Preprocessing Speed-Up Techniques Is Hard

Bauer, Reinhard; Columbus, Tobias; Katz, Bastian; Krug, Markus; Wagner, Dorothea

doi:10.1007/978-3-642-13073-1_32

Cited by 32 publications

(14 citation statements)

References 20 publications

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“…An obvious question is whether one could efficiently determine the best such choices for a particular input so as to minimize the query search space (a natural proxy for query times). Bauer et al [36] have determined that finding optimal landmarks for ALT is NP-hard. The same holds for Arc Flags (with respect to the partition), SHARC (with respect to the shortcuts), Multilevel Overlay Graphs (with respect to the separator), Contraction Hierarchies (with respect to the vertex order), and Hub Labels (with respect to the hubs) [252].…”

Section: Theoretical Resultsmentioning

confidence: 99%

“…The same holds for Arc Flags (with respect to the partition), SHARC (with respect to the shortcuts), Multilevel Overlay Graphs (with respect to the separator), Contraction Hierarchies (with respect to the vertex order), and Hub Labels (with respect to the hubs) [252]. In fact, minimizing the number of shortcuts for CH is APX-hard [36,194]. For SHARC, however, a greedy factor-k approximation algorithm exists [38].…”

Section: Theoretical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Route Planning in Transportation Networks

Bast

Delling

Goldberg

et al. 2016

Lecture Notes in Computer Science

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463

388

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We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs. *

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Section: Theoretical Resultsmentioning

confidence: 99%

Section: Theoretical Resultsmentioning

confidence: 99%

Route Planning in Transportation Networks

Bast

Delling

Goldberg

et al. 2016

Lecture Notes in Computer Science

Self Cite

463

388

View full text Add to dashboard Cite

show abstract

“…As roads only change slowly over time, the preprocessing phase can be slow as it does not have to be rerun very frequently. Computing the auxiliary data usually involves optimizing some criteria, which most of the time is NP-hard [4]. In this application, it is therefore important to produce solutions of good quality but it is not as important to do this fast.…”

Section: Applications and Related Workmentioning

confidence: 99%

Graph Bisection with Pareto Optimization

Hamann

Strasser

2018

ACM J. Exp. Algorithmics

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We introduce FlowCutter, a novel algorithm to compute a set of edge cuts or node separators that optimize cut size and balance in the Pareto-sense. Our core algorithm heuristically solves the balanced connected st-edge-cut problem, where two given nodes s and t must be separated by removing edges to obtain two connected parts. Using the core algorithm as subroutine, we build variants that compute node separators which are independent of s and t. From the computed Pareto-set, we can identify cuts with a particularly good tradeoff between cut size and balance that can be used to compute contraction and minimum fill-in orders, which can be used in Customizable Contraction Hierarchies (CCH), a speed-up technique for shortest path computations. Our core algorithm runs in O(c|E|) time where E is the set of edges and c is the size of the largest outputted cut. This makes it wellsuited for separating large graphs with small cuts, such as road graphs, which is the primary application motivating our research. For road graphs, we present an extensive experimental study demonstrating that FlowCutter outperforms the current state-of-the-art both in terms of cut sizes and CCH performance. By evaluating FlowCutter on a standard graph partitioning benchmark, we further show that FlowCutter also finds small, balanced cuts on non-road graphs. Another application is the computation of small tree-decompositions.To evaluate the quality of our algorithm in this context, we entered the PACE 2016 challenge [13] and won the first place in the corresponding sequential competition track. We can therefore conlude that our FlowCutter algorithm finds small, balanced cuts on a wide variety of graphs.

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“…Since MinAvgCasePartition is N P-hard in general [1], we investigate restricted input instances. Along the lines of Section 3, we examine paths, cycles, stars, and trees.…”

Section: Minimizing the Average Search-space Sizementioning

confidence: 99%

“…The choice of the partition C has a large impact on query times in the on-line phase. Bauer et al prove that it is is N P-hard to compute a partition that minimizes the average search-space size (sss) of on-line queries [1]. However, the graph used in their reduction has a number of properties unlikely to be shared by realistic instances.…”

Section: Introductionmentioning

confidence: 99%

On the Complexity of Partitioning Graphs for Arc-Flags

Bauer¹,

Baum²,

Rutter³

et al. 2013

JGAA

Self Cite

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Precomputation of auxiliary data in an additional off-line step is a common approach towards improving the performance of shortest-path queries in large-scale networks. One such technique is the arc-flags algorithm, where the preprocessing involves computing a partition of the input graph. The quality of this partition significantly affects the speed-up observed in the query phase. It is evaluated by considering the search-space size of subsequent shortest-path queries, in particular its maximum or its average over all queries. In this paper, we substantially strengthen existing hardness results of Bauer et al. and show that optimally filling this degree of freedom is N P-hard for trees with unit-length edges, even if we bound the height or the degree. On the other hand, we show that optimal partitions for paths can be computed efficiently and give approximation algorithms for cycles and trees. ACM Subject Classification G.2.2 Graph Theory

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Preprocessing Speed-Up Techniques Is Hard

Cited by 32 publications

References 20 publications

Route Planning in Transportation Networks

Route Planning in Transportation Networks

Graph Bisection with Pareto Optimization

On the Complexity of Partitioning Graphs for Arc-Flags

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