Algorithms sequential and parallel: a unified approach by Miller R., Boxer L.

By Miller R., Boxer L.

For a one-semester, junior/senior-level path in Algorithms. Attuned to the quickly altering panorama in machine know-how, this detailed and extremely revolutionary textual content is helping scholars comprehend the applying and research of algorithmic paradigms to either the conventional sequential version of computing and to numerous parallel models-offering a unified, totally built-in insurance of either version varieties in order that scholars can discover ways to realize how resolution concepts should be shared between machine paradigms and architectures

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K) E I. are independent of the starting point v. As will be argued in the following chapters. it is more efficient to take vectors which are dependent on v. This also allows us to take any point in Sn or S as the starting point of an algorithm, whereas in the case of the Q- or Q'-triangulation the starting point must lie in QO. Triangulations which allow for an arbitrary starting point v will be m defined in the following sections. It is obvious that such triangulations depend on the point v. 4.

Each utility function uh , h = 1, ••. ,H, is assumed to be con- > uh(x)), and strict strict monotone (y ~ x, y ~ x implies uh(y) > ~} is strict convex, ~ h, h = 1, •.. ,H, is a convex quasi-concave (the set {x E Xhluh(x) E R). , i = 1, •.. ,n+l}, + + i 1 with the vector w = EH wh Given a price vector p E Rn +1 \{0}, each h=l + consumer maximizes his utility over his budget set. •• ,H, is then given by aggregated demand function d is given by d(p) = EH dh(p). This funch=l tion d is well defined and is continuous on Rn +1 \{0}.

Independent point. Observe that. in the case N cides with the V-triangulation of 8n The vec- € I. dependent on a certain starting point. whereas = 1. k). k) € I. k}. We now introduce a triangulation which uses vectors j e(Io} v. e. all elements in I of this vector can be nonzero. The triangulation of 8 using these vectors e(Io} - v is called the V-triangulation of 8. 1)! b. The V'-triangulation «1,1)), r Let ment. say (j,k 1° j ), = UNj = 1 1°j x with r 82 , l = 1. 1}). e. there is °exactly one index j' all other j.

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