Related papers: Symmetry-Based Search Space Reduction For Grid Map…
Path planning is a fundamental problem in road networks, with the goal of finding a path that optimizes objectives such as shortest distance or minimal travel time. Existing methods typically use graph indexing to ensure the efficiency of…
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…
We present an iterative method to efficiently solve the optimal transportation problem for a class of strictly convex costs which includes quadratic and p-power costs. Given two probability measures supported on a discrete grid with n…
3D Gaussian Splatting (3DGS) has recently gained significant attention for high-quality and efficient view synthesis, making it widely adopted in fields such as AR/VR, robotics, and autonomous driving. Despite its impressive algorithmic…
The minimisation of cost functions is crucial in various optimisation fields. However, identifying their global minimum remains challenging owing to the huge computational cost incurred. This work analytically expresses the computational…
In this work, we investigate how exploiting symmetry when creating and modifying structural models may speed up global atomistic structure optimization. We propose a search strategy in which models start from high symmetry configurations…
In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique…
In this paper we introduce two algorithms for neural architecture search (NASGD and NASAGD) following the theoretical work by two of the authors [5] which used the geometric structure of optimal transport to introduce the conceptual basis…
Maintaining a map online is resource-consuming while a robust navigation system usually needs environment abstraction via a well-fused map. In this paper, we propose a mapless planner which directly conducts such abstraction on the unfused…
Bidirectional motion planning often reduces planning time compared to its unidirectional counterparts. It requires connecting the forward and reverse search trees to form a continuous path. However, this process could fail and restart the…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
We present a novel characterization of the mapping of multiple parallelism forms (e.g. data and model parallelism) onto hierarchical accelerator systems that is hierarchy-aware and greatly reduces the space of software-to-hardware mapping.…
The efficient fusion of depth maps is a key part of most state-of-the-art 3D reconstruction methods. Besides requiring high accuracy, these depth fusion methods need to be scalable and real-time capable. To this end, we present a novel…
We propose a novel algorithm to solve multi-robot motion planning (MRMP) rapidly, called Simultaneous Sampling-and-Search Planning (SSSP). Conventional MRMP studies mostly take the form of two-phase planning that constructs roadmaps and…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
This paper presents an enhanced version of the Interactive Voting-Based Map Matching algorithm, designed to efficiently process trajectories with varying sampling rates. The main aim is to reconstruct GPS trajectories with high accuracy,…
Path planning for autonomous driving with dynamic obstacles poses a challenge because it needs to perform a higher-dimensional search (with time-dimension) while still meeting real-time constraints. This paper proposes an algorithm-hardware…
In this work, we propose a novel adaptive grid mapping approach, the Adaptive Patched Grid Map, which enables a situational aware grid based perception for autonomous vehicles. Its structure allows a flexible representation of the…
Considering a 2D matrix of positive and negative numbers, how might one draw a rectangle within it whose contents sum higher than all other rectangles'? This fundamental problem, commonly known the maximum rectangle problem or subwindow…