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...test path of length d(s, t) between a given source s and target t. Unfortunately, the algorithm is far too slow to be used on huge datasets. Thus, several speed-up techniques have been developed (see =-=[14]-=- for an overview) yielding faster query times for typical instances, e.g., road or railway networks. In [26, 25], basic speed-up techniques have been combined systematically. One key observation of th...

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...tself, which allows us to maintain several metrics in memory simultaneously. 1 Introduction The past decade has seen a great deal of research on finding point-to-point shortest paths on road networks =-=[7]-=-. Although Dijkstra’s algorithm [10] runs in almost linear time with very little overhead, it still takes a few seconds on continentalsized graphs. Practical algorithms use a two-stage approach: prepr...

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...s previous techniques with respect to query time using comparable or lower preprocessing time. 1 Introduction In recent years, there has been considerable work on routing in static road networks (see =-=[8]-=- for an overview). It is now possible to compute shortest path distances in road networks several orders of magnitude faster than with Dijkstra’s algorithm. However, this does not mean that routing is...

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...rated” cells is a fundamental problem in computer science with applications in areas such as VLSI design [5], computer vision [23], image analysis [38], distributed computing [24], and route planning =-=[10]-=-. Most variants of this problem are known to be NPhard [13] and focus on minimizing the cut size, i.e., the number of edges linking vertices from different cells. Given its importance, there is a rich...

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...roblem with many applications. Dijkstra’s algorithm [14] solves this problem in nearlinear time [18], but for some graph classes sublinear-time queries are possible if preprocessing is allowed (e.g., =-=[12, 16]-=-). In particular, Gavoille et al.’s distance labeling algorithm [16] precomputes a label for each vertex such that the distance between any two vertices s and t can be computed given only their labels...

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...rithm [31, 32]. Motivated by web-based map services and autonomous navigation systems, the problem of finding shortest paths in road networks has received a great deal of attention recently; see e.g. =-=[14, 15]-=- for overviews. However, most research focused on accelerating point-to-point queries, in which both a source s and a target t are known. Up to now, Dijkstra’s algorithm was still the fastest known so...

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... [12] finds a shortest path between a given source s and target t. Unfortunately, the algorithm is far too slow to be used on huge datasets. Thus, several speed-up techniques have been developed (see =-=[9]-=- for an overview) yielding faster query times for typical instances, e.g., road or railway networks. A major drawback of most existing speed-up techniques is that their correctness depends on the fact...