Adaptive Energy-aware Scheduling of Dynamic Event Analytics across Edge and Cloud Resources

The growing deployment of sensors as part of Internet of Things (IoT) is generating thousands of event streams. Complex Event Processing (CEP) queries offer a useful paradigm for rapid decision-making over such data sources. While often centralized in the Cloud, the deployment of capable edge devices on the field motivates the need for cooperative event analytics that span Edge and Cloud computing. Here, we identify a novel problem of query placement on edge and Cloud resources for dynamically arriving and departing analytic dataflows. We define this as an optimization problem to minimize the total makespan for all event analytics, while meeting energy and compute constraints of the resources. We propose 4 adaptive heuristics and 3 rebalancing strategies for such dynamic dataflows, and validate them using detailed simulations for 100 - 1000 edge devices and VMs. The results show that our heuristics offer O(seconds) planning time, give a valid and high quality solution in all cases, and reduce the number of query migrations. Furthermore, rebalance strategies when applied in these heuristics have significantly reduced the makespan by around 20 - 25%.Comment: 11 pages, 7 figure

Speeding up shortest path algorithms

Given an arbitrary, non-negatively weighted, directed graph $G=(V,E)$ we present an algorithm that computes all pairs shortest paths in time $\mathcal{O}(m^* n + m \lg n + nT_\psi(m^*, n))$, where $m^*$ is the number of different edges contained in shortest paths and $T_\psi(m^*, n)$ is a running time of an algorithm to solve a single-source shortest path problem (SSSP). This is a substantial improvement over a trivial $n$ times application of $\psi$ that runs in $\mathcal{O}(nT_\psi(m,n))$. In our algorithm we use $\psi$ as a black box and hence any improvement on $\psi$ results also in improvement of our algorithm. Furthermore, a combination of our method, Johnson's reweighting technique and topological sorting results in an $\mathcal{O}(m^*n + m \lg n)$ all-pairs shortest path algorithm for arbitrarily-weighted directed acyclic graphs. In addition, we also point out a connection between the complexity of a certain sorting problem defined on shortest paths and SSSP.Comment: 10 page

Extended high dimensional indexing approach for reachability queries on very large graphs

Given a directed acyclic graph G = (V,A) and two vertices u, v ∈ V , the reachability problem is to answer if there is a path from u to v in the graph. In the context of very large graphs, with millions of vertices and a series of queries to be answered, it is not practical to search the graph for each query. On the other hand, the storage of the full transitive closure of the graph is also impractical due to its O(|V |2) size. Scalable approaches aim to create indices used to prune the search during its execution. Negative indices may be able to determine (in constant time) that a query has a negative answer while positive indices may determine (again in constant time) that a query has a positive answer. In this paper we propose novel scalable approach called LYNX that uses a large number of topological sorts of G as a negative cut index without degrading the query time. A similar strategy is applied regarding a positive cut index. In addition, LYNX proposes a user-defined index size that enables the user to control the ratio between negative and positive cuts depending on the expected query pattern. We show by computational experiments that LYNX consistently outperforms the state-of-the-art approach in terms of query-time using the same index-size for graphs with high reachability ratio. In intelligent computer systems that rely on frequent tests of connectivity in graphs, LYNX can reduce the time delay experience by end users through a reduced query time. This comes at the expense of an increased setup time whenever the underlying graph is updated. Keywords: directed acyclic graphs, topological sorts, reachability queries, graph indexingpublishedVersio

Graph Deep Learning: Methods and Applications

The past few years have seen the growing prevalence of deep neural networks on various application domains including image processing, computer vision, speech recognition, machine translation, self-driving cars, game playing, social networks, bioinformatics, and healthcare etc. Due to the broad applications and strong performance, deep learning, a subfield of machine learning and artificial intelligence, is changing everyone\u27s life.Graph learning has been another hot field among the machine learning and data mining communities, which learns knowledge from graph-structured data. Examples of graph learning range from social network analysis such as community detection and link prediction, to relational machine learning such as knowledge graph completion and recommender systems, to mutli-graph tasks such as graph classification and graph generation etc.An emerging new field, graph deep learning, aims at applying deep learning to graphs. To deal with graph-structured data, graph neural networks (GNNs) are invented in recent years which directly take graphs as input and output graph/node representations. Although GNNs have shown superior performance than traditional methods in tasks such as semi-supervised node classification, there still exist a wide range of other important graph learning problems where either GNNs\u27 applicabilities have not been explored or GNNs only have less satisfying performance.In this dissertation, we dive deeper into the field of graph deep learning. By developing new algorithms, architectures and theories, we push graph neural networks\u27 boundaries to a much wider range of graph learning problems. The problems we have explored include: 1) graph classification; 2) medical ontology embedding; 3) link prediction; 4) recommender systems; 5) graph generation; and 6) graph structure optimization.We first focus on two graph representation learning problems: graph classification and medical ontology embedding.For graph classification, we develop a novel deep GNN architecture which aggregates node features through a novel SortPooling layer that replaces the simple summing used in previous works. We demonstrate its state-of-the-art graph classification performance on benchmark datasets. For medical ontology embedding, we propose a novel hierarchical attention propagation model, which uses attention mechanism to learn embeddings of medical concepts from hierarchically-structured medical ontologies such as ICD-9 and CCS. We validate the learned embeddings on sequential procedure/diagnosis prediction tasks with real patient data.Then we investigate GNNs\u27 potential for predicting relations, specifically link prediction and recommender systems. For link prediction, we first develop a theory unifying various traditional link prediction heuristics, and then design a framework to automatically learn suitable heuristics from a given network based on GNNs. Our model shows unprecedented strong link prediction performance, significantly outperforming all traditional methods. For recommender systems, we propose a novel graph-based matrix completion model, which uses a GNN to learn graph structure features from the bipartite graph formed by user and item interactions. Our model not only outperforms various matrix completion baselines, but also demonstrates excellent transfer learning ability -- a model trained on MovieLens can be directly used to predict Douban movie ratings with high performance.Finally, we explore GNNs\u27 applicability to graph generation and graph structure optimization. We focus on a specific type of graphs which usually carry computations on them, namely directed acyclic graphs (DAGs). We develop a variational autoencoder (VAE) for DAGs and prove that it can injectively map computations into a latent space. This injectivity allows us to perform optimization in the continuous latent space instead of the original discrete structure space. We then apply our VAE to two types of DAGs, neural network architectures and Bayesian networks. Experiments show that our model not only generates novel and valid DAGs, but also finds high-quality neural architectures and Bayesian networks through performing Bayesian optimization in its latent space

Topological Sorting with Regular Constraints

We introduce the constrained topological sorting problem (CTS): given a regular language K and a directed acyclic graph G with labeled vertices, determine if G has a topological sort that forms a word in K. This natural problem applies to several settings, e.g., scheduling with costs or verifying concurrent programs. We consider the problem CTS[K] where the target language K is fixed, and study its complexity depending on K. We show that CTS[K] is tractable when K falls in several language families, e.g., unions of monomials, which can be used for pattern matching. However, we show that CTS[K] is NP-hard for K = (ab)^* and introduce a shuffle reduction technique to show hardness for more languages. We also study the special case of the constrained shuffle problem (CSh), where the input graph is a disjoint union of strings, and show that CSh[K] is additionally tractable when K is a group language or a union of district group monomials. We conjecture that a dichotomy should hold on the complexity of CTS[K] or CSh[K] depending on K, and substantiate this by proving a coarser dichotomy under a different problem phrasing which ensures that tractable languages are closed under common operators