Efficient Computation of Distance Labeling for Decremental Updates in Large Dynamic Graphs

Since today's real-world graphs, such as social network graphs, are evolving all the time, it is of great importance to perform graph computations and analysis in these dynamic graphs. Due to the fact that many applications such as social network link analysis with the existence of inactive users need to handle failed links or nodes, decremental computation and maintenance for graphs is considered a challenging problem. Shortest path computation is one of the most fundamental operations for managing and analyzing large graphs. A number of indexing methods have been proposed to answer distance queries in static graphs. Unfortunately, there is little work on answering such queries for dynamic graphs. In this paper, we focus on the problem of computing the shortest path distance in dynamic graphs, particularly on decremental updates (i.e., edge deletions). We propose maintenance algorithms based on distance labeling, which can handle decremental updates efficiently. By exploiting properties of distance labeling in original graphs, we are able to efficiently maintain distance labeling for new graphs. We experimentally evaluate our algorithms using eleven real-world large graphs and confirm the effectiveness and efficiency of our approach. More specifically, our method can speed up index re-computation by up to an order of magnitude compared with the state-of-the-art method, Pruned Landmark Labeling (PLL)

Answering Shortest Path Distance Queries in Large Complex Networks

The \emph{distance query} problem is to find the shortest-path distance between an arbitrary pair of vertices in a graph. It is considered as a fundamental problem in graph theory. Despite a tremendous amount of research on the subject, there is still no satisfactory solution that can scale to large complex networks which may have billions of vertices and edges. Furthermore, many real-world complex networks such as social networks and web graphs are typically dynamic, undergoing discrete changes such as edge insertion and deletion in their topological structure over time. Thus, there is also a pressing need to address the distance query problem on dynamic networks. The goal of this thesis is to address the distance query problem on large static and dynamic complex networks. Labelling-based methods are well-known for rendering fast response time to distance queries; however, existing labelling-based methods can only construct distance labelling for moderately large graphs with millions of vertices and edges and cannot scale to large graphs with billions of vertices and edges due to their prohibitively large space requirements and unbearably long pre-processing time. This thesis proposes a scalable approach that enables fast construction of a distance labelling of a limited size, which contains only distance information from all vertices in a graph to some ``important" vertices (not all) - called \emph{landmarks}. Such a distance labelling is considered as a \emph{partial distance labelling}, in contrast to a \emph{full distance labelling} that contains distance information for all pairs of vertices in a graph. Then, we combine a partial distance labelling that can be computed in an offline manner with online searching to leverage the advantages from both sides - accelerating query processing through a small sized partial distance labelling that provides a good approximation to bound online searches. The proposed method can efficiently construct a distance labelling for a graph with billions of vertices and edges, and enable fast distance computation, e.g. in the order of milliseconds. Since graphs in real-world are dynamic that undergo changes such as edge insertion or deletion in their topological structure, existing labelling-based methods still greatly suffer from the drawback of scalability on dynamic graphs and they can hardly update a distance labelling efficiently. In this thesis, we propose a fully dynamic method which can efficiently reflect graph changes (i.e., single edge insertions or deletions) by dynamically maintaining a distance labelling in order to answer distance queries on dynamice graphs. At its core, our proposed method incorporates two building blocks: (i) \emph{incremental algorithm} for handling incremental update operations, i.e. edge insertion, and (ii) \emph{decremental algorithm} for handling decremental update operations, i.e. edge deletion. Moreover, this thesis also introduces a batch-dynamic method which can process batch of updates (i.e., batches of edge insertions and deletions) efficiently to further improve the performance of answering distance queries on graphs that undergo rapid changes in their topological structure. The proposed batch-dynamic method enables us to unify edge insertions and deletion, helps us to avoid unnecessary and repeated computations, and allows us to exploit the potential of parallelism which as a result is much more efficient than processing graph changes separately one by one. In this thesis, we have conducted extensive experiments on 15-17 real-world networks from a variety of application domains to test the scalability, efficiency, and robustness of the proposed static and dynamic methods against existing state-of-the-art static and dynamic methods

Recent Advances in Fully Dynamic Graph Algorithms

In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms

Comparative Study of Speed-Up Routing Algorithms in Road Networks

We study the problem of finding the shortest distance and the shortest path from one node to another in graphs modeling large road networks. Classical algorithms like Dijkstra and Astar do not have good performance in such networks. In recent years, two new approaches called Contraction Hierarchy and Hub Labeling which use preprocessing to generate auxiliary data to improve the query time performance were proposed, and many variants have followed. These algorithms are very efficient on large networks when a large number of queries is expected. In the literature, these algorithms are called speed-up algorithms. More recently, dynamic routing algorithms have been proposed, such as Customizable Contraction Hierarchy and Dynamic Hierarchical Hub Labeling. These are designed to respond efficiently to edge weight changes resulting from changes in traffic. In this thesis, we present an experimental study of the performance of the above static and dynamic routing algorithms on two different road networks, in terms of travel time and query processing time. Our results show that Customizable Contraction Hierarchy is the best for shortest path query in both the static and dynamic settings, while Hub Labeling is the most efficient in answering shortest distance queries in the static setting. We also show that Dynamic Hub Labeling’s edge weight update operations are inefficient in practice

Shared Arrangements: practical inter-query sharing for streaming dataflows

Current systems for data-parallel, incremental processing and view maintenance over high-rate streams isolate the execution of independent queries. This creates unwanted redundancy and overhead in the presence of concurrent incrementally maintained queries: each query must independently maintain the same indexed state over the same input streams, and new queries must build this state from scratch before they can begin to emit their first results. This paper introduces shared arrangements: indexed views of maintained state that allow concurrent queries to reuse the same in-memory state without compromising data-parallel performance and scaling. We implement shared arrangements in a modern stream processor and show order-of-magnitude improvements in query response time and resource consumption for interactive queries against high-throughput streams, while also significantly improving performance in other domains including business analytics, graph processing, and program analysis

Deterministic Decremental Reachability, SCC, and Shortest Paths via Directed Expanders and Congestion Balancing

Let $G = (V,E,w)$ be a weighted, digraph subject to a sequence of adversarial edge deletions. In the decremental single-source reachability problem (SSR), we are given a fixed source $s$ and the goal is to maintain a data structure that can answer path-queries $s \rightarrowtail v$ for any $v \in V$. In the more general single-source shortest paths (SSSP) problem the goal is to return an approximate shortest path to $v$, and in the SCC problem the goal is to maintain strongly connected components of $G$ and to answer path queries within each component. All of these problems have been very actively studied over the past two decades, but all the fast algorithms are randomized and, more significantly, they can only answer path queries if they assume a weaker model: they assume an oblivious adversary which is not adaptive and must fix the update sequence in advance. This assumption significantly limits the use of these data structures, most notably preventing them from being used as subroutines in static algorithms. All the above problems are notoriously difficult in the adaptive setting. In fact, the state-of-the-art is still the Even and Shiloach tree, which dates back all the way to 1981 and achieves total update time $O(mn)$. We present the first algorithms to break through this barrier: 1) deterministic decremental SSR/SCC with total update time $mn^{2/3 + o(1)}$ 2) deterministic decremental SSSP with total update time $n^{2+2/3+o(1)}$. To achieve these results, we develop two general techniques of broader interest for working with dynamic graphs: 1) a generalization of expander-based tools to dynamic directed graphs, and 2) a technique that we call congestion balancing and which provides a new method for maintaining flow under adversarial deletions. Using the second technique, we provide the first near-optimal algorithm for decremental bipartite matching.Comment: Reuploaded with some generalizations of previous theorem