By Mario Szegedy (auth.), Andrei A. Bulatov, Arseny M. Shur (eds.)
ISBN-10: 3642385354
ISBN-13: 9783642385353
ISBN-10: 3642385362
ISBN-13: 9783642385360
This e-book constitutes the lawsuits of the eighth overseas machine technological know-how Symposium in Russia, CSR 2013, held in Ekaterinburg, Russia, in June 2013. The 29 complete papers provided during this quantity have been rigorously reviewed and chosen from fifty two submissions. additionally the booklet includes eight invited lectures. The papers are equipped in topical sections on: algorithms; automata; common sense and facts complexity; complexity; phrases and languages; and common sense and automata.
Read or Download Computer Science – Theory and Applications: 8th International Computer Science Symposium in Russia, CSR 2013, Ekaterinburg, Russia, June 25-29, 2013. Proceedings PDF
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Extra resources for Computer Science – Theory and Applications: 8th International Computer Science Symposium in Russia, CSR 2013, Ekaterinburg, Russia, June 25-29, 2013. Proceedings
Example text
The proof of these results are postponed to Sect. 3. 75n. 88m in the average case. 28 V. Diekert and A. Weiß For the mathematical analysis better theoretical bounds can be used. The best result we are aware of is due to Chen et al. in [5]. 625m + o(m). 625m + o(m), but Gonnet and Munro used O(m) extra bits to get this result, whereas the new result of Chen et al. is in-place (by using only O(lg m) extra bits). During the execution of QuickHeapsort over n elements, every element is part of a heap only once.
Green nodes satisfy the standard heap-condition, children of red nodes are red. Twolayer-heaps were defined in [11]. In [2] for the same concept a different language is used (they describe the algorithm in terms of External Heapsort). Now we are ready to describe the QuickHeapsort algorithm as it has been proposed in [2]. 26 V. Diekert and A. n]. First, we choose a pivot p. This is the randomized part of the algorithm. Then, just as in Quicksort, we rearrange the array according to p. That means, using n − 1 comparisons the partitioning function returns an index k and rearranges the array A so that A[i] ≥ A[k] for i < k, A[k] = p, and A[k] ≥ A[j] for k < j.
First use Lemma 1 and Lemma 2 to compute M (w1 , w2 , . . , wn ) . Then note that the fractional part of the answer must be equal to some frac(wi ). We can compute it using a binary search inside which we use Lemma 1 and Lemma 3 (again) to check if a chosen frac(wi ) is bigger than frac(M (w1 , w2 , . . , wn )). To accelerate the O(n log n) time procedure, we must somehow reuse the information found by the successive steps of binary search. We split the whole {1, 2, . . , n} into three parts L, C, and R.
Computer Science – Theory and Applications: 8th International Computer Science Symposium in Russia, CSR 2013, Ekaterinburg, Russia, June 25-29, 2013. Proceedings by Mario Szegedy (auth.), Andrei A. Bulatov, Arseny M. Shur (eds.)
by Edward
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