Finding the biconnected components of a graph has a large number of applications in many other graph problems including planarity testing, computing the centrality metrics, finding the (weighted) vertex cover, coloring, and the like. Recent years saw the design of efficient algorithms for this problem across sequential and parallel computational models. However, current algorithms do not work in the setting where the underlying graph changes over time in a dynamic manner via the insertion or deletion of edges. Dynamic algorithms in the sequential setting that obtain the biconnected components of a graph upon insertion or deletion of a single edge are known from over two decades ago. Parallel algorithms for this problem are not heavily studied. In this paper, we design shared-memory parallel algorithms that obtain the biconnected components of a graph subsequent to the insertion or deletion of a batch of edges. Our algorithms hence will be capable of exploiting the parallelism adduced due to a batch of updates. We implement our algorithms on an AMD EPYC 7742 CPU having 128 cores. Our experiments on a collection of 10 real-world graphs from multiple classes indicate that our algorithms outperform parallel state-of-the-art static algorithms.11The implementation and an extended version of this paper is at [5].

Shared-Memory Parallel Algorithms for Fully Dynamic Maintenance of 2-Connected Components

Rapid technological developments in autonomous unmanned aerial vehicles (or drones) could soon lead to their large-scale implementation in the last-mile delivery of products. However, drones have a number of problems such as limited energy budget, limited carrying capacity, etc. On the other hand, trucks have a larger carrying capacity, but they cannot reach all the places easily. Intriguingly, last-mile delivery cooperation between drones and trucks can synergistically improve delivery efficiency. In this paper, we present a drone-truck co-operated delivery framework under time-varying dynamics. Our framework minimizes the total delivery time while considering low energy consumption as the secondary objective. The empirical results support our claim and show that our algorithm can help to complete the deliveries time efficiently and saves energy.

Drone-Truck Cooperated Delivery Under Time Varying Dynamics

We present the first GPU-based parallel algorithm to efficiently update vertex coloring on large dynamic networks. For single GPU, we introduce the concept of loosely maintained vertex color update that reduces computation and memory requirements. For multiple GPUs, in distributed environments, we propose priority-based ordering of vertices to reduce the communication time. We prove the correctness of our algorithms and experimentally demonstrate that for graphs of over 16 million vertices and over 134 million edges on a single GPU, our dynamic algorithm is as much as 20x faster than state-of-the-art algorithm on static graphs. For larger graphs with over 130 million vertices and over 260 million edges, our distributed implementation with 8 GPUs produces updated color assignments within 160 milliseconds. In all cases, the proposed parallel algorithms produce comparable or fewer colors than state-of-the-art algorithms.

Parallel Vertex Color Update on Large Dynamic Networks

Community detection is a key aspect of network analysis, as it allows for the identiﬁcation of groups and patterns within a network. With the ever-increasing size of networks, it is crucial to have fast algorithms to analyze them efﬁciently. It is a modularity-based greedy algorithm that divides a network into disconnected communities better over several iterations. Even in big, dense networks, it is renowned for establishing high-quality communities. However it can be at least a factor of ten slower than community discovery techniques that rely on label-propagation, which are generally extremely fast but obtain communities of lower quality. The researchers have suggested a number of methods for parallelizing and improving the Louvain algorithm. To decide which strategy is generally the best ﬁt and which parameter values produce the highest performance without compromising community quality, it is crit-ical to assess the performance and accuracy of these existing approaches. As we implement the single-threaded and multi-threaded versions of the static Louvain algorithm in this report, we carefully examine the method’s speciﬁcs, make the required tweaks and optimizations, and determine the right parameter values. The tolerance between each pass can be changed to adjust the method’s performance. With an initial tolerance of 0.01 and a tolerance decline factor of 10, an asynchronous version of the algorithm produced the best results. Generally speak-ing, according to our ﬁndings, the approach is not well suited for shared-memory parallelism; however, one potential workaround is to break the graph into manageable chunks that can be independently executed and then merged back together.

Enhancing Efficiency in Parallel Louvain Algorithm for Community Detection

Community detection is an essential task in network analysis as it helps identify groups and patterns within a network. High-speed community detection algorithms are necessary to ana-lyze large-scale networks in a reasonable amount of time. Researchers have made signiﬁcant contributions in the development of high-speed community detection algorithms, particularly in the area of label-propagation based disjoint community detection. These algorithms have been proven to be highly effective in analyzing large-scale networks in a reasonable amount of time. However, it is important to evaluate the performance and accuracy of these existing methods to determine which algorithm is best suited for a particular type of network and speciﬁc research problem. In this report, we investigate the RAK, COPRA, and SLPA, three label-propagation-based static community discovery techniques. We pay close attention to each algorithm’s minute details as we implement both its single-threaded and multi-threaded OpenMP-based variants, making any necessary adjustments or optimizations and obtaining the right parameter values. The RAK algorithm is found to perform well with a tolerance of 0.05 and OpenMP-based strict RAK with 12 threads was 6.75x faster than the sequential non-strict RAK. The COPRA algorithm works well with a single label for road networks and max labels of 4-16 for other classes of graphs. The SLPA algorithm performs well with increasing memory size, but overall doesn’t offer a favourable return on investment. The RAK algorithm is recommended for label-propagation based disjoint community detection.

Selecting a suitable Parallel Label-propagation based algorithm for Disjoint Community Detection

The Single Source Shortest Path (SSSP) problem is a classic graph theory problem that arises frequently in various practical scenarios; hence, many parallel algorithms have been developed to solve it. However, these algorithms operate on static graphs, whereas many real-world problems are best modeled as dynamic networks, where the structure of the network changes with time. This gap between the dynamic graph modeling and the assumed static graph model in the conventional SSSP algorithms motivates this work. We present a novel parallel algorithmic framework for updating the SSSP in large-scale dynamic networks and implement it on the shared-memory and GPU platforms. The basic idea is to identify the portion of the network affected by the changes and update the information in a rooted tree data structure that stores the edges of the network that are most relevant to the analysis. Extensive experimental evaluations on real-world and synthetic networks demonstrate that our proposed parallel updating algorithm is scalable and, in most cases, requires significantly less execution time than the state-of-the-art recomputing-from-scratch algorithms.

A Parallel Algorithm Template for Updating Single-Source Shortest Paths in Large-Scale Dynamic Networks

Graph queries on large networks leverage the stored graph properties to provide faster results. Since real-world graphs are mostly dynamic, i.e., the graph topology changes over time, the corresponding graph attributes also change over time. In certain situations, recompiling or updating earlier properties is necessary to maintain the accuracy of a response to a graph query. Here, we first propose a generic framework for developing parallel algorithms to update graph properties on large dynamic networks. We use our framework to develop algorithms for updating Single Source Shortest Path (SSSP) and Vertex Color. Then we propose applications of the developed algorithms in Unmanned Aerial Vehicle (UAV) based delivery systems under time-varying dynamics. Finally, we implement our SSSP and vertex color update algorithms for Nvidia GPU architecture and show empirically that the developed algorithms can update properties in large dynamic networks faster than the state-of-the-art techniques.

Arindam Khanda

Papers

A Parallel Algorithm Template for Updating Single-Source Shortest Paths in Large-Scale Dynamic Networks

Drone-Truck Cooperated Delivery Under Time Varying Dynamics

Parallel Vertex Color Update on Large Dynamic Networks

A Parallel Framework for Efficiently Updating Graph Properties in Large Dynamic Networks