John G. Webster (Editor) 's 14.Computers PDF

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A set of n items with (distinct) keys from a set ͕1, . , m͖, m Ն n, can be stored in an array A of size m, with an item whose key is ALGORITHM THEORY k stored in position A[k]. The basic operations—insert, delete, and search by key—can all be done in constant time. However, this method is too wasteful if m is very large. In such cases, we use a hash function h, which is a map from the universe of keys to a smaller set S. An item with key k is now stored in position A[h(k)]. This approach requires only ͉S͉ storage.

Let wii0 ϭ 0 and wij0 ϭ ȍ for i ϶ j. For any vertex k ϶ j, we can express the minimum-weight of a path from i to j with at most m edges (m Ն 1) and with k as j’s predecessor, as the sum wikmϪ1 ϩ edgewt(k, j), where edge-wt(k, j) is the weight of the edge (k, j) (infinity if k and j are not connected by an edge). Therefore, to get the weight of a min-weight path of length at most m from i to j, we minimize this expression with respect to k, including k ϭ j with the understanding that edge-wt( j, j) ϭ 0.

In this example a PCI interface is currently implemented on a fast Altera EPLD which communicates with a SRAM-based Altera CPLD containing the user’s application. These authors suggest that their system could be advantageously applied to prototyping ASIC-oriented designs before going to large-scale manufacture. They are also proposing to develop PCI-compliant add-on boards for image filtering and cryptography, both of which would eventually combine the PCI interface function and back-end application in a single CPLD.

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14.Computers by John G. Webster (Editor)

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