By Inge Li Gørtz, R. Ravi

This ebook constitutes the refereed court cases of the 14th overseas Scandinavian Symposium and Workshops on set of rules conception, 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 study and canopy quite a lot of subject matters within the box of layout and research of algorithms and knowledge 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 video game theory.

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

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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**

It assumes that the incoming job sequence σ contains exactly vi jobs with a processing time in Ii , for i = 1, . . , l. Moreover, it pessimistically assumes that each processing time in Ii takes the largest possible value (1 + ε )i ε . Hence, initially Av computes an optimal schedule Sv∗ for a job sequence consisting of vi jobs with a processing time of (1 + ε )i ε , for i = 1, . . , l. Small jobs are ignored. Let n∗i (j) denote the number of jobs with a processing time of (1 + ε )i ε ∈ Ii assigned to machine Mj in Sv∗ , l where 1 ≤ i ≤ l and 1 ≤ j ≤ m.

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). References 1. : Better bounds for online scheduling. SIAM J. Comput. 29, 459–473 (1999) 2. : On the value of job migration in online makespan minimization. , Ferragina, P. ) ESA 2012.

Assume without loss of generality that opt(σ) = 1. Then all job processing times are in (0, 1]. Set ε = ε/2. First we partition the range of possible job processing times into intervals I0 , . . , Il such that, within each interval Ii with i ≥ 1, the values diﬀer by a factor of at most 1 + ε . g. in the PTAS for oﬄine makespan minimization [20]. Let l = log(1/ε )/ log(1 + ε ) . Set I0 = (0, ε ] and Ii = ((1 + ε )i−1 ε , (1 + ε )i ε ], for i = 1, . . , l. Obviously I0 ∪ . . ∪ Il = (0, (1 + ε )l ε ] and (0, 1] ⊆ (0, (1 + ε )l ε ].