By Klaus Jansen (auth.), Roberto Solis-Oba, Giuseppe Persiano (eds.)
This booklet constitutes the completely refereed post-proceedings of the ninth foreign Workshop on Approximation and on-line Algorithms, WAOA 2011, held in Saarbrücken, Germany, in September 2011. The 21 papers awarded have been conscientiously reviewed and chosen from forty eight submissions. the quantity additionally includes a longer summary of the invited speak of Prof. Klaus Jansen. The Workshop on Approximation and on-line Algorithms makes a speciality of the layout and research of algorithms for on-line and computationally challenging difficulties. either different types of difficulties have a good number of functions in a large choice of fields. issues of curiosity for WAOA 2011 have been: algorithmic online game idea, approximation sessions, coloring and partitioning, aggressive research, computational finance, cuts and connectivity, geometric difficulties, inapproximability effects, mechanism layout, community layout, packing and masking, paradigms for layout and research of approximation and on-line algorithms, parameterized complexity, randomization options and scheduling problems.
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Extra info for Approximation and Online Algorithms: 9th International Workshop, WAOA 2011, Saarbrücken, Germany, September 8-9, 2011, Revised Selected Papers
Example text
By (5), we E [Πs (n1 , n2 , ω, α)] = Hence, for any n1 (n1 + 1) n2 (n2 + 1) (1 − ) + + n1 n2 (1 − ). 2 2 > 0, there exists an > 0 for which the lemma holds. Lemma 4. For any n1 , n2 ≥ 0, there exist parameter settings ω > 0, and α > 1 1 2 such that α1ω−1 < αω = 1 and 2 −1 E [Π∗ (n1 , n2 , ω, α)] < n1 + for any n1 (n1 + 1) n2 (n2 + 1) + + , 2 2 > 0. Proof. Consider the following policy Π: first process one job of class J2 , observing realization y, and schedule all remaining jobs according to SEPT.
Tn (n may be ∞), the action of an algorithm is determined by a sequence w1 , w2 , . . , wn , where wi is standby time after ith request is leaving. In other words, the problem is how to determine wi from t1 , t2 , . . , ti . For each i = 2, . . , n, let ui = ti − ti−1 be an idle period. OPT’s cost for n−1 this redefined problem is OPT(σ) = a + i=1 min{ti+1 − ti , a}. We denote ALG’s cost for input σ by ALG(σ) and the competitive ratio of ALG for σ by RALG (σ) = ALG(σ)/OPT(σ). Let Σ be the set of whole inputs σ.
From a simple observation we see that x1 gives a lower bound of RDRA : Observation 1. RDRA ≥ 1 + a/x1 . Proof. Let m be an integer. For an input σ = x1 , 2x1 , . . , mx1 , OPT’s total cost is a + (m − 1)x1 and DRA’s total cost is m(a + x1 ). Thus the competitive ratio of them is the following: RDRA ≥ RDRA (σ) = m(a + x1 ) a + (m − 1)x1 (m→∞) → 1+ a . x1 ✷ From this observation, it follows that x1 cannot be much smaller than a, otherwise RDRA becomes very large. In other words, if the difference between a and x1 is small, the effect to RDRA is not so large.