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 foreign Scandinavian Symposium and Workshops on set of rules idea, SWAT 2014, held in Copenhagen, Denmark, in July 2014. The 33 papers have been rigorously reviewed and chosen from a complete of 134 submissions. The papers current unique learn and canopy quite a lot of themes within the box of layout and research of algorithms and information 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 video game theory.

**Read Online or Download Algorithm Theory – SWAT 2014: 14th Scandinavian Symposium and Workshops, Copenhagen, Denmark, July 2-4, 2014. Proceedings PDF**

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This ebook constitutes the refereed lawsuits of the 14th foreign Scandinavian Symposium and Workshops on set of rules thought, 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 issues 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 conception.

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

**Example text**

However, in order to achieve a constant number of schedules, we have to reﬁne this scheme and incorporate new ideas. First, the job classes have to be chosen properly so as to allow a compact packing of jobs on the machines. An important, new aspect in the construction of A2 (ε) is that we will not consider the entire set V of tuples specifying how large jobs of an input sequence σ are distributed over the job classes. Instead we will deﬁne a suitable sparsiﬁcation V of V . Each v ∈ V represents an estimate or guess on the number of large jobs arising in σ.

For instance, any algorithm with a competitive ratio smaller than 1 + 1/12 requires Ω(m2 ) schedules. Any algorithm with a competitiveness smaller than 1 + 1/16 needs Ω(m3 ) schedules. Theorem 5. Let A be a deterministic online algorithm for MPS or MPSopt . If A achieves a competitive ratio smaller than 1 + ε, where 0 < ε ≤ 1/4, +h−1 then it must maintain at least m h−1 schedules, where m = m/2 and h = 1/(4ε) . The binomial coeﬃcient increases as ε decreases and is at least √ Ω((εm) 1/(4ε) −1/2 / m).

We develop a (4/3 + ε)-competitive algorithm, for any 0 < ε ≤ 1, that uses a constant number of 1/εO(log(1/ε)) schedules. Furthermore, we give a (1 + ε)-competitive algorithm, for any 0 < ε ≤ 1, that uses a polynomial number of schedules. The number is (m/ε)O(log(1/ε)/ε) , which depends on m but is independent of the job sequence σ. These performance guarantees are nearly best possible. The algorithms are obtained via some intermediate results that may be of independent interest. First, in Section 2 we show that the original problem MPS can be reduced to the variant MPSopt in which the optimum makespan is known.

### 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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