Recent work for visualizing big graphs uses a proxy graph approach: the original graph is replaced by a proxy graph, which is much smaller than the original graph. The challenge for the proxy graph approach is to ensure that the proxy graph is a good representation of the original graph. However, previous work to compute proxy graphs using graph sampling techniques often fails to preserve connectivity and important global skeletal structure in the original graph. This paper introduces two new families of proxy graph methods BCP-W and BCP-E, tightly integrating graph sampling methods with the BC (Block Cut-vertex) tree, which represents the decomposition of a graph into biconnected components. Experimental results using graph sampling quality metrics show that our new BC treebased proxy graph methods produce significantly better results than existing sampling-based proxy graph methods: 25% improvement by BCP-W and 15% by BCP-E on average. We also present DBCP, a BC tree-based proxy graph method for distributed environment. Experiments on the Amazon Cloud EC2 demonstrate that DBCP is scalable for big graph data sets; runtime speed-up of 77% for distributed 5-server on average. Visual comparison using a graph layout method and the proxy quality metrics confirm that our new BC tree-based proxy graph methods are significantly better than existing sampling-based proxy graph method. Our main results lead to guidelines for computing sampling-based proxy graphs for visualization of big graphs.

This paper introduces a new kind of geometric graph, called the degree-sensitive neighbourhood graph (dNNG), for a more precise modelling of neighbourhoods. Based on dNNG, we define better shape-based metrics and then propose a neighbourhood-driven force-directed algorithm, called NEFO, for neighbourhood faithfulness. Our evaluation on both real-world and randomly generated graphs shows that the dNNG gives more effective shape-based measures when compared to existing geometric graphs. The NEFO algorithm is shown to be effective for improving neighbourhood faithfulness of graph drawings.

Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.

Readability criteria have been commonly used to measure the quality of graph visualizations. In this paper we argue that readability criteria, while necessary, are not sufficient. We propose a new kind of criterion, generically termed faithfulness, for evaluating graph layout methods. We propose a general model for quantifying faithfulness, and contrast it with the well established readability criteria. We use examples of multidimensional scaling, edge bundling and several other visualization metaphors (including matrix-based and map-based visualizations) to illustrate faithfulness.

This paper describes a generalisation of modulo scheduling to parallelize loops for SpMT processors that exploits simultaneously both instruction-level parallelism and thread-level parallelism while preserving the simplicity and effectiveness of modulo scheduling. Our generalisation is simple, drops easily into traditional modulo scheduling algorithms such as Swing in GCC 4.1.1 and produces good speedups for SPECfp2000 benchmarks, particularly in terms of its ability in parallelising DOACROSS loops.

This paper describes a graph coloring compiler framework to allocate on-chip SRF(Stream Register File) storage for optimizing scientific applications on stream processors. Our framework consists of first applying enabling optimizations such as loop unrolling to expose stream reuse and opportunities for maximizing parallelism, i.e., overlapping kernel execution and memory transfers.Then the three SRF management tasks are solved in a unified manner via graph coloring: (1) placing streams in the SRF, (2) exploiting stream use, and (3) maximizing parallelism. We evaluate the performance of our compiler framework by actually running nine representative scientific computing kernels on our FT64 stream processor. Our preliminary results show that compiler management achieves an average speedup of 2.3x compared to First-Fit allocation. In comparison with the performance results obtained from running these benchmarks on Itanium 2, an average speedup of 2.1x is observed.

Existing methods place data or code in scratchpad memory, i.e., SPM by either relying on heuristics or resorting to integer programming or mapping it to a graph coloring problem.