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We investigate the number of maximal independent set queries required to reconstruct the edges of a hidden graph. We show that randomised adaptive algorithms need at least $\Omega(\Delta^2 \log(n / \Delta) / \log \Delta)$ queries to…

We reexamine fundamental problems from computational geometry in the word RAM model, where input coordinates are integers that fit in a machine word. We develop a new algorithm for offline point location, a two-dimensional analog of sorting…

This article provides a comprehensive systematic literature review of academic studies, industrial applications, and real-world deployments from 2018 to 2025, providing a practical guide and detailed overview of modern Retrieval-Augmented…

We study networked binary classification on a directed acyclic graph (DAG) where each agent observes only a subset of the feature columns of a shared dataset. Agents act sequentially along the DAG: each receives prediction columns from its…

Learning the underlying Bayesian Networks (BNs), represented by directed acyclic graphs (DAGs), of the concerned events from purely-observational data is a crucial part of evidential reasoning. This task remains challenging due to the large…

Retrieval-augmented generation (RAG) has become a cornerstone for knowledge-intensive tasks. However, the efficacy of RAG is often bottlenecked by the ``one-size-fits-all'' retrieval paradigm, as different queries exhibit distinct…

In this paper, we develop a new approach to learning high-dimensional Poisson directed acyclic graphical (DAG) models from only observational data without strong assumptions such as faithfulness and strong sparsity. A key component of our…

We present the first optimal randomized algorithm for constructing the order-$k$ Voronoi diagram of $n$ points in two dimensions. The expected running time is $O(n\log n + nk)$, which improves the previous, two-decades-old result of Ramos…

We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound, both involving the visit of an $n$-node tree of height $h$ under the assumption that a node can…

Dense Associative Memory (DAM) generalizes Hopfield networks through higher-order interactions and achieves storage capacity that scales as $O(N^{n-1})$ under suitable pattern separation conditions. Existing dynamical analyses primarily…

We present practical linear and almost linear-time algorithms to compute a chain decomposition of a directed acyclic graph (DAG), $G=(V,E)$. The number of vertex-disjoint chains computed is very close to the minimum. The time complexity of…

This paper addresses the guessing game in building production RAG. Classical rank-centric IR metrics (nDCG/MAP/MRR) are a poor fit for RAG, where LLMs consume a set of passages rather than a browsed list; position discounts and…

In this paper, we investigate a new variant of neural architecture search (NAS) paradigm -- searching with random labels (RLNAS). The task sounds counter-intuitive for most existing NAS algorithms since random label provides few information…

Learning graphical structures based on Directed Acyclic Graphs (DAGs) is a challenging problem, partly owing to the large search space of possible graphs. A recent line of work formulates the structure learning problem as a continuous…

Retrieval-augmented generation (RAG) has emerged as a promising paradigm for improving factual accuracy in large language models (LLMs). We introduce a benchmark designed to evaluate RAG pipelines as a whole, evaluating a pipeline's ability…

Test-time scaling has emerged as a critical avenue for enhancing the reasoning capabilities of Large Language Models (LLMs). Though the straight-forward ''best-of-$N$'' (BoN) strategy has already demonstrated significant improvements in…

Depth First Search (DFS) tree is a fundamental data structure for solving graph problems. The DFS tree of a graph $G$ with $n$ vertices and $m$ edges can be built in $O(m+n)$ time. Till date, only a few algorithms have been designed for…

Convolutional Neural Networks (CNN) have been regarded as a capable class of models for visual recognition problems. Nevertheless, it is not trivial to develop generic and powerful network architectures, which requires significant efforts…

We study reachability and shortest paths problems in dynamic directed graphs. Whereas algebraic dynamic data structures supporting edge updates and reachability/distance queries have been known for quite a long time, they do not, in…

Neural Architecture Search (NAS) achieves significant progress in many computer vision tasks. While many methods have been proposed to improve the efficiency of NAS, the search progress is still laborious because training and evaluating…