We use a novel decomposition to create succinct data structures – supporting a wide range of operations on static trees in constant time – for a variety tree classes, extending results of Munro, Nicholson, Benkner, and Wild. Motivated by the class of AVL trees, we further derive asymptotics for the information-theoretic lower bound on the number of bits needed to store tree classes whose generating functions satisfy certain functional equations. In particular, we prove that AVL trees require approximately 0.938 bits per node to encode.

Different outdoor illumination conditions drastically alter the appearance of urban scenes, and they can harm the performance of image-based robot perception systems if not seen during training. Camera simulation provides a cost-effective solution to create a large dataset of images captured under different lighting conditions. Towards this goal, we propose LightSim, a neural lighting camera simulation system that enables diverse, realistic, and controllable data generation. LightSim automatically builds lighting-aware digital twins at scale from collected raw sensor data and decomposes the scene into dynamic actors and static background with accurate geometry, appearance, and estimated scene lighting. These digital twins enable actor insertion, modification, removal, and rendering from a new viewpoint, all in a lighting-aware manner. LightSim then combines physically-based and learnable deferred rendering to perform realistic relighting of modified scenes, such as altering the sun location and modifying the shadows or changing the sun brightness, producing spatially- and temporally-consistent camera videos. Our experiments show that LightSim generates more realistic relighting results than prior work. Importantly, training perception models on data generated by LightSim can significantly improve their performance. Our project page is available at https://waabi.ai/lightsim/.

As self-driving systems become better, simulating scenarios where the autonomy stack may fail becomes more important. Traditionally, those scenarios are generated for a few scenes with respect to the planning module that takes ground-truth actor states as input. This does not scale and cannot identify all possible autonomy failures, such as perception failures due to occlusion. In this paper, we propose AdvSim, an adversarial framework to generate safety-critical scenarios for any LiDAR-based autonomy system. Given an initial traffic scenario, AdvSim modifies the actors’ trajectories in a physically plausible manner and updates the LiDAR sensor data to match the perturbed world. Importantly, by simulating directly from sensor data, we obtain adversarial scenarios that are safety-critical for the full autonomy stack. Our experiments show that our approach is general and can identify thousands of semantically meaningful safety-critical scenarios for a wide range of modern self-driving systems. Furthermore, we show that the robustness and safety of these systems can be further improved by training them with scenarios generated by AdvSim.