Computing downwards accumulations on trees quickly
نویسندگان
چکیده
منابع مشابه
Computing Downwards Accumulations on Trees Quickly
Downwards accumulations on binary trees are essentially functions which pass information down a tree, from the root towards the leaves. Under certain conditions, a downwards accumulation is bothèecient' (computable in a functional style in parallel time proportional to the depth of the tree) and`manipulable' (enjoying a number of distributivity properties useful in program construction). In thi...
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A downwards accumulation is a higher-order operation that distributes information downwards through a data structure, from the root towards the leaves. The concept was originally introduced in an ad hoc way for just a couple of kinds of tree. We generalize the concept to an arbitrary polynomial datatype; our generalization proceeds via the notion of a path in such a datatype.
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Accumulations are higher-order operations on structured objects; they leave the shape of an object unchanged, but replace elements of that object with accumulated information about other elements. Upwards and downwards accumulations on trees are two such operations; they form the basis of many tree algorithms. We present two Erew Pram algorithms for computing accumulations on trees taking O(log...
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The accumulation strategy consists of generalizing a function over an algebraic data structure by inclusion of an extra parameter, an accumulating parameter, for reusing and propagating intermediate results. It is one of the standard optimization techniques taught to functional programmers 13). However , there remain two major diculties in this accumulation strategy. One is to determine where a...
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For a tree T on n vertices, we study the Maker-Breaker game, played on the edge set of the complete graph on n vertices, which Maker wins as soon as the graph she builds contains a copy of T . We prove that if T has bounded maximum degree, then Maker can win this game within n+ 1 moves. Moreover, we prove that Maker can build almost every tree on n vertices in n−1 moves and provide non-trivial ...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1996
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(96)00114-4