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We present a major revamp of the point-location data structure for general two-dimensional subdivisions via randomized incremental construction, implemented in CGAL, the Computational Geometry Algorithms Library. We can now guarantee that…

Many applications like pointer analysis and incremental compilation require maintaining a topological ordering of the nodes of a directed acyclic graph (DAG) under dynamic updates. All known algorithms for this problem are either only…

We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…

We show that every directed graph $G$ with $n$ vertices and $m$ edges admits a directed acyclic graph (DAG) with $m^{1+o(1)}$ edges, called a DAG projection, that can either $(1+1/\text{polylog} (n))$-approximate distances between all pairs…

We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…

With the flourish of differentiable neural architecture search (NAS), automatically searching latency-constrained architectures gives a new perspective to reduce human labor and expertise. However, the searched architectures are usually…

We present a new and surprisingly simple analysis of random-shift decompositions -- originally proposed by Miller, Peng, and Xu [SPAA'13]: We show that decompositions for exponentially growing scales $D = 2^0, 2^1, \ldots,…

Parallel real-time systems (e.g., autonomous driving systems) often contain functionalities with complex dependencies and execution uncertainties, leading to significant timing variability which can be represented as a probabilistic…

Recent advances have established the identifiability of a directed acyclic graph (DAG) under additive noise models (ANMs), spurring the development of various causal discovery methods. However, most existing methods make restrictive model…

One of the key challenges in Neural Architecture Search (NAS) is to efficiently rank the performances of architectures. The mainstream assessment of performance rankers uses ranking correlations (e.g., Kendall's tau), which pay equal…

Graph expansion analysis of computational DAGs is useful for obtaining communication cost lower bounds where previous methods, such as geometric embedding, are not applicable. This has recently been demonstrated for Strassen's and…

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches…

Stochastic variance-reduced algorithms such as Stochastic Average Gradient (SAG) and SAGA, and their deterministic counterparts like the Incremental Aggregated Gradient (IAG) method, have been extensively studied in large-scale machine…

In this paper, we introduce a new reinforcement learning (RL) based neural architecture search (NAS) methodology for effective and efficient generative adversarial network (GAN) architecture search. The key idea is to formulate the GAN…

In Bayesian Network Structure Learning (BNSL), one is given a variable set and parent scores for each variable and aims to compute a DAG, called Bayesian network, that maximizes the sum of parent scores, possibly under some structural…

Owing to their unprecedented comprehension capabilities, large language models (LLMs) have become indispensable components of modern web search engines. From a technical perspective, this integration represents retrieval-augmented…

Graph-based approaches to nearest neighbor search are popular and powerful tools for handling large datasets in practice, but they have limited theoretical guarantees. We study the worst-case performance of recent graph-based approximate…

We develop a statistical proxy framework for retrieval-augmented generation (RAG), designed to formalize how a language model (LM) should balance its own predictions with retrieved evidence. For each query x, the system combines a frozen…

Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms. We present a randomized Las Vegas dynamic connectivity data structure with $O(\log n(\log\log n)^2)$ amortized expected update time and $O(\log…

\textit{Differentiable ARchiTecture Search} (DARTS) has recently become the mainstream of neural architecture search (NAS) due to its efficiency and simplicity. With a gradient-based bi-level optimization, DARTS alternately optimizes the…