Recent advances in algorithms for the multidimensional multiple choice knapsack problems have enabled us to solve rather large problem instances. However, these algorithms are evaluated with very limited benchmark instances. In this study, we propose new methods to systematically generate comprehensive benchmark instances. Some instances with special correlation properties between parameters are found to be several orders of magnitude harder than those currently used for benchmarking the algorithms. Experiments on an existing exact algorithm and two generic solvers show that instances whose weights are uncorrelated with the profits are easier compared with weakly or strongly correlated cases. Instances with classes containing similar set of profits for items and with weights strongly correlated to the profits are the hardest among all instance groups investigated. These hard instances deserve further study and understanding their properties may shed light to better algorithms.

Cost efficiency is a key aspect in deploying distributed service in networks within decentralized service delivery architectures. In this paper, we address this aspect from an optimization and algorithmic standpoint. The research deals with the placement of service components to network sites, where the performance metric is the cost for acquiring components between the sites. The resulting optimization problem, which we refer to as the k-Component Multisite Placement Problem, is applicable to service distribution in a wide range of communication networking scenarios. We provide a theoretical analysis of the problem's computational complexity, and develop an integer programming model for providing reference results for performance benchmarking. On the algorithmic side, we present four approaches: an algorithm with approximation guarantee and three heuristics algorithms. The first heuristic is derived from graph theory on domatic partition. The second heuristic, built on intuition, admits distributed computation. The third heuristic emphasizes on fairness in cost distribution among the sites. We report simulation results for sets of networks where cost is represented by round-trip time (RTT) originating from real measurements. For small networks, the integer model is used to study algorithm performance in terms of optimality. Large networks are used to compare the al- * Corresponding author1 The work of this author is supported by CENIIT, Linköping University, Sweden 2 The work of this author is supported by Vipeer project and Agence Nationale de la Recherche, France February 11, 2011 gorithms relatively to each other. Among the algorithms, the heuristic based on intuition has close-to-optimal performance, and the fairness heuristic achieves a good balance between single-site cost and the overall one. In addition, the experiments demonstrate the significance of optimization for cost reduction in comparison to a the random allocation strategy. Preprint submitted to Elsevier

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Given a graph and a root, the Maximum Bounded Rooted-Tree Packing (MBRTP) problem aims at finding K rooted-trees that span the largest subset of vertices, when each vertex has a limited outdegree. This problem is motivated by peerto-peer streaming overlays in under-provisioned systems. We prove that the MBRTP problem is NP-complete. We present two polynomial-time algorithms that computes an optimal solution on complete graphs and trees respectively.