We give a (1 − 1/e)-approximation algorithm for the Max-Profit Generalized Assignment Problem (Max-GAP) with fixed profits when the profit (but not necessarily the size) of every item is independent from the bin it is assigned to. The previously best known approximation ratio for this problem was 1/2. Key-words. Generalized assignment, Approximation algorithm.

Given a set of m identical bins of size 1, the online input consists of a (potentially, infinite) stream of items in (0, 1]. Each item is to be assigned to a bin upon arrival. The goal is to cover all bins, that is, to reach a situation where a total size of items of at least 1 is assigned to each bin. The cost of an algorithm is the sum of all used items at the moment when the goal is first fu...

We study the problem of abstracting a table of data about individuals so that no selection query can identify fewer than k individuals. As is common in existing work on this k-anonymization problem, the means we investigate to perform this anonymization is to generalize values of quasi-identifying attributes into equivalence classes. Since such data tables are intended for use in data mining, w...

We present the Generalized Bin Packing Problem (GBPP), a new packing problem where, given a set of items characterized by volume and profit and a set of bins with given volumes and costs, one aims to select the subsets of profitable items and appropriate bins to optimize an objective function which combines the cost of using the bins and the profit yielded by loading the selected items. The GBP...

The design of nature reserves is becoming, more and more, a crucial task for ensuring the conservation endangered wildlife. In order to guarantee preservation species general ecological functioning, designed must typically verify series spatial requirements. Among required characteristics, practitioners researchers have pointed out two aspects: (i) connectivity, so as avoid fragmentation, (ii) ...

We consider a variant of the generalized assignment problem (GAP) where the amount of space used in each bin is restricted to be either zero (if the bin is not opened) or above a given lower bound (aminimum quantity). We provide several complexity results for different versions of the problem and give polynomial time exact algorithms and approximation algorithms for restricted cases. For the mo...

We consider three variants of the open-end bin packing problem. Such variants of bin packing allow the total size of items packed into a bin to exceed the capacity of a bin, provided that a removal of the last item assigned to a bin would bring the contents of the bin below the capacity. In the first variant, this last item is the minimum sized item in the bin, that is, each bin must satisfy th...

Several combinatorial optimization problems can be formulated as large size SetCovering Problems. In this work, we use the Set-Covering formulation to obtain a general heuristic algorithm for this type of problems, and describe our implementation of the algorithm for solving two variants of the well-known (One-Dimensional) Bin Packing Problem: the Two-Constraint Bin Packing Problem and the basi...