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By Dorothea Baumeister, Gábor Erdélyi, Jörg Rothe (auth.), Ronen I. Brafman, Fred S. Roberts, Alexis Tsoukià s (eds.)

This publication constitutes the refereed complaints of the second one overseas convention on Algorithmic selection concept, ADT 2011, held in Piscataway, NJ, united states, in October 2011. The 24 revised complete papers provided have been rigorously reviewed and chosen from 50 submissions.

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Extra resources for Algorithmic Decision Theory: Second International Conference, ADT 2011, Piscataway, NJ, USA, October 26-28, 2011. Proceedings

Sample text

Each cell is computed by using the recursion W [p + pi , i] = min{W [p + pi , i − 1], W [p, i − 1] + wi }. For instance, the dark gray cell is computed from the light gray cells. p (0, 0, 0) (0, 0, 1) (0, 0, 2) (0, 1, 1) (0, 1, 2) (0, 2, 2) (1, 1, 1) (1, 1, 2) (1, 2, 2) (2, 2, 2) i 1 2 3 4 0 0 0 0 7 7 7 min(7, 0 + 1) = 1 7 7 7 7 7 min(7, 0 + 2) = 2 2 2 7 7 7 3 7 7 min(7, 2 + 4) = 6 6 min(7, 0 + 5) = 5 5 5 5 7 7 7 min(7, 5 + 1) = 6 7 7 7 7 7 7 7 7 34 C. Delort, O. Spanjaard, and P. Weng In order to determine the complexity of this procedure, we assume that the number C of preference classes is fixed.

A solution S is characterized by a binary n-vector x, where xi = 1 iff i ∈ S. A solution is feasible if binary vector n n x satisfies the constraints i=1 wi xi ≤ B and i=1 xi = K. e. one feasible solution by non-dominated cumulative vector), which can be formally stated as follows: n pic xi maximize c ∈ {1, . . , C} i=1 n subject to wi xi ≤ B i=1 n i=1 i xi = K x ∈ {0, 1} i ∈ {1, . . e. pi1 ≤ . . ≤ piC ), the image of all feasible solutions is a subset of 0, K C ↑ , which denotes the set of nondecreasing vectors in 0, K C = {0, .

This observation justifies that we focus on feasible solutions of this type. Now, the branching scheme can be simply explained. Let P (k, c, p, b) denote the subproblem where one wants to select k items whose total weight is less than budget b, where the remaining items are classified in classes (c, . . , C) and the profit vector of the already selected items is p ∈ 0, K C ↑ . The initial problem is then denoted by P (K, 1, (0, . . , 0), B). A node in the enumeration tree represents a problem P (k, c, p, b) where p = (p1 , .

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