By Inge Li Gørtz, R. Ravi

ISBN-10: 3319084038

ISBN-13: 9783319084039

ISBN-10: 3319084046

ISBN-13: 9783319084046

This booklet constitutes the refereed court cases 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 rigorously reviewed and chosen from a complete of 134 submissions. The papers current unique examine and canopy a variety of subject matters within the box of layout and research of algorithms and information buildings together with yet now not 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 online game theory.

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

**Sample text**

4 Algorithm – RAM Details In this section we describe how to execute each step of the algorithm outlined in Section 2. e. advance one level in the recursion. Then we describe how to use the output of the recursion 1 We use ↑ and ↓ as the shift operations where x ↑ y is x · 2y and x ↓ y is x div 2y . 32 D. S. S. 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.

Il = (0, (1 + ε )l ε ] and (0, 1] ⊆ (0, (1 + ε )l ε ]. A job is small if its processing time is at most ε and hence contained in I0 ; otherwise the job is large. Each σ with opt(σ) = 1 contains at most m/ε large jobs. For each possible distribution of large jobs over the processing time intervals I1 , . . , Il , algorithm A1 (ε) prepares one algorithm/schedule. Let V = {(v1 , . . , vl ) ∈ Nl0 | vi ≤ m/ε }. There holds |V | = ( m/ε + 1)l . Let A1 (ε) = {Av }v∈V . For any vector v = (v1 , .

3 A (1 + ε)-Competitive Algorithm for MPSopt We present an algorithm A1 (ε) for MPSopt that attains a competitive ratio of 1 + ε, for any ε > 0. The algorithms will yield a (1 + ε)-competitive strategy for MPS and will be useful in the next section where we develop a (4/3 + ε)competitive algorithm for MPSopt . There A1 (ε) will be used as subroutine for a small, constant number of m. Description of A1 (ε): Let ε > 0 be arbitrary. Assume without loss of generality that opt(σ) = 1. Then all job processing times are in (0, 1].

### 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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