On the Minimum Eccentricity Shortest Path Problem

Dragan, Feodor F.; Leitert, Arne

doi:10.1007/978-3-319-21840-3_23

Cited by 8 publications

(19 citation statements)

References 14 publications

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“…It may arise in determining a "most accessible" speedy linear route in a network and can find applications in communication networks, transportation planning, water resource management and fluid transportation. It was also shown in [13,14] that a minimum eccentricity shortest path plays a crucial role in obtaining the best to date approximation algorithm for a minimum distortion embedding of a graph into the line. Specifically, every graph G with a shortest path of eccentricity r admits an embedding f of G into the line with distortion at most (8r + 2) ld(G), where ld(G) is the minimum line-distortion of G (see [14] for details).…”

Section: Introductionmentioning

confidence: 99%

“…It was also shown in [13,14] that a minimum eccentricity shortest path plays a crucial role in obtaining the best to date approximation algorithm for a minimum distortion embedding of a graph into the line. Specifically, every graph G with a shortest path of eccentricity r admits an embedding f of G into the line with distortion at most (8r + 2) ld(G), where ld(G) is the minimum line-distortion of G (see [14] for details). Furthermore, if a shortest path of G of eccentricity r is given in advance, then such an embedding f can be found in linear time.…”

Section: Introductionmentioning

confidence: 99%

“…In [14], the Minimum Eccentricity Shortest Path problem was investigated in general graphs. It was shown that its decision version is NP-complete (even for graphs with vertex degree at most 3).…”

Section: Introductionmentioning

confidence: 99%

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Minimum Eccentricity Shortest Paths in Some Structured Graph Classes

Dragan

Leitert

2016

Graph-Theoretic Concepts in Computer Science

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We investigate the Minimum Eccentricity Shortest Path problem in some structured graph classes. It asks for a given graph to find a shortest path with minimum eccentricity. Although it is NP-hard in general graphs, we demonstrate that a minimum eccentricity shortest path can be found in linear time for distancehereditary graphs (generalizing the previous result for trees) and give a generalised approach which allows to solve the problem in polynomial time for other graph classes. This includes chordal graphs, dually chordal graphs, graphs with bounded tree-length, and graphs with bounded hyperbolicity. Additionally, we give a simple algorithm to compute an additive approximation for graphs with bounded tree-length and graphs with bounded hyperbolicity.⋆ Results of this paper were partially presented at WG 2015 [15].

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Minimum Eccentricity Shortest Paths in Some Structured Graph Classes

Dragan

Leitert

2016

Graph-Theoretic Concepts in Computer Science

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“…Subsequently, every vertex v of G at distance at most k from the subpath between v i P min and v i P max is at distance at most 3k of P . One may think, at first glance, that this lemma looks similar to the following: Lemma 2 (from Dragan et al [9]). If G has a shortest path of eccentricity at most k from s to t, then every path Q with s in Q and d(s, t) ≤ max v∈Q d(s, v) has eccentricity at most 3k.…”

Section: Definitions and Notationsmentioning

confidence: 68%

“…In the present paper, we study the latter problem in which the covering path is required to be a shortest path between its end-vertices. It was introduced in [9] as the Minimum Eccentricity Shortest Path Problem, and shown to be linked to the minimum line distortion problem [14].…”

Section: Introductionmentioning

confidence: 99%

Minimum Eccentricity Shortest Path Problem: An Approximation Algorithm and Relation with the k-Laminarity Problem

Birmelé

Montgolfier

Planche

2016

Combinatorial Optimization and Applications

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Abstract. The Minimum Eccentricity Shortest Path (MESP) Problem consists in determining a shortest path (a path whose length is the distance between its extremities) of minimum eccentricity in a graph. It was introduced by Dragan and Leitert [9] who described a linear-time algorithm which is an 8-approximation of the problem. In this paper, we study deeper the double-BFS procedure used in that algorithm and extend it to obtain a linear-time 3-approximation algorithm. We moreover study the link between the MESP problem and the notion of laminarity, introduced by Völkel et al [12], corresponding to its restriction to a diameter (i.e. a shortest path of maximum length), and show tight bounds between MESP and laminarity parameters.

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Minimum Eccentricity Shortest Path Problem with Respect to Structural Parameters

Kučera

Suchý

2021

Lecture Notes in Computer Science

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The Minimum Eccentricity Shortest Path Problem consists in finding a shortest path with minimum eccentricity in a given undirected graph. The problem is known to be NP-complete and W[2]-hard with respect to the desired eccentricity. We present fpt algorithms for the problem parameterized by the modular width, distance to cluster graph, the combination of distance to disjoint paths with the desired eccentricity, and maximum leaf number.

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On the Minimum Eccentricity Shortest Path Problem

Cited by 8 publications

References 14 publications

Minimum Eccentricity Shortest Paths in Some Structured Graph Classes

Minimum Eccentricity Shortest Paths in Some Structured Graph Classes

Minimum Eccentricity Shortest Path Problem: An Approximation Algorithm and Relation with the k-Laminarity Problem

Minimum Eccentricity Shortest Path Problem with Respect to Structural Parameters

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