We study the data structure version of the element distinctness problem: preprocess an array of n elements from an alphabet of size σ to answer All-Distinct queries, asking whether a given range contains only distinct elements. We first focus on uniformly random arrays: in the encoding model, where access to the input at query time is not allowed, we prove a lower bound on the expected space; for instance, the lower bound is n, 1.3627n, 1.5153n, 1.5824n bits for σ= 2,3,4,5, and approximately n√(π/(2σ)) bits for σ=ω(1). We complement this by designing different average-case optimal encodings, supporting All-Distinct queries in worst-case time O(1), o(log^2logn), or O(loglogn) depending on σ, and O(1) expected time for any σ= ω(1). We then switch to worst-case (non-random) arrays: in the indexing model, where access to the input is allowed, we prove a cell-probe space-time tradeoff lower bound showing that any index using n/b bits must have Ω(b/logb) query time. We conclude by presenting a simple index almost matching this lower bound.

In pattern matching on strings, a locate query asks for an enumeration of all the occurrences of a given pattern in a given text. The r-index [Gagie et al., 2018] is a recently presented compressed self index that stores the text and auxiliary information in compressed space. With some modifications, locate queries can be answered in optimal time [Nishimoto Tabei, 2021], which has recently been proven relevant in practice in the form of Move-r [Bertram et al., 2024]. However, there remains the practical bottleneck of evaluating function for every occurrence to report. This motivates enhancing the index by a compressed representation of the suffix array featuring efficient random access, trading off space for faster answering of locate queries [Puglisi Zhukova, 2021]. In this work, we build upon this idea considering two suitable compression schemes: Relative Lempel-Ziv [Kuruppu et al., 2010], improving the work by Puglisi and Zhukova, and LZ-End [Kreft Navarro, 2010], introducing a different trade-off where compression is better than for Relative Lempel-Ziv at the cost of slower access times. We enhance both the r-index and Move-r by the compressed suffix arrays and evaluate locate query performance in an experiment. We show that locate queries can be sped up considerably in both the r-index and Move-r, especially if the queried pattern has many occurrences. The choice between two different compression schemes offers new trade-offs regarding index size versus query performance.

We present the fastest practical construction algorithms for Huffman-shaped wavelet trees, closing the gap between theory and practice by utilizing SIMD instructions.

Automated vehicles require carefully designed cost functions, which are challenging to specify due to the complexity of the behavior they need to cover. Inverse reinforcement learning is a principled methodology for deriving cost functions, but it requires high-quality expert demonstrations, which are expensive to obtain. Recently, scenario-based testing has emerged as a promising approach for validation of driving behavior. In this paper, we introduce a novel methodology that circumvents the need for costly expert driving demonstrations by harnessing scenario-based testing. Our Test-Driven Inverse Reinforcement Learning approach leverages Bayesian inference, utilizing the outcomes of scenario tests as observations to infer cost functions. We rigorously evaluate our method on simulated and real-world scenarios and demonstrate its ability to learn cost functions that successfully pass the respective scenario tests. We also show that the learned cost function generalizes well by also passing scenario tests from an unseen validation set and illustrate that few scenario tests are sufficient to learn meaningful cost functions. This innovative framework not only streamlines the cost function specification process but also offers a cost-effective and practical solution for advancing automated driving systems.

Fast and accurate trajectory prediction is crucial for the development and validation of automated driving systems. Using driver models for prediction is a promising approach to achieve this since they can produce realistic driving behavior at low computational cost. To produce high-quality predictions, the driver model parameters need to be adapted to the current traffic situation and observed driving behavior online. Our work combines data-driven methods with driver models to obtain realistic short-term trajectory predictions. We propose to train machine learning models to predict the driver model parameters that best capture the observed behavior of other vehicles. We use attention-based architectures to process sequential input data and predict the driver model parameters as a weighted sum of prototypes, thus ensuring that the predicted driving model parameters are realistic. Compared to particle filter-based state-of-the-art methods, our approach profits from the rich representational capabilities of learned models and the high online runtime efficiency of driver models. We show that our approach outperforms state-of-the-art methods for online driver model parameter estimation on a real-world traffic dataset.

Validating robotic systems in safety-critical appli-cations requires testing in many scenarios including rare edgecases that are unlikely to occur, requiring to complement real-world testing with testing in simulation. Generative models canbe used to augment real-world datasets with generated data toproduce edge case scenarios by sampling in a learned latentspace. Autoencoders can learn said latent representation for aspecific domain by learning to reconstruct the input data froma lower-dimensional intermediate representation. However, theresulting trajectories are not necessarily physically plausible, butinstead typically contain noise that is not present in the inputtrajectory. To resolve this issue, we propose the novel Physics-Informed Trajectory Autoencoder (PITA) architecture, whichincorporates a physical dynamics model into the loss functionof the autoencoder. This results in smooth trajectories that notonly reconstruct the input trajectory but also adhere to thephysical model. We evaluate PITA on a real-world dataset ofvehicle trajectories and compare its performance to a normalautoencoder and a state-of-the-art action-space autoencoder.

