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

By Inge Li Gørtz, R. Ravi

This e-book constitutes the refereed complaints of the 14th overseas 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 learn and canopy a variety of themes 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, 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 thought.

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**Sample text**

Cμ ) encodes inputs containing 2|{cj ∈ {c1 , . . cμ } : cj = i}| class-i jobs, for i = 1, . . , l, as well as |{cj ∈ {c1 , . . cμ } : cj = i}| class-i jobs, for i = l + 1, . . , 2l − 1. Hence, for an incoming job sequence, instead of considering estimates on the number of class-i jobs, for any 1 ≤ i ≤ 2l − 1, we can equivalently consider target conﬁgurations. Unfortunately, it will not be possible to 22 S. Albers and M. Hellwig work with all target conﬁgurations c ∈ {0, . . , 2l − 1}μ since the resulting number of schedules to be constructed would be (2l)μ = (log(1/ε))Ω(m) .

Initially, upon the arrival of the ﬁrst job J1 , the guesses are initialized as γ1 = p1 and γi = (1+ε)γi−1 , for i = 2, . . , h. Each job Jt , 1 ≤ t ≤ n, is handled in the following way. Of course each such job is sequenced in every schedule Sik , 1 ≤ i ≤ h and 1 ≤ k ≤ |K|. Algorithm A∗ (ε, h) checks if Ak using γi fails when having to sequence Jt in Sik . This check can be performed easily by just verifying if one of the conditions (i–iii) holds. If Ak using γi does not fail and has not failed since the last adjustment of γi , then in Sik job Jt is assigned to the machine speciﬁed by Ak using γi .

Ii) There holds (j) + pt > ργ, for machine Mj to which Ak would assign Jt in Sk . (iii) There holds γ < t ≤t pt /m or γ < pt . Algorithm for MPS: We describe our algorithm A∗ (ε, h) for MPS, where 0 < ε ≤ 1 and h ∈ N may be chosen arbitrarily. The construction takes as input any algorithm A = {Ak }k∈K for MPSopt . For a proper choice of h, A∗ (ε, h) will be (ρ + ε)-competitive, provided that A is ρ-competitive. At any time A∗ (ε, h) works with h guesses γ1 < . . < γh on the optimum makespan for the incoming job sequence σ.