Algorithm Theory -- SWAT 2014: 14th Scandinavian Symposium by Inge Li Gørtz, R. Ravi

By Inge Li Gørtz, R. Ravi

This ebook constitutes the refereed complaints of the 14th foreign Scandinavian Symposium and Workshops on set of rules conception, SWAT 2014, held in Copenhagen, Denmark, in July 2014. The 33 papers have been conscientiously reviewed and chosen from a complete of 134 submissions. The papers current unique examine and canopy a variety of themes within the box of layout and research of algorithms and information constructions together with yet no longer constrained to approximation algorithms, parameterized algorithms, computational biology, computational geometry and topology, dispensed algorithms, external-memory algorithms, exponential algorithms, graph algorithms, on-line algorithms, optimization algorithms, randomized algorithms, streaming algorithms, string algorithms, sublinear algorithms and algorithmic video game concept.

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Additional info for Algorithm Theory -- SWAT 2014: 14th Scandinavian Symposium and Workshops, SWAT 2014, Copenhagen, Denmark, July 2-4, 2014. Proceedings (Lecture Notes in Computer Science)

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On the outermost recursion level we take the input x1 , x2 , . . , xn and produce the list (1, x1 ), (1, x2 ), . . , (1, xn ), solve this problem, and use the ranks π1 , π2 , . . , πn returned to permute the input in sorted order in O(n) time. To describe the recursion we need the following definitions. Definition 1 ([6]). The Patricia trie consists of all the branching nodes and leaves of the corresponding compacted trie as well as their connecting edges. All the edges in the Patricia trie are labeled only by the first character of the corresponding edge in the compacted trie.

Thorup established that maintaining RAM priority queues and RAM sorting are equivalent problems by proving that if we can sort in time O(n · f (n)) then there is a priority queue using O(f (n)) time per operation [15]. Our results. We consider for which word sizes we can sort n w-bit integers in the word-RAM model in expected linear time. We improve the previous best word size of Ω(log2+ε n) [3] to Ω(log2 n log log n). Word-level parallelism is used extensively and we rely on a new packed sorting algorithm (see Section 5) in intermediate steps.

Nielsen for T i+1 to get the ranks of the input elements for level i. Finally the analysis of the algorithm is given. The input to the ith recursion is a list of pairs: (id, e) using log n + 2wi bits each and satisfying the invariants stated in Section 2. The list is packed tightly i ) ) words. e. e. they occupy O( w ) words. The main challenge of this section is to be able to compute the necessary operations, even when the input elements and output ranks are packed in words. For convenience and simplicity we assume tuples are not split between words.

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