Sorting and Selecting in Rounds
نویسندگان
چکیده
منابع مشابه
Sorting and Selecting in Rounds
We present upper bounds for sorting and selecting the median in a fixed number of rounds. These bounds match the known lower bounds to within logarithmic factors. They also have the merit of being "explicit modulo expansion"; that is, probabilistic arguments are used only to obtain expanding graphs, and when explicit constructions for such graphs are found, explicit algorithms for sorting and s...
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An mn matrix A is called totally monotone if for all i1 < i2 and j1 < j2, Ai1; j1] > Ai1; j2] implies Ai2; j1] > Ai2; j2]. We consider the complexity of comparison-based selection and sorting algorithms in such matrices. Although our selection algorithm counts only comparisons its advantage on all previous work is that it can also handle selection of elements of diierent (and arbitrary) ranks i...
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Expanding graphs are relevant to theoretical computer science in several ways. Here we show that the points versus hyperplanes incidence graphs of finite geometries form highly (nonlinear) expanding graphs with essentially the smallest possible number of edges. The expansion properties of the graphs are proved using the eigenvalues of their adjacency matrices. These graphs enable us to improve ...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 1987
ISSN: 0097-5397,1095-7111
DOI: 10.1137/0216066