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