138 research outputs found

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    Using Incremental Many-to-One Queries to Build a Fast and Tight Heuristic for A* in Road Networks

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    We study exact, efficient, and practical algorithms for route planning applications in large road networks. On the one hand, such algorithms should be able to answer shortest path queries within milliseconds. On the other hand, routing applications often require integrating the current traffic situation, planning ahead with predictions for future traffic, respecting forbidden turns, and many other features depending on the specific application. Therefore, such algorithms must be flexible and able to support a variety of problem variants. In this work, we revisit the A* algorithm to build a simple, extensible, and unified algorithmic framework applicable to many route planning problems. A* has been previously used for routing in road networks. However, its performance was not competitive because no sufficiently fast and tight distance estimation function was available. We present a novel, efficient, and accurate A* heuristic using Contraction Hierarchies, another popular speedup technique. The core of our heuristic is a new Contraction Hierarchies query algorithm called Lazy RPHAST, which can efficiently compute shortest distances from many incrementally provided sources toward a common target. Additionally, we describe A* optimizations to accelerate the processing of low-degree vertices, which are typical in road networks, and present a new pruning criterion for symmetrical bidirectional A*. An extensive experimental study confirms the practicality of our approach for many applications

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Enabling Scalability: Graph Hierarchies and Fault Tolerance

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    In this dissertation, we explore approaches to two techniques for building scalable algorithms. First, we look at different graph problems. We show how to exploit the input graph\u27s inherent hierarchy for scalable graph algorithms. The second technique takes a step back from concrete algorithmic problems. Here, we consider the case of node failures in large distributed systems and present techniques to quickly recover from these. In the first part of the dissertation, we investigate how hierarchies in graphs can be used to scale algorithms to large inputs. We develop algorithms for three graph problems based on two approaches to build hierarchies. The first approach reduces instance sizes for NP-hard problems by applying so-called reduction rules. These rules can be applied in polynomial time. They either find parts of the input that can be solved in polynomial time, or they identify structures that can be contracted (reduced) into smaller structures without loss of information for the specific problem. After solving the reduced instance using an exponential-time algorithm, these previously contracted structures can be uncontracted to obtain an exact solution for the original input. In addition to a simple preprocessing procedure, reduction rules can also be used in branch-and-reduce algorithms where they are successively applied after each branching step to build a hierarchy of problem kernels of increasing computational hardness. We develop reduction-based algorithms for the classical NP-hard problems Maximum Independent Set and Maximum Cut. The second approach is used for route planning in road networks where we build a hierarchy of road segments based on their importance for long distance shortest paths. By only considering important road segments when we are far away from the source and destination, we can substantially speed up shortest path queries. In the second part of this dissertation, we take a step back from concrete graph problems and look at more general problems in high performance computing (HPC). Here, due to the ever increasing size and complexity of HPC clusters, we expect hardware and software failures to become more common in massively parallel computations. We present two techniques for applications to recover from failures and resume computation. Both techniques are based on in-memory storage of redundant information and a data distribution that enables fast recovery. The first technique can be used for general purpose distributed processing frameworks: We identify data that is redundantly available on multiple machines and only introduce additional work for the remaining data that is only available on one machine. The second technique is a checkpointing library engineered for fast recovery using a data distribution method that achieves balanced communication loads. Both our techniques have in common that they work in settings where computation after a failure is continued with less machines than before. This is in contrast to many previous approaches that---in particular for checkpointing---focus on systems that keep spare resources available to replace failed machines. Overall, we present different techniques that enable scalable algorithms. While some of these techniques are specific to graph problems, we also present tools for fault tolerant algorithms and applications in a distributed setting. To show that those can be helpful in many different domains, we evaluate them for graph problems and other applications like phylogenetic tree inference

    Scalable Graph Algorithms using Practically Efficient Data Reductions

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    Engineering Algorithms for Dynamic and Time-Dependent Route Planning

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    Efficiently computing shortest paths is an essential building block of many mobility applications, most prominently route planning/navigation devices and applications. In this thesis, we apply the algorithm engineering methodology to design algorithms for route planning in dynamic (for example, considering real-time traffic) and time-dependent (for example, considering traffic predictions) problem settings. We build on and extend the popular Contraction Hierarchies (CH) speedup technique. With a few minutes of preprocessing, CH can optimally answer shortest path queries on continental-sized road networks with tens of millions of vertices and edges in less than a millisecond, i.e. around four orders of magnitude faster than Dijkstra’s algorithm. CH already has been extended to dynamic and time-dependent problem settings. However, these adaptations suffer from limitations. For example, the time-dependent variant of CH exhibits prohibitive memory consumption on large road networks with detailed traffic predictions. This thesis contains the following key contributions: First, we introduce CH-Potentials, an A*-based routing framework. CH-Potentials computes optimal distance estimates for A* using CH with a lower bound weight function derived at preprocessing time. The framework can be applied to any routing problem where appropriate lower bounds can be obtained. The achieved speedups range between one and three orders of magnitude over Dijkstra’s algorithm, depending on how tight the lower bounds are. Second, we propose several improvements to Customizable Contraction Hierarchies (CCH), the CH adaptation for dynamic route planning. Our improvements yield speedups of up to an order of magnitude. Further, we augment CCH to efficiently support essential extensions such as turn costs, alternative route computation and point-of-interest queries. Third, we present the first space-efficient, fast and exact speedup technique for time-dependent routing. Compared to the previous time-dependent variant of CH, our technique requires up to 40 times less memory, needs at most a third of the preprocessing time, and achieves only marginally slower query running times. Fourth, we generalize A* and introduce time-dependent A* potentials. This allows us to design the first approach for routing with combined live and predicted traffic, which achieves interactive running times for exact queries while allowing live traffic updates in a fraction of a minute. Fifth, we study extended problem models for routing with imperfect data and routing for truck drivers and present efficient algorithms for these variants. Sixth and finally, we present various complexity results for non-FIFO time-dependent routing and the extended problem models

    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum
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