By Spyros Angelopoulos (auth.), Evripidis Bampis, Klaus Jansen (eds.)
This e-book constitutes the completely refereed publish workshop court cases of the seventh foreign Workshop on Approximation and on-line Algorithms, WAOA 2009, held in Copenhagen, Denmark, in September 2009 as a part of the ALGO 2009 convention occasion. The 22 revised complete papers offered have been rigorously reviewed and chosen from sixty two submissions. The workshop coated parts equivalent to algorithmic video game conception, approximation periods, coloring and partitioning, aggressive research, computational finance, cuts and connectivity, geometric difficulties, inapproximability effects, mechanism layout, community layout, packing and overlaying, paradigms for layout and research of approximation and on-line algorithms, parameterized complexity, randomization strategies, real-world functions, and scheduling difficulties.
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Additional info for Approximation and Online Algorithms: 7th International Workshop,WAOA 2009, Copenhagen Denmark, September 10-11, 2009. Revised Papers
3 The set of resulting rectangles Lv is now considered as an instance of RPA with OPTRP A (L) = SIZE(Lv ). Apply kRP A to k bins of unit size and ﬁnd for an accuracy ε ≤ 1/4 a packing for a subset Lv ⊂ Lv with total area (1 − ε)SIZE(Lv ). By rescaling the rectangles of Lv we get k bins of height v. 4 For the total area of the remaining rectangles in Lv \Lv we have SIZE(Lv \Lv ) = εSIZE(Lv ) ≤ k/4. Pack those rectangles according to Lemma 2 into k bins and rescale the rectangles. This results again in k bins of height at most v.
The worst-case ratio between these two amounts is called competitive ratio. A well-known result [11,12] states that the best deterministic online strategy is to rent skis for s − 1 day and then to buy them on day s. It is easy to check that such a strategy achieves a competitive ratio of (2 − 1/s). In this paper, we extend this model, so that the rental price p may evolve with time. Therefore, the instance of the problem includes not only the duration of the process in days, but also a sequence of prices in consecutive days.
SWAT 2004. LNCS, vol. 3111, pp. 174–186. Springer, Heidelberg (2004) 12. : Solving integer programs over monotone inequalities in three variables: a framework of half integrality and good approximations. European Journal of Operational Research 140(2), 291–321 (2002) 13. : On the equivalence between the primal-dual schema and the local ratio technique. SIAM J. Disc. Math. 19(3), 762–797 (2005) 14. : The minimum generalized vertex cover problem. ACM Trans. Alg. 2(1), 66–78 (2006) 15. : Improved complexity bounds for location problems on the real line.
Approximation and Online Algorithms: 7th International Workshop,WAOA 2009, Copenhagen Denmark, September 10-11, 2009. Revised Papers by Spyros Angelopoulos (auth.), Evripidis Bampis, Klaus Jansen (eds.)