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We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a $(1+\epsilon)$…
Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
Recent advancements have significantly enhanced the performance of large language models (LLMs) in tackling complex reasoning tasks, achieving notable success in domains like mathematical and logical reasoning. However, these methods…
Nowadays, Large Language Models (LLMs) have been gradually employed to solve complex tasks. To face the challenge, task decomposition has become an effective way, which proposes to divide a complex task into multiple simpler subtasks and…
This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
HyperLTL, the extension of Linear Temporal Logic by trace quantifiers, is a uniform framework for expressing information flow policies by relating multiple traces of a security-critical system. HyperLTL has been successfully applied to…
We present a new algorithm, Fractional Decomposition Tree (FDT) for finding a feasible solution for an integer program (IP) where all variables are binary. FDT runs in polynomial time and is guaranteed to find a feasible integer solution…
We show that the regular separability problem of VASS reachability languages is decidable and $\mathbf{F}_{\omega}$-complete. At the heart of our decision procedure are doubly-marked graph transition sequences, a new proof object that…
Vision Transformers (ViTs) excel in semantic segmentation but demand significant computation, posing challenges for deployment on resource-constrained devices. Existing token pruning methods often overlook fundamental visual data…
Large Reasoning Models (LRMs) achieve remarkable inference-time improvements through parallel thinking. However, existing methods rely on redundant sampling of reasoning trajectories, failing to effectively explore the reasoning space to…
Generating overtaking trajectories in high-speed scenarios is typically addressed through hierarchical planning, which often suffers from local optima due to single initial solutions and low computational efficiency during numerical…
Stochastic local search (SLS) is a successful paradigm for solving the satisfiability problem of propositional logic. A recent development in this area involves solving not the original instance, but a modified, yet logically equivalent…
In response to the lack of trust in Artificial Intelligence (AI) for sequential planning, we design a Computational Tree Logic-guided large language model (LLM)-based natural language explanation framework designed for the Monte Carlo Tree…
The advent of large-scale self-supervised learning (SSL) has produced a vast zoo of medical foundation models. However, selecting optimal medical foundation models for specific segmentation tasks remains a computational bottleneck. Existing…
In this article, we study the hierarchical structure of metastability in the reversible inclusion process. We fully characterize the third time scale of metastability subject to any underlying geometry of the system and prove that this is…
We describe a new set of public, self-contained, and versatile computational tools for the investigation, manipulation, and evaluation of tree-level amplitudes in pure (super)Yang-Mills and (super)Gravity, $\phi^p$-scalar field theory, and…
This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…
Unconditionally stable time stepping schemes are useful and often practically necessary for advancing parabolic operators in multi-scale systems. However, serious accuracy problems may emerge when taking time steps that far exceed the…