Efficient Algorithms for Distributed Detection of Holes and Boundaries in Wireless Networks

We propose two novel algorithms for distributed and location-free boundary recognition in wireless sensor networks. Both approaches enable a node to decide autonomously whether it is a boundary node, based solely on connectivity information of a small neighborhood. This makes our algorithms highly applicable for dynamic networks where nodes can move or become inoperative. We compare our algorithms qualitatively and quantitatively with several previous approaches. In extensive simulations, we consider various models and scenarios. Although our algorithms use less information than most other approaches, they produce significantly better results. They are very robust against variations in node degree and do not rely on simplified assumptions of the communication model. Moreover, they are much easier to implement on real sensor nodes than most existing approaches.Comment: extended version of accepted submission to SEA 201

Doing More for Less -- Cache-Aware Parallel Contraction Hierarchies Preprocessing

Contraction Hierarchies is a successful speedup-technique to Dijkstra's seminal shortest path algorithm that has a convenient trade-off between preprocessing and query times. We investigate a shared-memory parallel implementation that uses $O(n+m)$ space for storing the graph and O(1) space for each core during preprocessing. The presented data structures and algorithms consequently exploits cache locality and thus exhibit competitive preprocessing times. The presented implementation is especially suitable for preprocessing graphs of planet-wide scale in practice. Also, our experiments show that optimal data structures in the PRAM model can be beaten in practice by exploiting memory cache hierarchies

Heuristic Contraction Hierarchies with Approximation Guarantee

We present a new heuristic point-to-point shortest path algorithm based on contraction hierarchies (CH). Given an epsilon > 0, we can prove that the length of the path computed by our algorithm is at most (1 + epsilon) times the length of the optimal (shortest) path. Exact CH is based on node contraction: removing nodes from a network and adding shortcuts to preserve shortest path distances. Our heuristic CH tries to avoid adding shortcuts even when a replacement path is (1 + epsilon) times longer. However, we cannot avoid all such shortcuts, as we need to ensure that errors do not stack. Combinations with goal-directed techniques bring further speed-ups

Lifetime Maximization of Monitoring Sensor Networks

We study the problem of maximizing the lifetime of a sensor network assigned to monitor a given area. Our main result is a linear time dual approximation algorithm that comes arbitrarily close to the optimal solution if we additionally allow the sensing ranges to increase by a small factor. The best previous result is superlinear and has a logarithmic approximation ratio. We also provide the first proof of the NP completeness of this specific problem

An Algorithmic View on Sensor Networks - Surveillance, Localization, and Communication

This thesis focuses on scalability issues of diverse problems on sensor networks and presents efficient solutions. First, we show that it is NP-hard to find optimal activation schedules for monitoring areas and provide an EPTAS algorithm. Second, we present a distributed algorithm for the detection of network boundaries that only requires local connectivity information. Finally, we introduce an FPTAS for computing shortest paths and describe an algorithm for determining alternative routes

Gaussian Mixture Reduction via Clustering

Recursive processing of Gaussian mixture functions inevitably leads to a large number of mixture components. In order to keep the computational complexity at a feasible level, the number of their components has to be reduced periodically. There already exists a variety of algorithms for this purpose, bottom-up and top-down approaches, methods that take the global structure of the mixture into account or that work locally and consider few mixture components at the same time. The mixture reduction algorithm presented in this paper can be categorized as global top-down approach. It takes a clustering algorithm originating from the field of theoretical computer science and adapts it for the problem of Gaussian mixture reduction. The achieved results are on the same scale as the results of the current “state-of-the-art” algorithm PGMR, but, depending on the input size, the whole procedure performs significantly faster

Evolution and Evaluation of the Penalty Method for Alternative Graphs

Computing meaningful alternative routes in a road network is a complex problem -- already giving a clear definition of a best alternative seems to be impossible. Still, multiple methods describe how to compute reasonable alternative routes, each according to their own quality criteria. Among these methods, the penalty method has received much less attention than the via-node or plateaux based approaches. A mayor cause for the lack of interest might be the unavailability of an efficient implementation. In this paper, we take a closer look at the penalty method and extend upon its ideas. We provide the first viable implementation --suitable for interactive use-- using dynamic runtime adjustments to perform up to multiple orders of magnitude faster queries than previous implementations. Using our new implementation, we thoroughly evaluate the penalty method for its flaws and benefits