Algorithms for communication optimization

In this thesis, we present algorithms for communication problems. We consider two different combinatorial optimization problems to optimize communication in two different scenarios, namely the Buffer-Allocation Problem and the k-Observer Problem. The Buffer-Allocation Problem has emerged as a new challenge from recent progress in the design of multi-core platforms. With the availability of advanced multi-core platforms and emerging interface technologies, it is no longer possible, due to the huge design space, to compute an optimal allocation of logical data buffers to physical memories manually. Besides the allocation of the logical data buffers to memories, also an optimal routing for data flows through the multi-core platform must be computed. A data flow is an abstract representation of an application that emerges from a processing element and accesses a logical data buffer. We formalize these requirements by the Buffer-Allocation Problem. We also show that this problem is NP-hard and furthermore that this problem is APX-hard, this implies that it cannot be approximated arbitrarily close to the value of the optimal solution, unless P = NP. Despite of this, we introduce a (Mixed) Integer-Linear Program formulation to compute an optimal solution that is inspired by an extension of a Multi-Commodity Flow Problem. We also present a heuristic that computes a solution in polynomial time. Although, modern Linear-Program solver can compute optimal solutions for non-worst-case instances for Integer-Linear Programs with an acceptable running time, we evaluate the running time of a state-of-the-art solver and of our heuristic for representative data from the Long-Term-Evolution standard (LTE). Besides the running time, we also compare the quality of the computed solutions to show the applicability of our heuristic. We show that our heuristic outperforms the Linear-Program solver in this real-life instances. In the second part of this thesis, we consider the k-Observer Problem. Given a graph G = (V,E) as an abstract representation of a wireless sensor network, there has to be found a minimal set of nodes C ⊆ V such that the nodes observe all paths of a fixed length k in G. As a generalization of the well-known vertex cover problem, this problem is NP-hard. The nodes in C can, e.g., be used to observe traffic of a given network or provide data integrity in a sensor network. First, we focus on d-regular networks, where every node as a bounded constant degree of d ∈ N. We show, for the case k = 2, a (1 + 1 2d−2)-approximation for bipartite regular graphs. For general d-regular graphs, we present a (2 − o(1))-approximation algorithm, again for the case k = 2. For larger