To plan safely in uncertain environments, agents must balance utility with safety constraints. Safe planning problems can be modeled as a chance-constrained partially observable Markov decision process (CC-POMDP) and solutions often use expensive rollouts or heuristics to estimate the optimal value and action-selection policy. This work introduces the ConstrainedZero policy iteration algorithm that solves CC-POMDPs in belief space by learning neural network approximations of the optimal value and policy with an additional network head that estimates the failure probability given a belief. This failure probability guides safe action selection during online Monte Carlo tree search (MCTS). To avoid overemphasizing search based on the failure estimates, we introduce Δ-MCTS, which uses adaptive conformal inference to update the failure threshold during planning. The approach is tested on a safety-critical POMDP benchmark, an aircraft collision avoidance system, and the sustainability problem of safe CO₂ storage. Results show that by separating safety constraints from the objective we can achieve a target level of safety without optimizing the balance between rewards and costs.

Model predictive control (MPC) is widely used for motion planning, particularly in autonomous driving. Real-time capability of the planner requires utilizing convex approximation of optimal control problems (OCPs) for the planner. However, such approximations confine the solution to a subspace, which might not contain the global optimum. To address this, we propose using safe reinforcement learning (SRL) to obtain a new and safe reference trajectory within MPC. By employing a learning-based approach, the MPC can explore solutions beyond the close neighborhood of the previous one, potentially finding global optima. We incorporate constrained reinforcement learning (CRL) to ensure safety in automated driving, using a handcrafted energy function-based safety index as the constraint objective to model safe and unsafe regions. Our approach utilizes a state-dependent Lagrangian multiplier, learned concurrently with the safe policy, to solve the CRL problem. Through experimentation in a highway scenario, we demonstrate the superiority of our approach over both MPC and SRL in terms of safety and performance measures.

As an important part of automated vehicle development and testing, simulation makes heavy use of driver models to reproduce the behavior of traffic participants. Due to their simplicity, most models fail to capture driver behavior in interactive situations like lane changes or merging, where drivers need to consider multiple vehicles simultaneously and smoothly approach gaps. We propose the Gap APproaching Intelligent Driver Model (GAP-IDM), an extension of IDM that takes an arbitrary number of target vehicles into account and produces realistic behavior for approaching traffic gaps, even when the ego vehicle has to overtake or fall behind target vehicles. To this end, we use a target distance rectification to produce smooth behaviors even for small or negative distances, and to enforce time or distance limits on the maneuver. We evaluate the proposed model in an optional and a necessary lane change scenario and demonstrate that it generates realistic driving behavior. Possible applications of our model include simulations of interactive scenarios, development of complex driver models with multiple target vehicles, or the use as a low-level policy in a high-level behavior planning module.

Designing a safe and human-like decision-making system for an autonomous vehicle is a challenging task. Generative imitation learning is one possible approach for automating policy-building by leveraging both real-world and simulated decisions. Previous work that applies generative imitation learning to autonomous driving policies focuses on learning a low-level controller for simple settings. However, to scale to complex settings, many autonomous driving systems combine fixed, safe, optimization-based low-level controllers with high-level decision-making logic that selects the appropriate task and associated controller. In this paper, we attempt to bridge this gap in complexity by employing Safety-Aware Hierarchical Adversarial Imitation Learning (SHAIL), a method for learning a high-level policy that selects from a set of low-level controller instances in a way that imitates low-level driving data on-policy. We introduce an urban roundabout simulator that controls non-ego vehicles using real data from the Interaction dataset. We then demonstrate empirically that even with simple controller options, our approach can produce better behavior than previous approaches in driver imitation that have difficulty scaling to complex environments. Our implementation is available at https://github.com/sisl/InteractionImitation.

The Lempel-Ziv (LZ) 77 factorization of a string is a widely-used algorithmic tool that plays a central role in compression and indexing. For a length-n string over a linearly-sortable alphabet, e.g., = {1, … , σ} with σ = n^𝒪(1) , it can be computed in 𝒪(n) time. It is unknown whether this time can be achieved for the rightmost LZ parsing, where each referencing phrase points to its rightmost previous occurrence. The currently best solution takes 𝒪(n (1 + logσ/√(log n))) time (Belazzougui Puglisi SODA2016). We show that this problem is much easier to solve for the LZ-End factorization (Kreft Navarro DCC2010), where the rightmost factorization can be obtained in 𝒪(n) time for the greedy parsing (with phrases of maximal length), and in 𝒪(n + z √(log z)) time for any LZ-End parsing of z phrases. We also make advances towards a linear time solution for the general case. We show how to solve multiple non-trivial subsets of the phrases of any LZ-like parsing in 𝒪(n) time. As a prime example, we can find the rightmost occurrence of all phrases of length (log ^6.66 n / log ^2 σ ) in 𝒪(n / log _σ n) time and space.