most common method for circle detection exhibiting robustness but adversely demanding a considerable computational load and large storage. Alternative approaches include heuristic methods that employ…
Vertex Descent is a local search algorithm which forms the basis of a wide spectrum of tabu search, simulated annealing and hybrid evolutionary algorithms for graph colouring. These algorithms are usually treated as experimental and provide…
We propose an algorithmic framework for efficient anytime motion planning on large dense geometric roadmaps, in domains where collision checks and therefore edge evaluations are computationally expensive. A large dense roadmap (graph) can…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
Using the 20 questions estimation framework with query-dependent noise, we study non-adaptive search strategies for a moving target over the unit cube with unknown initial location and velocities under a piecewise constant velocity model.…
Creating mobile robots which are able to find and manipulate objects in large environments is an active topic of research. These robots not only need to be capable of searching for specific objects but also to estimate their poses often…
Searching for collisions in random functions is a fundamental computational problem, with many applications in symmetric and asymmetric cryptanalysis. When one searches for a single collision, the known quantum algorithms match the query…
We propose approximately exact line search (AELS), which uses only function evaluations to select a step size within a constant fraction of the exact line search minimizer of a unimodal objective. We bound the number of iterations and…
The study of optimal decision trees has gained increasing attention in recent years; however, despite substantial progress, it still suffers from two major challenges: First, trees constructed by existing optimal decision tree (ODT)…
We study the convergence of the Augmented Decomposition Algorithm (ADA) proposed in [32] for solving multi-block separable convex minimization problems subject to linear constraints. We show that the global convergence rate of the exact ADA…
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…
Computing optimal control policies for complex dynamical systems requires approximation methods to remain computationally tractable. Several approximation methods have been developed to tackle this problem. However, these methods do not…
Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by most existing methods. We…
To overcome the obstructions imposed by high-dimensional bipedal models, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The process begins with trajectory optimization to design an…
Searching for high-dimensional vector data with high accuracy is an inevitable search technology for various types of data. Graph-based indexes are known to reduce the query time for high-dimensional data. To further improve the query time…
The Maximum k-plex Problem is an important combinatorial optimization problem with increasingly wide applications. Due to its exponential time complexity, many heuristic methods have been proposed which can return a good-quality solution in…
Higher-dimensional rewriting is founded on a duality of rewrite systems and cell complexes, connecting computational mathematics to higher categories and homotopy theory: the two sides of a rewrite rule are two halves of the boundary of an…
Klee's measure problem (computing the volume of the union of $n$ axis-parallel boxes in $\mathbb{R}^d$) is well known to have $n^{\frac{d}{2}\pm o(1)}$-time algorithms (Overmars, Yap, SICOMP'91; Chan FOCS'13). Only recently, a conditional…
This work proposes a sampling-based (non-intrusive) approach within the context of low-rank separated representations to tackle the issue of curse-of-dimensionality associated with the solution of models, e.g., PDEs/ODEs, with…