By Kook Jin Ahn, Sudipto Guha, Andrew McGregor (auth.), Prasad Raghavendra, Sofya Raskhodnikova, Klaus Jansen, José D. P. Rolim (eds.)
This publication constitutes the court cases of the sixteenth overseas Workshop on Approximation Algorithms for Combinatorial Optimization difficulties, APPROX 2013, and the seventeenth foreign Workshop on Randomization and Computation, RANDOM 2013, held in August 2013 within the united states. the complete of forty eight conscientiously reviewed and chosen papers awarded during this quantity include 23 APPROX papers chosen out of forty six submissions, and 25 RANDOM papers chosen out of fifty two submissions. APPROX 2013 specializes in algorithmic and complexity theoretic concerns correct to the advance of effective approximate ideas to computationally tough difficulties, whereas RANDOM 2013 specializes in functions of randomness to computational and combinatorial problems.
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Additional info for Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 16th International Workshop, APPROX 2013, and 17th International Workshop, RANDOM 2013, Berkeley, CA, USA, August 21-23, 2013. Proceedings
Wenner Table 1. Known results and our improvements Problem MAS Max BTW Max NBTW m-OCSP Approx. factor 1/2 + Ω(1/log n) 1/3 2/3 1/m!  UG-inapprox. 1/2 + ε  1/3 + ε  2/3 + ε  1/m! + ε  NP-inapprox. 65/66 + ε  47/48 + ε  - This work 14/15 + ε 1/2 + ε 2/3 + ε 1/ m/2 ! + ε 65/66 + ε . For Max BTW, we show a factor (1/2 + ε)-inapproximability improving from 47/48 + ε . Theorem 1. For every ε > 0, it is NP-hard to distinguish between MAS instances with value at least 15/18 − ε from instances with value at most 14/18 + ε.
22 S. Alaei, M. Hajiaghayi, and V. Liaghat (I) The leftmost γ-fraction of the sand is selected by first identifying the smallest threshold θi ∈ R+ such that FWi (θi ) ≥ γ and then selecting all the sand in the interval [0, θi ) and selecting a fraction of the sand at position θi itself such that the total amount of selected sand is equal to γ. Formally, if Gi (w) denotes the total amount of sand selected from [0, w], the selection of sand is such that Gi (w) = min(FWi (w), γ), for every w ∈ R+ .
The wand has k units of mana . , the magician learns FXi upon seeing box i). , cannot make any changes once the process has started). The magician’s problem introduced in  is a special case of this model where Xi = 1 for every i. The magician could fail to open a box either because (a) he might choose to skip the box, or (b) his wand might run out of mana before getting to the box. Note that once the magician fixes his strategy, the best strategy for the villain is to put the prize in the box which, based on the magician’s strategy, has the lowest ex ante probability of being opened.