Approximate algorithms for some generalized knapsack problems

Algorithms for Some Generalized Network Problems

Approximation Algorithms for Constrained Knapsack Problems

We study constrained versions of the knapsack problem in which dependencies between items are given by a graph. In one version, an item can be selected only if one of its neighbours is also selected. In the other version, an item can be selected only when all its neighbours are also selected. These problems generalize and unify several problems including the prize collecting and budgeted maximu...

One-Pass Algorithms for Some Generalized Network Problems

Exact and approximate algorithms for discounted {0-1} knapsack problem

The D iscounted {0-1} K napsack P roblem (D{0-1}KP) is an extension of the classical 0-1 knapsack problem (0-1 KP) that consists of selecting a set of item groups where each group includes three items and at most one of the three items can be selected. The D{0-1}KP is more challenging than the 0-1 KP because four choices of items in an item group diversify the selection of the items. In this pa...

Some existence results for generalized vector quasi-equilibrium problems

‎In this paper‎, ‎we introduce and study a class of generalized vector quasi-equilibrium problem‎, ‎which includes many vector equilibrium problems‎, ‎equilibrium problems‎, ‎vector variational inequalities and variational inequalities as special cases‎. ‎Using one person game theorems‎, ‎the concept of escaping sequences and without convexity assumptions‎, ‎we prove some existence results for ...