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Proxy caching of large multimedia objects on the edge of the Internet has become increasingly important for reducing network latency. For a large media object, such as a two-hour video, treating the whole media as a single object for caching is not appropriate. In this paper, we study three media segmentation approaches to proxy caching: fixed, pyramid, and skyscraper. Blocks of a media stream are grouped into various segments for cache management. The cache admission and replacement policies attach different caching priorities to individual segments, taking into account the access frequency of the media object and the segment distance from the start of the media. These caching policies give preferential treatment to the beginning segments. As such, most user requests can be quickly played back from the proxy servers without delay. Event-driven simulations are conducted to evaluate the segmentation approaches and compare them with whole media caching. The results show that: 1) compared with whole media caching, segmentation-based caching is more effective not only in increased byte-hit ratio but also in lowered fraction of requests that requires delayed start; 2) pyramid segmentation, where segment size increases exponentially, is the best segmentation approach; and 3) segmentation-based caching is especially advantageous when the cache size is limited, when the set of hot media objects changes over time, when the media file size is large, and when there are a large number of distinct media objects.