We propose a novel branch-and-price (B&P) approach to solve the maximum weighted independent set problem (MWISP). Our approach uses clones of vertices to create edge-disjoint partitions from vertex-disjoint partitions. We solve the MWISP on sub-problems based on these edge-disjoint partitions using a B&P framework, which coordinates sub-problem solutions by involving an equivalence relationship between a vertex and each of its clones. We present test results for standard instances and randomly generated graphs for comparison. We show analytically and computationally that our approach gives tight bounds and it solves both dense and sparse graphs quite quickly.

We propose a novel branch-and-price (B&P) approach to solve the maximum weighted independent set problem (MWISP). Our approach uses clones of vertices to create edge-disjoint partitions from vertex-disjoint partitions. We solve the MWISP on sub-problems based on these edge-disjoint partitions using a B&P framework, which coordinates sub-problem solutions by involving an equivalence relationship between a vertex and each of its clones. We present test results for standard instances and randomly generated graphs for comparison. We show analytically and computationally that our approach gives tight bounds and it solves both dense and sparse graphs quite quickly.

This dissertation addresses two fundamental problems in computer vision—namely, multitarget tracking and event recognition in videos. These problems are challenging because uncertainty may arise from a host of sources, including motion blur, occlusions, and dynamic cluttered backgrounds. We show that these challenges can be successfully addressed by using a multiscale, volumetric video representation, and taking into account various constraints between events offered by domain knowledge. The dissertation presents our two alternative approaches to multitarget tracking. The first approach seeks to transitively link object detections across consecutive video frames by finding the maximum independent set of a graph of all object detections. Two maximum-independent-set algorithms are specified, and their convergence properties theoretically analyzed. The second approach hierarchically partitions the space-time volume of a video into tracks of objects, producing a segmentation graph of that video. The resulting tracks encode rich contextual cues between salient video parts in space and time, and thus facilitate event recognition, and segmentation in space and time. We also describe our two alternative approaches to event recognition. The first approach seeks to learn a structural probabilistic model of an event class from training videos represented by hierarchical segmentation graphs. The graph model is then used for inference of event occurrences in new videos. Learning and inference algorithms are formulated within the same framework, and their convergence rates theoretically analyzed. The second approach to event recognition uses probabilistic first-order logic for reasoning over continuous time intervals. We specify the syntax, learning, and inference algorithms of this probabilistic event logic. Qualitative and quantitative results on benchmark video datasets are also presented. The results demonstrate that our approaches provide consistent video interpretation with respect to acquired domain knowledge. We outperform most of the state-of-the-art approaches on benchmark datasets. We also present our new basketball dataset that complements existing benchmarks with new challenges. / Graduation date: 2011 / Access restricted to the OSU Community at author's request from May 12, 2011 - May 12, 2012