Résultats de recherche pour « Dynamic graph processing »

The emerging field of graph signal processing (GSP) allows to transpose classical signal processing operations (e.g., filtering) to signals on graphs. The GSP framework is generally built upon the graph Laplacian, which plays a crucial role to study graph properties and measure graph signal smoothness. Here instead, we propose the graph modularity matrix as the centerpiece of GSP, in order to incorporate knowledge about graph community structure when processing signals on the graph, but without the need for community detection. We study this approach in several generic settings such as filtering, optimal sampling and reconstruction, surrogate data generation, and denoising. Feasibility is illustrated by a small-scale example and a transportation network dataset, as well as one application in human neuroimaging where community-aware GSP reveals relationships between behavior and brain features that are not shown by Laplacian-based GSP. This work demonstrates how concepts from network science can lead to new meaningful operations on graph signals.

Graph as one of the most fundamental and representative data structures has found a wide spectrum of emerging application domains such as social media, financial transactions, biology science, and road networks. Recently, with the proliferation of graph applications, graph processing has attracted much attention in both industry and academia. Among them, most existing works focus on the static graphs in which the vertices and edges are immutable. However, in the real world, graphs are constantly and dynamically changing, bringing tricky challenges to process such dynamic graphs. This paper surveys the recent advances in dynamic graph processing, including centrality, graph coloring, cohesive subgraph, path traversal, and graph separation. We summarize the computational complexity models for dynamic algorithm analysis, theoretically compare the efficiency of algorithms among different research topics. Moreover, we also explore the research opportunities for the future.

This paper provides an overview of the current landscape of signal processing (SP) on directed graphs (digraphs). Directionality is inherent to many real-world (information, transportation, biological) networks and it should play an integral role in processing and learning from network data. We thus lay out a comprehensive review of recent advances in SP on digraphs, offering insights through comparisons with results available for undirected graphs, discussing emerging directions, establishing links with related areas in machine learning and causal inference in statistics, as well as illustrating their practical relevance to timely applications. To this end, we begin by surveying (orthonormal) signal representations and their graph frequency interpretations based on novel measures of signal variation for digraphs. We then move on to filtering, a central component in deriving a comprehensive theory of SP on digraphs. Indeed, through the lens of filter-based generative signal models, we explore a unified framework to study inverse problems (e.g., sampling and deconvolution on networks), statistical analysis of random signals, and topology inference of digraphs from nodal observations.

An unprecedented growth in data generation is taking place. Data about larger dynamic systems is being accumulated, capturing finer granularity events, and thus processing requirements are increasingly approaching real-time. To keep up, data-analytics pipelines need to be viable at massive scale, and switch away from static, offline scenarios to support fully online analysis of dynamic systems. This paper uses a challenge problem, graph colouring, to explore massive-scale analytics for dynamic graph processing. We present an event-based infrastructure, and a novel, online, distributed graph colouring algorithm. Our implementation for colouring static graphs, used as a performance baseline, is up to an order of magnitude faster than previous results and handles massive graphs with over 257 billion edges. Our framework supports dynamic graph colouring with performance at large scale better than GraphLab's static analysis. Our experience indicates that online solutions are feasible, and can be more efficient than those based on snapshotting.

We present an algorithm for updating the Reeb graph under fully dynamic changes of the function values. The basic event is the interchange of two consecutive vertex values. The algorithm updates the Reeb graph in $O(l g{n})$ worst-case deterministic time for each such interchange, where $l$ is an upper bound on the size of the star of the involved vertices, and g(n) is a worst-case bound for the dynamic graph connectivity problem. Moreover, we argue that $O(l)$ is a lower bound for this operation in general.

With the rapid growth in data volume, workloads from various domains have undergone drastic changes in recent years. Today, streaming workloads are commonplace. This generates the need for systems and algorithms that can receive and process streams of data with high throughput. Various graph applications are shifting away from the static graph model and incorporating a dynamic model, where updates to the graph can be received. In a dynamic setting, solutions to algorithms need to be updated alongside the graph. However, re-processing the whole graph every time can be infeasible given the size of current graphs. This raises a series of questions regarding how to process dynamic graph algorithms in a reasonable amount of time. In this paper, we explore the existing methods in the literature used to achieve scalable dynamic graph processing. We define different aspects and abstractions used for dynamic graph processing and categorize all approaches on the basis of their scalability.

The \textit{generalized Turán number} $\mathrm{ex}(n, T, F)$ is the maximum possible number of copies of $T$ in an $F$-free graph on $n$ vertices for any two graphs $T$ and $F$. For the book graph $B_t$, there is a close connection between $\ex(n,K_3,B_t)$ and the Ruzsa-Szemerédi triangle removal lemma. Motivated by this, in this paper, we study the generalized Turán problem for generalized theta graphs, a natural extension of book graphs. Our main result provides a complete characterization of the magnitude of $\ex(n,K_3,H)$ when $H$ is a generalized theta graph, indicating when it is quadratic, when it is nearly quadratic, and when it is subquadratic. Furthermore, as an application, we obtain the exact value of $\ex(n, K_r, kF)$, where $F$ is an edge-critical generalized theta graph, and $3\le r\le k+1$, extending several recent results.

Many real-world systems, such as social networks, rely on mining efficiently large graphs, with hundreds of millions of vertices and edges. This volume of information requires partitioning the graph across multiple nodes in a distributed system. This has a deep effect on performance, as traversing edges cut between partitions incurs a significant performance penalty due to the cost of communication. Thus, several systems in the literature have attempted to improve computational performance by enhancing graph partitioning, but they do not support another characteristic of real-world graphs: graphs are inherently dynamic, their topology evolves continuously, and subsequently the optimum partitioning also changes over time. In this work, we present the first system that dynamically repartitions massive graphs to adapt to structural changes. The system optimises graph partitioning to prevent performance degradation without using data replication. The system adopts an iterative vertex migration algorithm that relies on local information only, making complex coordination unnecessary. We show how the improvement in graph partitioning reduces execution time by over 50%, while adapting the partitioning to a large number of changes to the graph in three real-world scenarios.

Multi-channel acoustic signal processing is a well-established and powerful tool to exploit the spatial diversity between a target signal and non-target or noise sources for signal enhancement. However, the textbook solutions for optimal data-dependent spatial filtering rest on the knowledge of second-order statistical moments of the signals, which have traditionally been difficult to acquire. In this contribution, we compare model-based, purely data-driven, and hybrid approaches to parameter estimation and filtering, where the latter tries to combine the benefits of model-based signal processing and data-driven deep learning to overcome their individual deficiencies. We illustrate the underlying design principles with examples from noise reduction, source separation, and dereverberation.

An efficient data structure is fundamental to meeting the growing demands in dynamic graph processing. However, the dual requirements for graph computation efficiency (with contiguous structures) and graph update efficiency (with linked list-like structures) present a conflict in the design principles of graph structures. After experimental studies of state-of-the-art dynamic graph structures, we observe that the overhead of cache misses accounts for a major portion of the graph computation time. This paper presents GastCoCo, a system with graph storage and coroutine-based prefetch co-design. By employing software prefetching via stackless coroutines and designing a prefetch-friendly data structure CBList, GastCoCo significantly alleviates the performance degradation caused by cache misses. Our results show that GastCoCo outperforms state-of-the-art graph storage systems by 1.3× - 180× in graph updates and 1.4× - 41.1× in graph computation.