arXiv subjects

Albert Weng

Publications and source records attributed to Albert Weng.

3 recordsLinked to original sources

arXiv2026

Computing Flows in Subquadratic Space

Space complexity is a critical factor in various computational models, including streaming, parallel/distributed computing, and communication complexity. We study the space complexity of the minimum-cost flow problem, a generalization of the st-max flow problem, focusing on computing flows in subquadratic space. In the general case with arbitrary capacities, minimum cost and $st$-maximum flows can use up to $\Omega(n^2)$ edges, so computing the flow on each edge (rather than just the size/cost) seems impossible in subquadratic space. Indeed, there are lower bounds proving quadratic space is needed to store the flow on every edge, which has been used to prove lower bounds on streaming algorithms. However, we show that these lower bounds can be circumvented, opening up improvements for streaming and communication complexity. For a directed graph with integer capacities and costs bounded by $W$, we provide a $\tilde O(n^{1.5}\log (W/\epsilon))$-space $\tilde O(\sqrt{n} \log(W/\epsilon))$-pass streaming algorithm, which during the last pass returns the flow on each edge up to an additive error of $\epsilon$. Crucially, the algorithm does not return the flow at the end of the last pass but returns the flow on an edge, as the edge is read in the stream. This allows us to circumvent existing $\Omega(n^2)$ space lower bounds. In the 2-party communication model, our algorithm implies $\tilde O(n^{1.5}\log^2 W)$ bits of communication.

cs.DS↗

arXiv2025

Adaptive Matrix Sparsification and Applications to Empirical Risk Minimization

Consider the empirical risk minimization (ERM) problem, which is stated as follows. Let $K_1, \dots, K_m$ be compact convex sets with $K_i \subseteq \mathbb{R}^{n_i}$ for $i \in [m]$, $n = \sum_{i=1}^m n_i$, and $n_i\le C_K$ for some absolute constant $C_K$. Also, consider a matrix $A \in \mathbb{R}^{n \times d}$ and vectors $b \in \mathbb{R}^d$ and $c \in \mathbb{R}^n$. Then the ERM problem asks to find \[ \min_{\substack{x \in K_1 \times \dots \times K_m\\ A^\top x = b}} c^\top x. \] We give an algorithm to solve this to high accuracy in time $\widetilde{O}(nd + d^6\sqrt{n}) \le \widetilde{O} (nd + d^{11})$, which is nearly-linear time in the input size when $A$ is dense and $n \ge d^{10}$. Our result is achieved by implementing an $\widetilde{O}(\sqrt{n})$-iteration interior point method (IPM) efficiently using dynamic data structures. In this direction, our key technical advance is a new algorithm for maintaining leverage score overestimates of matrices undergoing row updates. Formally, given a matrix $A \in \mathbb{R}^{n \times d}$ undergoing $T$ batches of row updates of total size $n$ we give an algorithm which can maintain leverage score overestimates of the rows of $A$ summing to $\widetilde{O}(d)$ in total time $\widetilde{O}(nd + Td^6)$. This data structure is used to sample a spectral sparsifier within a robust IPM framework to establish the main result.

cs.DS↗

arXiv2024

Flickering pulsations in bright X-ray pulsars: the evidence of gravitationally lensed and eclipsed accretion column

It is expected that extreme mass accretion rate onto strongly magnetised neutron star results in appearance of accretion columns above stellar surface. For a distant observer, rotation of a star results in periodic variations of X-ray flux. Because the mass accretion rate fluctuates around the average value, the pulse profiles are not stable and demonstrate fluctuations as well. In the case of bright X-ray pulsars, however, pulse fluctuations are not solely attributed to variations in the mass accretion rate. They are also influenced by the variable height of the columns, which is dependent on the mass accretion rate. This study delves into the process of pulse profile formation in bright X-ray pulsars, taking into account stochastic fluctuations in the mass accretion rate, the corresponding variations in accretion column geometry and gravitational bending. Our analysis reveals that potential eclipses of accretion columns by a neutron star during their spin period should manifest specific features in pulse profile variability. Applying a novel pulse profile analysis technique, we successfully detect these features in the bright X-ray transient V0332+53 at luminosities $\gtrsim 2\times 10^{38}\,{\rm erg\,s^{-1}}$. This detection serves as compelling evidence for the eclipse of an accretion column by a neutron star. Detection of the eclipse places constraints on the relation between neutron star mass, radius and accretion column height. Specifically, we can establish an upper limit on the accretion column height, which is crucial for refining theoretical models of extreme accretion.

astro-ph.HE↗