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This paper studies the problem of imposing an existing hierarchical semantic structure onto a corresponding spoken document in which the structures are embedded, with the goal of indexing such documents for easier access. We propose a graph-partitioning framework to solve a semantic tree-to-string alignment problem through optimizing a normalized-cut criterion. We present models with different modeling capabilities and time complexities in this framework and provide experimental evidence of their performance. We relate graph partitioning to conventional dynamic time warping (DTW) as it applies to this problem, and show that the proposed framework can naturally include topic segmentation to accommodate cohesion constraints.