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By Inge Li Gørtz, R. Ravi

This ebook constitutes the refereed complaints of the 14th overseas Scandinavian Symposium and Workshops on set of rules idea, 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 study and canopy quite a lot of subject matters within the box of layout and research of algorithms and knowledge constructions together with yet now not restricted 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 online game theory.

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Extra info for Algorithm Theory – SWAT 2014: 14th Scandinavian Symposium and Workshops, Copenhagen, Denmark, July 2-4, 2014. Proceedings

Example text

Since each relative rank consists of 2 log n bits we can sort them fast using packed sorting (Section 5) and finally the actual ranks can be returned based on that. 30 3 D. S. S. Nielsen Tools This section is a summary of standard word-parallel algorithms used by our sorting algorithm; for an extensive treatment see [12]. In particular the prefix sum and word packing algorithms can be derived from [13]. For those familiar with “bit tricks” this section can be skipped. We adopt the notation and techniques used in [3].

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.

Definition 2. The Patricia trie of x1 , x2 , . . , xn of detail i, denoted T i , is the i Patricia trie of x1 , . . , xn when considered over the alphabet Σ i = {0, 1}w/2 . The input to the ith recursion satisfies the following invariants, provided the algorithm has not made any errors so far: i. The number of bits in an element is |e| = 2wi . ii. There is a bijection from id’s to non leaf nodes in T i . iii. The pair (id, e) is in the input if and only if there is an edge from a node v ∈ T i corresponding to id to a child labeled by a string in which e ∈ Σ i is the first character.

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