Motivated by a real world application, we study the multiple knapsack problem with assignment restrictions (MKAR): We are given a set of items N = f1; : : : ; ng and a set of knapsacks M = f1; : : : ;mg. Each item j 2 N has a positive real weight wj and each knapsack i 2 M has a positive real capacity ci associated with it. In addition, for each item j 2 N a set Aj M of knapsacks that can hold ...

In this paper, we present a new methodology to adapt any kind of lattice reduction algorithms to deal with the modular knapsack problem. In general, the modular knapsack problem can be solved using a lattice reduction algorithm, when its density is low. The complexity of lattice reduction algorithms to solve those problems is upper-bounded in the function of the lattice dimension and the maximu...

We consider variants of the classic bin packing and multiple knapsack problems, in which sets of items of di erent classes (colours) need to be placed in bins; the items may have di<erent sizes and values. Each bin has a limited capacity, and a bound on the number of distinct classes of items it can accommodate. In the class-constrained multiple knapsack (CCMK) problem, our goal is to maximize ...

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The multiple knapsack problem (MKP) is a classical combinatorial optimization problem. A recent algorithm for some classes of the MKP is bincompletion, a bin-oriented, branch-and-bound algorithm. We investigate mechanisms for detecting and breaking symmetry in the bin-completion search space. We propose path-symmetry and pathdominance, two new symmetry relations which are more powerful generali...

When investing in cyber security resources, information security managers have to follow effective decision-making strategies. We refer to this as the cyber security investment challenge. In this paper, we consider three possible decision-support methodologies for security managers to tackle this challenge. We consider methods based on game theory, combinatorial optimisation and a hybrid of the...

Real-time multimedia applications such as video and audio streaming, video conferencing and online collaboration are becoming increasingly popular. In order to guarantee effective support of many of these applications, the Internet must provide absolute Quality of Service (QoS) guarantees for such parameters as network bandwidth and end-to-end delay by incorporating session admission control, s...