Abstract. In [1], basic speed-up techniques for Dijkstra's algorithm have been combined. The key observation in their work was that it is most promising to combine hierarchical and goal-directed speed-up techniques. However, since its publication, impressive progress has been made in the field of speed-up techniques for Dijkstra's algorithm and huge data sets have been made available. Hence, we revisit the systematic combination of speed-up techniques in this work, which leads to the fastest known algorithms for various scenarios. Even for road networks, which have been worked on heavily during the last years, we are able to present an improvement in performance. Moreover, we gain interesting insights into the behavior of speed-up techniques when combining them.

During the last years, impressive speed-up techniques for Dijkstra's algorithm have been developed. Unfortunately, the most advanced techniques use bidirectional search which makes it hard to use them in scenarios where a backward search is prohibited. Even worse, such scenarios are widely spread, e.g., timetable-information systems or timedependent networks.In this work, we present a unidirectional speed-up technique which competes with bidirectional approaches. Moreover, we show how to exploit the advantage of unidirectional routing for fast exact queries in timetable information systems and for fast approximative queries in time-dependent scenarios. By running experiments on several inputs other than road networks, we show that our approach is very robust to the input.Related Work. To our best knowledge, three approaches exist that iteratively contract and prune the graph during preprocessing. This idea was introduced in [27]. First, the graph is contracted and afterwards partial trees are built in order to determine highway edges. Non-highway edges are removed from the graph. The contraction was significantly enhanced in [28] reducing preprocessing and query times drastically. The RE algorithm, introduced in [14,15], also uses the contraction from [28] but pruning is based on reach values

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Abstract. A dynamic shortest-path algorithm is called a batch algorithm if it is able to handle graph changes that consist of multiple edge updates at a time. In this paper we focus on fully-dynamic batch algorithms for singlesource shortest paths in directed graphs with positive edge weights. We give an extensive experimental study of the existing algorithms for the single-edge and the batch case, including a broad set of test instances. We further present tuned variants of the already existing SWSF-FP-algorithm being up to 15 times faster than SWSF-FP. A surprising outcome of the paper is the astonishing level of data dependency of the algorithms.

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