Computing the Geodesic Center of a Simple Polygon
Computing the Geodesic Center of a Simple Polygon
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It thus follows that in 0{n log n) time we can resolve each of the comparisons in the present parallel step of the [AKSS] algorithm, so that the entire sequential simulation of this algorithm (at the still unknown level y*) can be done in time 0(n log n log log n).
We have thus foipd the first median xq calculated in RELCEN* (actually we do not have an explicit value of xq, but only the hyperbolic branch -y^ on which the (unknown) point {xQ, y*) lies). The next step of RELCEN* is to calculate t...he maximimi of the n values dt{xQ, y*), from which the side of xq containing the relative minmax of F on C can be easily determined. To this end we run a second fast parallel algorithm, this time for finding the maximum of n numbers; we can use e. G. The algorithm of Valiant p/a] which also runs in 0(log log n) parallel time, and uses 0{n) processors. At each parallel step of this algorithm we perform 0{n) comparisons of the form ^tC^oJ*) vs. Di{xQ, y*), subject to the constraint that {xQ, y*) lies on the hyperbola 7^^, calculated by the preceding median-finding step.
What to read after Computing the Geodesic Center of a Simple Polygon?
You can find similar books in the "Read Also" column, or choose other free books by Richard Pollack to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
It thus follows that in 0{n log n) time we can resolve each of the comparisons in the present parallel step of the [AKSS] algorithm, so that the entire sequential simulation of this algorithm (at the still unknown level y*) can be done in time 0(n log n log log n).
We have thus foipd the first median xq calculated in RELCEN* (actually we do not have an explicit value of xq, but only the hyperbolic branch -y^ on which the (unknown) point {xQ, y*) lies). The next step of RELCEN* is to calculate t...he maximimi of the n values dt{xQ, y*), from which the side of xq containing the relative minmax of F on C can be easily determined. To this end we run a second fast parallel algorithm, this time for finding the maximum of n numbers; we can use e. G. The algorithm of Valiant p/a] which also runs in 0(log log n) parallel time, and uses 0{n) processors. At each parallel step of this algorithm we perform 0{n) comparisons of the form ^tC^oJ*) vs. Di{xQ, y*), subject to the constraint that {xQ, y*) lies on the hyperbola 7^^, calculated by the preceding median-finding step.
What to read after Computing the Geodesic Center of a Simple Polygon?
You can find similar books in the "Read Also" column, or choose other free books by Richard Pollack to read onlineMoreLess
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