By Inge Li Gørtz, R. Ravi

ISBN-10: 3319084038

ISBN-13: 9783319084039

ISBN-10: 3319084046

ISBN-13: 9783319084046

This publication constitutes the refereed complaints of the 14th overseas Scandinavian Symposium and Workshops on set of rules concept, 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 quite a lot of themes within the box of layout and research of algorithms and knowledge buildings together with yet no longer constrained to approximation algorithms, parameterized algorithms, computational biology, computational geometry and topology, disbursed 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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**Example text**

The bottleneck in our construction is O(log log n) levels of packed sorting of O(n) elements each of Θ(log n) bits, where each sorting requires 2 time O(n logw n ). For w = Ω(log2 n log log n), the overall time becomes O(n). This paper is structured as follows: Section 2 contains a high level description of the ideas and concepts used by our algorithm. In Section 3 we summarize the RAM operations adopted from [3] that are needed to implement the algorithm outlined in Section 2. In Section 4 we give the details of implementing the algorithm on a RAM and in Section 5 we present the packed sorting algorithm.

We deﬁne two further conditions when an algorithm Ak fails. The ﬁrst one identiﬁes situations where a makespan of ργ is not preserved and hence ρ-competitiveness may not be guaranteed. More precisely, Ak would assign Jt to a machine Mj such that (j)+pt > ργ, where (j) denotes Mj ’s machine load before the assignment. e. γ is smaller than the average machine load or the processing time of Jt . Formally, an algorithm Ak fails if a job Jt , 1 ≤ t ≤ n, has to be scheduled and one of the following conditions holds: (i) Ak does not specify a machine where to place Jt in the current schedule Sk .

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.

### Algorithm Theory – SWAT 2014: 14th Scandinavian Symposium and Workshops, Copenhagen, Denmark, July 2-4, 2014. Proceedings by Inge Li Gørtz, R. Ravi

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