Multi-threading a state-of-the-art maximum clique algorithm

We present a threaded parallel adaptation of a state-of-the-art maximum clique algorithm for dense, computationally challenging graphs. We show that near-linear speedups are achievable in practice and that superlinear speedups are common. We include results for several previously unsolved benchmark problems

Finding the Hierarchy of Dense Subgraphs using Nucleus Decompositions

Finding dense substructures in a graph is a fundamental graph mining operation, with applications in bioinformatics, social networks, and visualization to name a few. Yet most standard formulations of this problem (like clique, quasiclique, k-densest subgraph) are NP-hard. Furthermore, the goal is rarely to find the "true optimum", but to identify many (if not all) dense substructures, understand their distribution in the graph, and ideally determine relationships among them. Current dense subgraph finding algorithms usually optimize some objective, and only find a few such subgraphs without providing any structural relations. We define the nucleus decomposition of a graph, which represents the graph as a forest of nuclei. Each nucleus is a subgraph where smaller cliques are present in many larger cliques. The forest of nuclei is a hierarchy by containment, where the edge density increases as we proceed towards leaf nuclei. Sibling nuclei can have limited intersections, which enables discovering overlapping dense subgraphs. With the right parameters, the nucleus decomposition generalizes the classic notions of k-cores and k-truss decompositions. We give provably efficient algorithms for nucleus decompositions, and empirically evaluate their behavior in a variety of real graphs. The tree of nuclei consistently gives a global, hierarchical snapshot of dense substructures, and outputs dense subgraphs of higher quality than other state-of-the-art solutions. Our algorithm can process graphs with tens of millions of edges in less than an hour

A fast parallel maximum clique algorithm for large sparse graphs and temporal strong components

We propose a fast, parallel, maximum clique algorithm for large, sparse graphs that is designed to exploit characteristics of social and information networks. We observe roughly linear runtime scaling over graphs between 1000 vertices and 100M vertices. In a test with a 1.8 billion-edge social network, the algorithm finds the largest clique in about 20 minutes. For social networks, in particular, we found that using the core number of a vertex in combination with a good heuristic clique finder efficiently removes the vast majority of the search space. In addition, we parallelize the exploration of the search tree. In the algorithm, processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with especially large search spaces can be pruned by other processes. We use this clique finder to investigate the size of the largest temporal strong components in dynamic networks, which requires finding the largest clique in a particular temporal reachability graph

Implementation of asymmetric median tree method for the computation of a consensus phylogenetic tree

A phylogenetic tree displays evolutionary relationships between taxonomical units. Nowadays, they are constructed programmatically by using different methods of inference and relying on various data sources, such as DNA and RNA sequences. The resulting evolutionary hypotheses are often contradictory, and need to be resolved by applying consensus methods. In this thesis, asymmetric median tree method (AMT) for construction of consensus phylogenetic trees is described, and along with two other approximation methods implemented in Biopython. AMT was compared to methods of strict, majority and Adams consensus trees on a number of artificial and one real data set. The comparisons were evaluated using the Robinson-Foulds and the tree resolution metrics. The results show that AMT is often the least similar to the input trees. At the same time, it is the most resolved tree, and therefore it offers the most information about evolutionary history of taxonomical units

High Performance Large Graph Analytics by Enhancing Locality

Graphs are widely used in a variety of domains for representing entities and their relationship to each other. Graph analytics helps to understand, detect, extract and visualize insightful relationships between different entities. Graph analytics has a wide range of applications in various domains including computational biology, commerce, intelligence, health care and transportation. The breadth of problems that require large graph analytics is growing rapidly resulting in a need for fast and efficient graph processing. One of the major challenges in graph processing is poor locality of reference. Locality of reference refers to the phenomenon of frequently accessing the same memory location or adjacent memory locations. Applications with poor data locality reduce the effectiveness of the cache memory. They result in large number of cache misses, requiring access to high latency main memory. Therefore, it is essential to have good locality for good performance. Most graph processing applications have highly random memory access patterns. Coupled with the current large sizes of the graphs, they result in poor cache utilization. Additionally, the computation to data access ratio in many graph processing applications is very low, making it difficult to cover the memory latency using computation. It is also challenging to efficiently parallelize most graph applications. Many graphs in real world have unbalanced degree distribution. It is difficult to achieve a balanced workload for such graphs. The parallelism in graph applications is generally fine-grained in nature. This calls for efficient synchronization and communication between the processing units. Techniques for enhancing locality have been well studied in the context of regular applications like linear algebra. Those techniques are in most cases not applicable to the graph problems. In this dissertation, we propose two techniques for enhancing locality in graph algorithms: access transformation and task-set reduction. Access transformation can be applied to algorithms to improve the spatial locality by changing the random access pattern to sequential access. It is applicable to iterative algorithms that process random vertices/edges in each iteration. The task-set reduction technique can be applied to enhance the temporal locality. It is applicable to algorithms which repeatedly access the same data to perform certain task. Using the two techniques, we propose novel algorithms for three graph problems: k-core decomposition, maximal clique enumeration and triangle listing. We have implemented the algorithms. The results show that these algorithms provide significant improvement in performance and also scale well