Window-based Streaming Graph Partitioning Algorithm

In the recent years, the scale of graph datasets has increased to such a degree that a single machine is not capable of efficiently processing large graphs. Thereby, efficient graph partitioning is necessary for those large graph applications. Traditional graph partitioning generally loads the whole graph data into the memory before performing partitioning; this is not only a time consuming task but it also creates memory bottlenecks. These issues of memory limitation and enormous time complexity can be resolved using stream-based graph partitioning. A streaming graph partitioning algorithm reads vertices once and assigns that vertex to a partition accordingly. This is also called an one-pass algorithm. This paper proposes an efficient window-based streaming graph partitioning algorithm called WStream. The WStream algorithm is an edge-cut partitioning algorithm, which distributes a vertex among the partitions. Our results suggest that the WStream algorithm is able to partition large graph data efficiently while keeping the load balanced across different partitions, and communication to a minimum. Evaluation results with real workloads also prove the effectiveness of our proposed algorithm, and it achieves a significant reduction in load imbalance and edge-cut with different ranges of dataset

Dynamic Balanced Graph Partitioning

This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the objective is to service these requests efficiently by partitioning the nodes into $\ell$ clusters, each of size $k$, such that frequently communicating nodes are located in the same cluster. The partitioning can be updated dynamically by migrating nodes between clusters. The goal is to devise online algorithms which jointly minimize the amount of inter-cluster communication and migration cost. The problem features interesting connections to other well-known online problems. For example, scenarios with $\ell=2$ generalize online paging, and scenarios with $k=2$ constitute a novel online variant of maximum matching. We present several lower bounds and algorithms for settings both with and without cluster-size augmentation. In particular, we prove that any deterministic online algorithm has a competitive ratio of at least $k$, even with significant augmentation. Our main algorithmic contributions are an $O(k \log{k})$-competitive deterministic algorithm for the general setting with constant augmentation, and a constant competitive algorithm for the maximum matching variant

Community detection and graph partitioning

Many methods have been proposed for community detection in networks. Some of the most promising are methods based on statistical inference, which rest on solid mathematical foundations and return excellent results in practice. In this paper we show that two of the most widely used inference methods can be mapped directly onto versions of the standard minimum-cut graph partitioning problem, which allows us to apply any of the many well-understood partitioning algorithms to the solution of community detection problems. We illustrate the approach by adapting the Laplacian spectral partitioning method to perform community inference, testing the resulting algorithm on a range of examples, including computer-generated and real-world networks. Both the quality of the results and the running time rival the best previous methods.Comment: 5 pages, 2 figure

Graph Partitioning Induced Phase Transitions

We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree $k$. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any partitioning process (even if non-optimal) that partitions the graph into equal sized connected components (clusters), the system undergoes a percolation phase transition at $f=f_c=1-2/k$ where $f$ is the fraction of edges removed to partition the graph. For optimal partitioning, at the percolation threshold, we find $S \sim N^{0.4}$ where $S$ is the size of the clusters and $\ell\sim N^{0.25}$ where $\ell$ is their diameter. Additionally, we find that $S$ undergoes multiple non-percolation transitions for $f<f_c$

Extremal Optimization for Graph Partitioning

Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal optimization, focusing on the convergence of the average run as a function of runtime and system size. The method has a single free parameter, which we determine numerically and justify using a simple argument. Our numerical results demonstrate that on random graphs, extremal optimization maintains consistent accuracy for increasing system sizes, with an approximation error decreasing over runtime roughly as a power law t^(-0.4). On geometrically structured graphs, the scaling of results from the average run suggests that these are far from optimal, with large fluctuations between individual trials. But when only the best runs are considered, results consistent with theoretical arguments are recovered.Comment: 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher

Recent Advances in Graph Partitioning

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