By Nikhil Bansal, Irene Finocchi
This e-book constitutes the refereed court cases of the twelfth foreign Colloquium on Theoretical facets of Computing, ICTAC 2015, held in Cali, Colombia, in October 2015. The 25 revised complete papers provided including 7 invited talks, three device papers, and a pair of brief papers have been rigorously reviewed and chosen from ninety three submissions. The papers hide quite a few themes resembling algebra and classification concept; automata and formal languages; concurrency; constraints, good judgment and semantic; software program structure and component-based layout; and verification.
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Extra resources for Algorithms - ESA 2015: 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings
We begin with our base case, a “short and wide” w × m matrix M where w ≤ m. The algorithm repeats the following twice and then sorts the rows in ascending order. 1. Sort rows in alternating order (odd rows ascending, even rows descending). 2. , the ﬁrst w elements of the ﬁrst row form the ﬁrst column, the next w elements form the second column and so on). 3. Sort rows in ascending order. 4. , the ﬁrst m/w columns will form the ﬁrst row). Lemma 1. The above algorithm sorts the matrix correctly in O(m log m) time.
This will leave at most m dirty rows. Once again, we sort the columns, which will place the dirty rows in adjacent rows. We sort each m × m sub-matrix in alternating order, using Theorem 1, which will reduce the number of dirty rows to two. The rest of the argument is very similar to the one presented for Theorem 1. The next result might not sound very strong, but it will be very useful in the next section. It also reveals some diﬀerences between the partition and sorting problems. Note that the result is optimal as long as w is polynomial in m.
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Algorithms - ESA 2015: 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings by Nikhil Bansal, Irene Finocchi