arXiv subjects

Bartłomiej Wróblewski

Publications and source records attributed to Bartłomiej Wróblewski.

5 recordsLinked to original sources

arXiv2026

Parallel Scan on Ascend AI Accelerators

We design and implement parallel prefix sum (scan) algorithms using Ascend AI accelerators. Ascend accelerators feature specialized computing units: the cube units for efficient matrix multiplication and the vector units for optimized vector operations. A key feature of the proposed scan algorithms is their extensive use of matrix multiplications and accumulations enabled by the cube unit. To showcase the effectiveness of these algorithms, we also implement and evaluate several scan-based operators commonly used in AI workloads, including sorting, tensor masking, and top-$k$ / top-$p$ sampling. Our single-core results demonstrate substantial performance improvements, with speedups ranging from $5\times$ to $9.6\times$ compared to vector-only implementations for sufficiently large input lengths. Additionally, we present a multi-core scan algorithm that fully utilizes both the cube and vector units of Ascend, reaching up to 74.9\% of the memory bandwidth achieved by memory copy. Furthermore, our radix sort implementation, which utilizes matrix multiplications for its parallel splits, showcases the potential of matrix engines to enhance complex operations, offering up to $3.3\times$ speedup over the vector-only baseline.

cs.DC↗

arXiv2024

Edge coloring of products of signed graphs

In 2020, Behr defined the problem of edge coloring of signed graphs and showed that every signed graph $(G, σ)$ can be colored using exactly $Δ(G)$ or $Δ(G) + 1$ colors, where $Δ(G)$ is the maximum degree in graph $G$. In this paper, we focus on products of signed graphs. We recall the definitions of the Cartesian, tensor, strong, and corona products of signed graphs and prove results for them. In particular, we show that $(1)$ the Cartesian product of $Δ$-edge-colorable signed graphs is $Δ$-edge-colorable, $(2)$ the tensor product of a $Δ$-edge-colorable signed graph and a signed tree requires only $Δ$ colors and $(3)$ the corona product of almost any two signed graphs is $Δ$-edge-colorable. We also prove some results related to the coloring of products of signed paths and cycles.

math.CO↗

arXiv2023

Edge coloring of graphs of signed class 1 and 2

Recently, Behr introduced a notion of the chromatic index of signed graphs and proved that for every signed graph $(G$, $σ)$ it holds that \[ Δ(G)\leqχ'(G\text{, }σ)\leqΔ(G)+1\text{,} \] where $Δ(G)$ is the maximum degree of $G$ and $χ'$ denotes its chromatic index. In general, the chromatic index of $(G$, $σ)$ depends on both the underlying graph $G$ and the signature $σ$. In the paper we study graphs $G$ for which $χ'(G$, $σ)$ does not depend on $σ$. To this aim we introduce two new classes of graphs, namely $1^\pm$ and $2^\pm$, such that graph $G$ is of class $1^\pm$ (respectively, $2^\pm$) if and only if $χ'(G$, $σ)=Δ(G)$ (respectively, $χ'(G$, $σ)=Δ(G)+1$) for all possible signatures $σ$. We prove that all wheels, necklaces, complete bipartite graphs $K_{r,t}$ with $r\neq t$ and almost all cacti graphs are of class $1^\pm$. Moreover, we give sufficient and necessary conditions for a graph to be of class $2^\pm$, i.e. we show that these graphs must have odd maximum degree and give examples of such graphs with arbitrary odd maximum degree bigger that $1$.

cs.DM↗

arXiv2021

Closer Look at the Uncertainty Estimation in Semantic Segmentation under Distributional Shift

While recent computer vision algorithms achieve impressive performance on many benchmarks, they lack robustness - presented with an image from a different distribution, (e.g. weather or lighting conditions not considered during training), they may produce an erroneous prediction. Therefore, it is desired that such a model will be able to reliably predict its confidence measure. In this work, uncertainty estimation for the task of semantic segmentation is evaluated under a varying level of domain shift: in a cross-dataset setting and when adapting a model trained on data from the simulation. It was shown that simple color transformations already provide a strong baseline, comparable to using more sophisticated style-transfer data augmentation. Further, by constructing an ensemble consisting of models using different backbones and/or augmentation methods, it was possible to improve significantly model performance in terms of overall accuracy and uncertainty estimation under the domain shift setting. The Expected Calibration Error (ECE) on challenging GTA to Cityscapes adaptation was reduced from 4.05 to the competitive value of 1.1. Further, an ensemble of models was utilized in the self-training setting to improve the pseudo-labels generation, which resulted in a significant gain in the final model accuracy, compared to the standard fine-tuning (without ensemble).

cs.CV↗

arXiv2020

Efficient fully dynamic elimination forests with applications to detecting long paths and cycles

We present a data structure that in a dynamic graph of treedepth at most $d$, which is modified over time by edge insertions and deletions, maintains an optimum-height elimination forest. The data structure achieves worst-case update time $2^{{\cal O}(d^2)}$, which matches the best known parameter dependency in the running time of a static fpt algorithm for computing the treedepth of a graph. This improves a result of Dvořák et al. [ESA 2014], who for the same problem achieved update time $f(d)$ for some non-elementary (i.e. tower-exponential) function $f$. As a by-product, we improve known upper bounds on the sizes of minimal obstructions for having treedepth $d$ from doubly-exponential in $d$ to $d^{{\cal O}(d)}$. As applications, we design new fully dynamic parameterized data structures for detecting long paths and cycles in general graphs. More precisely, for a fixed parameter $k$ and a dynamic graph $G$, modified over time by edge insertions and deletions, our data structures maintain answers to the following queries: - Does $G$ contain a simple path on $k$ vertices? - Does $G$ contain a simple cycle on at least $k$ vertices? In the first case, the data structure achieves amortized update time $2^{{\cal O}(k^2)}$. In the second case, the amortized update time is $2^{{\cal O}(k^4)} + {\cal O}(k \log n)$. In both cases we assume access to a dictionary on the edges of $G$.

cs.DS↗