Connect the dot: Computing feed-links for network extension

Aronov, Boris; Buchin, Kevin; Buchin, Maike; Jansen, Bart M. P.; Jong, Tom de; Kreveld, Marc van; Löffler, Maarten; Luo, Jun; Silveira, Rodrigo I.; Speckmann, Bettina

doi:10.5311/josis.2011.3.47

Cited by 5 publications

(5 citation statements)

References 22 publications

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“…Luo and Wulff-Nilsen [36] improves the space requirement to linear. Aronov et al [3] provide a nearlylinear time algorithm in the special case where the graph is a simple polygon and an interior point. A variant of Problem 3 is to add k edges to a graph to minimise the diameter instead of the dilation.…”

Section: Related Workmentioning

confidence: 99%

“…Narasimham and Smid [38] stated Problem 3 as one of twelve open problems in the final chapter of their reference textbook. For over a decade, the only positive results for Problem 3 were for the special case where k = 1 [3,21,36,44]. In 2021, Gudmundsson and Wong [30] showed the first positive result for k ≥ 2, by providing an O(k)-approximation algorithm that runs in O(n 3 log n) time.…”

Section: Introductionmentioning

confidence: 99%

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Compact Flow Diagrams for State Sequences

Buchin

Gudmundsson

et al. 2016

Experimental Algorithms

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Abstract. We introduce the concept of compactly representing a large number of state sequences, e.g., sequences of activities, as a flow diagram. We argue that the flow diagram representation gives an intuitive summary that allows the user to detect patterns among large sets of state sequences. Simplified, our aim is to generate a small flow diagram that models the flow of states of all the state sequences given as input. For a small number of state sequences we present efficient algorithms to compute a minimal flow diagram. For a large number of state sequences we show that it is unlikely that efficient algorithms exist. More specifically, the problem is W [1]-hard if the number of state sequences is taken as a parameter. We thus introduce several heuristics for this problem. We argue about the usefulness of the flow diagram by applying the algorithms to two problems in sports analysis. We evaluate the performance of our algorithms on a football data set and generated data.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Compact Flow Diagrams for State Sequences

Buchin

Gudmundsson

et al. 2016

Experimental Algorithms

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“…In the parallel version, querying the distance data structure can be done with √ n processors, each performing O( τ /ε) amount of work, then combining the values to find the minimum in O(log n) time. Thus, T P = O(( t /ε) 4 • ( τ /ε + log n)). The time for the optimisation version is now O(N P T P + T P T S log N P ).…”

Section: Map-matching Segment Queriesmentioning

confidence: 99%

“…A geometric graph is a t-spanner if for any two vertices, the length of the shortest path between them in the graph is at most t times larger than the Euclidean distance between them. Road networks, in particular in urban areas, are typically good spanners [4,19]. For the example of Figure 1, it is clear that the road network is a t-spanner and λ-low density for low t and λ.…”

Section: Introductionmentioning

confidence: 98%

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Computing the Fréchet Distance with a Retractable Leash

Buchin

Leusden

et al. 2013

Lecture Notes in Computer Science

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract All known algorithms for the Fréchet distance between curves proceed in two steps: first, they construct an efficient oracle for the decision version; second, they use this oracle to find the optimum from a finite set of critical values. We present a novel approach that avoids the detour through the decision version. This gives the first quadratic time algorithm for the Fréchet distance between polygonal curves in R d under polyhedral distance functions (e.g., L 1 and L ∞ ). We also get a (1 + ε)-approximation of the Fréchet distance under the Euclidean metric, in quadratic time for any fixed ε > 0. For the exact Euclidean case, our framework currently yields an algorithm with running time O(n 2 log 2 n). However, we conjecture that it may eventually lead to a faster exact algorithm. Permanent repository link Editor in Charge: Kenneth ClarksonA preliminary version appeared as K.

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Shortcut sets for the locus of plane Euclidean networks

Cáceres

Garijo

González

et al. 2018

Applied Mathematics and Computation

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We study the problem of augmenting the locus N ℓ of a plane Euclidean network N by inserting iteratively a finite set of segments, called shortcut set, while reducing the diameter of the locus of the resulting network. There are two main differences with the classical augmentation problems: the endpoints of the segments are allowed to be points of N ℓ as well as points of the previously inserted segments (instead of only vertices of N ), and the notion of diameter is adapted to the fact that we deal with N ℓ instead of N . This increases enormously the hardness of the problem but also its possible practical applications to network design. Among other results, we characterize the existence of shortcut sets, compute them in polynomial time, and analyze the role of the convex hull of N ℓ when inserting a shortcut set. Our main results prove that, while the problem of minimizing the size of a shortcut set is NP-hard, one can always determine in polynomial time whether inserting only one segment suffices to reduce the diameter.

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Connect the dot: Computing feed-links for network extension

Cited by 5 publications

References 22 publications

Compact Flow Diagrams for State Sequences

Compact Flow Diagrams for State Sequences

Computing the Fréchet Distance with a Retractable Leash

Shortcut sets for the locus of plane Euclidean networks

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