By Richard E. Klima, Neil Sigmon, Ernest Stitzinger

ISBN-10: 0849381703

ISBN-13: 9780849381706

As well as conventional themes, this finished compendium of algorithms, information buildings, and concept of computation covers:oapplications components the place algorithms and information structuring suggestions are of particular significance ograph drawingorobot algorithmsoVLSI layoutovision and snapshot processing algorithmsoschedulingoelectronic cashodata compressionodynamic graph algorithmsoon-line algorithmsomultidimensional info structuresocryptographyoadvanced subject matters in combinatorial optimization and parallel/distributed computingUnique insurance of Algorithms and conception of Computation guide makes it a vital reference for researchers and practitioners in those functions components.

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**Example text**

Searching with Nonuniform Access Cost In the traditional RAM model we assume that any memory access has the same cost. However, this is not true if we consider the memory hierarchy of a computer: registers, cache and main memory, secondary storage, etc. As an example of this case, we use the hierarchical memory model introduced in [1]. That is, the access cost to position x is given by a function f (x). The traditional RAM model is when f (x) is a constant function. Based in access times of current devices, possible values are f (x) = log x or f (x) = x α with 0 < α ≤ 1.

However, we have two algorithms and not only one. Suppose that the element we are looking for is in position i and that the coin is fair (that is, the probability of heads or tails is the same). So, the number of comparisons to ﬁnd the element is i if it is heads, or n − i + 1 if it is tails. So, averaging over both algorithms (note that we are not averaging over all possible inputs), the expected worst case is 1 n+1 1 × i + × (n − i + 1) = 2 2 2 which is independent of where the element is! This is better than n.

Ei . Imagine what happens if we add the edge ei to Tmin : since Tmin is a spanning tree, the addition of ei causes a cycle containing ei . Let emax be the highest-cost edge on that cycle not among e1 , e2 , . . , ei . There must be such an emax because e1 , e2 , . . , ei are acyclic, since they are in the spanning tree constructed by Prim’s algorithm. Moreover, because Prim’s algorithm always makes a greedy choice—that is, chooses the lowest-cost available edge—the cost of ei is no more than the cost of any edge available to Prim’s algorithm when ei is chosen; the cost of emax is at least that of one of those unchosen edges, so it follows that the cost of ei is no more than the cost of emax .

### Algorithms and Theory of Computation Handbook by Richard E. Klima, Neil Sigmon, Ernest Stitzinger

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