Partitioning Complex Networks via Size-constrained Clustering

The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and edges until the graph is small enough to be partitioned by some other algorithm. A partition of the input graph is then constructed by successively transferring the solution to the next finer graph and applying a local search algorithm to improve the current solution. In this paper, we describe a novel approach to partition graphs effectively especially if the networks have a highly irregular structure. More precisely, our algorithm provides graph coarsening by iteratively contracting size-constrained clusterings that are computed using a label propagation algorithm. The same algorithm that provides the size-constrained clusterings can also be used during uncoarsening as a fast and simple local search algorithm. Depending on the algorithm's configuration, we are able to compute partitions of very high quality outperforming all competitors, or partitions that are comparable to the best competitor in terms of quality, hMetis, while being nearly an order of magnitude faster on average. The fastest configuration partitions the largest graph available to us with 3.3 billion edges using a single machine in about ten minutes while cutting less than half of the edges than the fastest competitor, kMetis

Tree-based Coarsening and Partitioning of Complex Networks

Many applications produce massive complex networks whose analysis would benefit from parallel processing. Parallel algorithms, in turn, often require a suitable network partition. For solving optimization tasks such as graph partitioning on large networks, multilevel methods are preferred in practice. Yet, complex networks pose challenges to established multilevel algorithms, in particular to their coarsening phase. One way to specify a (recursive) coarsening of a graph is to rate its edges and then contract the edges as prioritized by the rating. In this paper we (i) define weights for the edges of a network that express the edges' importance for connectivity, (ii) compute a minimum weight spanning tree $T^m$ with respect to these weights, and (iii) rate the network edges based on the conductance values of $T^m$'s fundamental cuts. To this end, we also (iv) develop the first optimal linear-time algorithm to compute the conductance values of \emph{all} fundamental cuts of a given spanning tree. We integrate the new edge rating into a leading multilevel graph partitioner and equip the latter with a new greedy postprocessing for optimizing the maximum communication volume (MCV). Experiments on bipartitioning frequently used benchmark networks show that the postprocessing already reduces MCV by 11.3%. Our new edge rating further reduces MCV by 10.3% compared to the previously best rating with the postprocessing in place for both ratings. In total, with a modest increase in running time, our new approach reduces the MCV of complex network partitions by 20.4%

Common Peptides Study of Aminoacyl-tRNA Synthetases

Aminoacyl tRNA synthetases (aaRSs) constitute an essential enzyme super-family, providing fidelity of the translation process of mRNA to proteins in living cells. They are common to all kingdoms and are of utmost importance to all organisms. It is thus of great interest to understand the evolutionary relationships among them and underline signature motifs defining their common domains.We utilized the Common Peptides (CPs) framework, based on extracted deterministic motifs from all aaRSs, to study family-specific properties. We identified novel aaRS–class related signatures that may supplement the current classification methods and provide a basis for identifying functional regions specific to each aaRS class. We exploited the space spanned by the CPs in order to identify similarities between aaRS families that are not observed using sequence alignment methods, identifying different inter-aaRS associations across different kingdom of life. We explored the evolutionary history of the aaRS families and evolutionary origins of the mitochondrial aaRSs. Lastly, we showed that prevalent CPs significantly overlap known catalytic and binding sites, suggesting that they have meaningful functional roles, as well as identifying a motif shared between aaRSs and a the Biotin-[acetyl-CoA carboxylase] synthetase (birA) enzyme overlapping binding sites in both families.The study presents the multitude of ways to exploit the CP framework in order to extract meaningful patterns from the aaRS super-family. Specific CPs, discovered in this study, may play important roles in the functionality of these enzymes. We explored the evolutionary patterns in each aaRS family and tracked remote evolutionary links between these families

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Multilevel method for modeling large-scale networks.

Understanding the behavior of real complex networks is of great theoretical and practical significance. It includes developing accurate artificial models whose topological properties are similar to the real networks, generating the artificial networks at different scales under special conditions, investigating a network dynamics, reconstructing missing data, predicting network response, detecting anomalies and other tasks. Network generation, reconstruction, and prediction of its future topology are central issues of this field. In this project, we address the questions related to the understanding of the network modeling, investigating its structure and properties, and generating artificial networks. Most of the modern network generation methods are based either on various random graph models (reinforced by a set of properties such as power law distribution of node degrees, graph diameter, and number of triangles) or on the principle of replicating an existing model with elements of randomization such as R-MAT generator and Kronecker product modeling. Hierarchical models operate at different levels of network hierarchy but with the same finest elements of the network. However, in many cases the methods that include randomization and replication elements on the finest relationships between network nodes and modeling that addresses the problem of preserving a set of simplified properties do not fit accurately enough the real networks. Among the unsatisfactory features are numerically inadequate results, non-stability of algorithms on real (artificial) data, that have been tested on artificial (real) data, and incorrect behavior at different scales. One reason is that randomization and replication of existing structures can create conflicts between fine and coarse scales of the real network geometry. Moreover, the randomization and satisfying of some attribute at the same time can abolish those topological attributes that have been undefined or hidden from researchers. We propose to develop multilevel methods to model complex networks. The key point of the proposed strategy is that it will help to preserve part of the unknown structural attributes by guaranteeing the similar behavior of the real and artificial model on different scales

Recent advances in graph partitioning

We survey recent trends in practical algorithms for balanced graph partitioning, point to applications and discuss future research directions