Network of workstation (NOW) is a cost-effective alternative to massively parallel supercomputers. As commercially available off-the-shelf processors become cheaper and faster, it is now possible to build a cluster that provides high computing power within a limited budget. However, a cluster may consist of different types of processors and this heterogeneity complicates the design of efficient collective communication protocols. For example, it is a very hard combinatorial problem to find an optimal reduction schedule for such heterogeneous clusters. Nevertheless, we show that a simple technique called slowest-node-first (SNF) is very effective in designing efficient reduction protocols for heterogeneous clusters. First, we show that SNF is actually a 2-approximation algorithm, which means that an SNF schedule length is always within twice of the optimal schedule length, no matter what kind of cluster is given. In addition, we show that SNF does give the optimal reduction time when the cluster consists of two types of processors, when the ratio of communication speed between them is at least two. When the communication speed ratio is less than two, we develop a dynamic programming technique to find the optimal schedule. Our dynamic programming utilizes the monotone property of the objective function, and can significantly reduce the amount of computation time. Finally, combined with an approximation algorithm for broadcast 2004, we propose an all-reduction algorithm which sends the reduction answer to all processors, with approximation ratio 3.5. We conduct three groups of experiments. First, we show that SNF performs better than the built-in MPI_Reduce in a test cluster. Second, we observe a factor of 93 times saving in computation time to find the optimal schedule, when compared with a naive dynamic programming implementation. Thirdly, we apply the theoretical results to a branch-and-bound search and show that they can reduce the search time of the optimal reduction schedule by a factor of 500, when the cluster has three kinds of processors.

The effectiveness of 3D tree model simplification techniques and their objective and subjective performance evaluations are examined in this work. The simplification techniques developed in [1,2] were based on pixel-based metrics, which did not consider the tree model's leaf density. For performance improvement, we perform simplification based on the tree leaf density of rendered images viewed from multiple angles. Furthermore, objective performance analysis is conducted to evaluate how well different algorithms are able to simplify tree models that appear as close to the original tree model with a given budget on the number of tree leaves in the model. To this end, a performance metric based on the Gabor filter is developed to analyze the orientation and spatial relationship within the rendered tree models. Finally, subjective evaluation is conducted by a group of 23 people. Both the objective and the subject evaluations reach a consistent conclusion; namely, the newly proposed densitybased simplification technique offers the best results.

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Human motion understanding based on motion capture (mocap) data is investigated. Recent rapid developments and applications of mocap systems have resulted in a large corpus of mocap sequences, and an automated annotation technique that can classify basic motion types into multiple categories is needed. A novel technique for automated mocap data classification is developed in this work. Specifically, we adopt the tree-structured vector quantization (TSVQ) method to approximate human poses by codewords and approximate the dynamics of mocap sequences by a codeword sequence. To classify mocap data into different categories, we consider three approaches: 1) the spatial domain approach based on the histogram of codewords, 2) the spatialtime domain approach via codeword sequence matching, and 3) a decision fusion approach. We test the proposed algorithm on the CMU mocap database using the n-fold cross validation procedure and obtain a correct classification rate of 97%.

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