Distributed Triangle Approximately Counting Algorithms in Simple Graph Stream

Recently, the counting algorithm of local topology structures, such as triangles, has been widely used in social network analysis, recommendation systems, user portraits and other fields. At present, the problem of counting global and local triangles in a graph stream has been widely studied, and numerous triangle counting steaming algorithms have emerged. To improve the throughput and scalability of streaming algorithms, many researches of distributed streaming algorithms on multiple machines are studied. In this article, we first propose a framework of distributed streaming algorithm based on the Master-Worker-Aggregator architecture. The two core parts of this framework are an edge distribution strategy, which plays a key role to affect the performance, including the communication overhead and workload balance, and aggregation method, which is critical to obtain the unbiased estimations of the global and local triangle counts in a graph stream. Then, we extend the state-of-the-art centralized algorithm TRIÈST into four distributed algorithms under our framework. Compared to their competitors, experimental results show that DVHT-i is excellent in accuracy and speed, performing better than the best existing distributed streaming algorithm. DEHT-b is the fastest algorithm and has the least communication overhead. What’s more, it almost achieves absolute workload balance.

A Framework for Adversarially Robust Streaming Algorithms

We investigate the adversarial robustness of streaming algorithms. In this context, an algorithm is considered robust if its performance guarantees hold even if the stream is chosen adaptively by an adversary that observes the outputs of the algorithm along the stream and can react in an online manner. While deterministic streaming algorithms are inherently robust, many central problems in the streaming literature do not admit sublinear-space deterministic algorithms; on the other hand, classical space-efficient randomized algorithms for these problems are generally not adversarially robust. This raises the natural question of whether there exist efficient adversarially robust (randomized) streaming algorithms for these problems.

Technical Perspective

Over the past two decades the data management community has devoted particular attention to handling data that arrives as a stream of updates. This captures a number of "big data" scenarios, ranging from monitoring networks to processing high volumes of transactions in commerce and finance. This has led to data streams becoming a mainstream data management topic, with many systems offering explicit support for handling such inputs. Within these systems, streaming algorithms are used to approximate various statistical and modeling queries, which would traditionally require random access to the full data to compute exactly.

Guest Column

Communication complexity studies the amount of communication necessary to compute a function whose value depends on information distributed among several entities. Yao [Yao79] initiated the study of communication complexity more than 40 years ago, and it has since become a central eld in theoretical computer science with many applications in diverse areas such as data structures, streaming algorithms, property testing, approximation algorithms, coding theory, and machine learning. The textbooks [KN06,RY20] provide excellent overviews of the theory and its applications.

Streaming Algorithms for Subspace Analysis: an Edge- and Hardware-oriented review

Subspace analysis is a basic tool for coping with high-dimensional data and is becoming a fundamental step in early processing of many signals elaboration tasks. Nowadays trend of collecting huge quantities of usually very redundant data by means of decentralized systems suggests these techniques be deployed as close as possible to the data sources. Regrettably, despite its conceptual simplicity, subspace analysis is ultimately equivalent to eigenspace computation and brings along non-negligible computational and memory requirements. To make this fit into typical systems operating at the edge, specialized streaming algorithms have been recently devised that we here classify and review giving them a coherent description, highlighting features and analogies, and easing comparisons. Implementation of these methods is also tested on a common edge digital hardware platform to estimate not only abstract functional and complexity features, but also more practical running times and memory footprints on which compliance with real-world applications hinges.

Streaming Algorithms for Subspace Analysis: an Edge- and Hardware-oriented review

Subspace analysis is a basic tool for coping with high-dimensional data and is becoming a fundamental step in early processing of many signals elaboration tasks. Nowadays trend of collecting huge quantities of usually very redundant data by means of decentralized systems suggests these techniques be deployed as close as possible to the data sources. Regrettably, despite its conceptual simplicity, subspace analysis is ultimately equivalent to eigenspace computation and brings along non-negligible computational and memory requirements. To make this fit into typical systems operating at the edge, specialized streaming algorithms have been recently devised that we here classify and review giving them a coherent description, highlighting features and analogies, and easing comparisons. Implementation of these methods is also tested on a common edge digital hardware platform to estimate not only abstract functional and complexity features, but also more practical running times and memory footprints on which compliance with real-world applications hinges.