Abstract: Methods and apparatuses for synchronizing displays of a local and a remote device using image compression to achieve efficiency gains are disclosed. A local device requests an update for a particular requested region of a remote device's display, receives an update region which is a portion of the requested region, and updates a stored local representation of the remote display based on the update region. A remote device compares, upon a request from a local device for an update, portions of the old and new stored images corresponding to the requested region. Compared pixels are then encoded to yield an update region and transmitted to the local device. In the encoding, pixels which changed between the old image and the new image are encoded opaque and with the color corresponding to the pixels in the new image, and at least one pixel which did not change between the old image and the new image is encoded transparent.

Abstract: An enumerator employs “indexing volumes” as the add-on values used to compute indexes for n-item ordered sets such as symbol sequences. Each indexing volume is associated with a different class into which the allowed ordered sets are partitioned. The indexing volumes all equal or exceed the number of ordered sets that belong to their respective classes. Additionally, the indexing volume Vi associated with a given class of i-item equals or exceeds the sum of the indexing volumes associated with the classes that contain the (i?1)-item prefixes of the ordered sets that belong to the given class.