Distributed-Memory Breadth-First Search on Massive Graphs

This chapter studies the problem of traversing large graphs using the breadth-first search order on distributed-memory supercomputers. We consider both the traditional level-synchronous top-down algorithm as well as the recently discovered direction optimizing algorithm. We analyze the performance and scalability trade-offs in using different local data structures such as CSR and DCSC, enabling in-node multithreading, and graph decompositions such as 1D and 2D decomposition.Comment: arXiv admin note: text overlap with arXiv:1104.451

Detection of Comparability Subgraphs from Large Networks

Real world large scale networks can be represented as graphs. This approach plays a key role in analysis in the domains of social networks [1] and bioinformatics [2], among others. Analyzing these networks is computationally complex and expensive, especially in terms of memory and time complexity. A popular technique subverting time and computation expense for analyzing networks is extracting substructures, which preserves more important information and less noise [12]. In this work, we use special a special substructure called comparability, which preserves transitive orientation. Our motive is to extract a maximal comparability subgraph since no algorithm exists. Our algorithm is able to find a maximal comparability subgraph from both undirected and directed graphs. Finding a clique of given size is a NP-complete problem, so we must implement some additional constraints to maximize time efficiency. If the given input graph is chordal, then extraction of the clique of size n becomes a problem that is solvable in polynomial time. So we have written an algorithm to find the clique of given size, and implemented the algorithm to find a maximal chordal subgraph. Since we worked on two different special subgraphs, we compared our results to investigate whether the given graph is chordal or comparability in nature. In our research, we have proposed a parallel sampling method for efficient network analysis

PAGE: A Partition Aware Graph Computation Engine

ABSTRACT Graph partitioning is one of the key components in parallel graph computation, and the partition quality significantly affects the overall computing performance. In the existing graph computing systems, "good" partition schemes are preferred as they have smaller edge cut ratio and hence reduce the communication cost among working nodes. However, in an empirical study on Giraph[1], we found that the performance over well partitioned graph might be even two times worse than simple partitions. The cause is that the local message processing cost in graph computing systems may surpass the communication cost in several cases. In this paper, we analyse the cost of parallel graph computing systems as well as the relationship between the cost and underlying graph partitioning. Based on these observation, we propose a novel Partition Aware Graph computation Engine named PAGE. PAGE is equipped with two newly designed modules, i.e., the communication module with a dual concurrent message processor, and a partition aware one to monitor the system's status. The monitored information can be utilized to dynamically adjust the concurrency of dual concurrent message processor with a novel Dynamic Concurrency Control Model (DCCM). The DCCM applies several heuristic rules to determine the optimal concurrency for the message processor. We have implemented a prototype of PAGE and conducted extensive studies on a moderate size of cluster. The experimental results clearly demonstrate the PAGE's robustness under different graph partition qualities and show its advantages over existing systems with up to 59% improvement

Parallel Adaptive Algorithms for Sampling Large Scale Networks

The study of real-world systems, represented as networks, has important application in many disciplines including social sciences [1], bioinformatics [2] and software engineering [3]. These networks are extremely large, and analyzing them is very expensive. Our research work involves developing parallel graph sampling methods for efficient analysis of gene correlation networks. Our sampling algorithms maintain important structural and informational properties of large unstructured networks. We focus on preserving the relative importance, based on combinatorial metrics, rather than the exact measures. We use a special subgraph technique, based on finding triangles called maximal chordal subgraphs, which maintains the highly connected portions of the network while increasing the distance between less connected regions. Our results show that even with significant reduction of the network we can obtain reliable subgraphs which conserve most of the relevant combinatorial and functional properties. Additionally, sampling reveals new functional properties which were previously undiscovered in the original system

The development of a weighted directed graph model for dynamic systems and application of Dijkstra’s algorithm to solve optimal control problems.

Master of Science (Chemical Engineering). University of KwaZulu-Natal. Durban, 2017.Optimal control problems are frequently encountered in chemical engineering process control applications as a result of the drive for more regulatory compliant, efficient and economical operation of chemical processes. Despite the significant advancements that have been made in Optimal Control Theory and the development of methods to solve this class of optimization problems, limitations in their applicability to non-linear systems inherent in chemical process unit operations still remains a challenge, particularly in determining a globally optimal solution and solutions to systems that contain state constraints. The objective of this thesis was to develop a method for modelling a chemical process based dynamic system as a graph so that an optimal control problem based on the system can be solved as a shortest path graph search problem by applying Dijkstra’s Algorithm. Dijkstra’s algorithm was selected as it is proven to be a robust and global optimal solution based algorithm for solving the shortest path graph search problem in various applications. In the developed approach, the chemical process dynamic system was modelled as a weighted directed graph and the continuous optimal control problem was reformulated as graph search problem by applying appropriate finite discretization and graph theoretic modelling techniques. The objective functional and constraints of an optimal control problem were successfully incorporated into the developed weighted directed graph model and the graph was optimized to represent the optimal transitions between the states of the dynamic system, resulting in an Optimal State Transition Graph (OST Graph). The optimal control solution for shifting the system from an initial state to every other achievable state for the dynamic system was determined by applying Dijkstra’s Algorithm to the OST Graph. The developed OST Graph-Dijkstra’s Algorithm optimal control solution approach successfully solved optimal control problems for a linear nuclear reactor system, a non-linear jacketed continuous stirred tank reactor system and a non-linear non-adiabatic batch reactor system. The optimal control solutions obtained by the developed approach were compared with solutions obtained by the variational calculus, Iterative Dynamic Programming and the globally optimal value-iteration based Dynamic Programming optimal control solution approaches. Results revealed that the developed OST Graph-Dijkstra’s Algorithm approach provided a 14.74% improvement in the optimality of the optimal control solution compared to the variational calculus solution approach, a 0.39% improvement compared to the Iterative Dynamic Programming approach and the exact same solution as the value–iteration Dynamic Programming approach. The computational runtimes for optimal control solutions determined by the OST Graph-Dijkstra’s Algorithm approach were 1 hr 58 min 33.19 s for the nuclear reactor system, 2 min 25.81s for the jacketed reactor system and 8.91s for the batch reactor system. It was concluded from this work that the proposed method is a promising approach for solving optimal control problems for chemical process-based dynamic systems