A Walk in the Clouds: Routing Through VNFs on Bidirected Networks

Foerster, Klaus-Tycho; Parham, Mahmoud; Schmid, Stefan

doi:10.1007/978-3-319-74875-7_2

Cited by 6 publications

(5 citation statements)

References 33 publications

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“…Lastly, for the case that all edges have a capacity of at least two and s = t , a direct connection of WRP to the subset traveling salesman problem (TSP) can be made [33]. In the subset TSP, the task is to find a shortest closed walk that visits a given subset of the vertices [40].…”

Section: Related Workmentioning

confidence: 99%

Walking Through Waypoints

2020

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We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $$G=(V,E)$$G=(V,E), find a shortest walk (“route”) from a source $${s\in V}$$s∈V to a destination $$t\in V$$t∈V that includes all vertices specified by a set $$WP \subseteq V$$WP⊆V: the waypoints. This Waypoint Routing Problem finds immediate applications in the context of modern networked systems. Our main contribution is an exact polynomial-time algorithm for graphs of bounded treewidth. We also show that if the number of waypoints is logarithmically bounded, exact polynomial-time algorithms exist even for general graphs. Our two algorithms provide an almost complete characterization of what can be solved exactly in polynomial time: we show that more general problems (e.g., on grid graphs of maximum degree 3, with slightly more waypoints) are computationally intractable.

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Section: Related Workmentioning

confidence: 99%

Walking Through Waypoints

2020

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“…Corollary 1: The ordered waypoint routing problem is strongly NP-complete on directed Eulerian graphs For the case of bidirected graphs, which are a subset of directed Eulerian graphs, optimally solving the ordered waypoint routing problem is NP-complete [22], but the hardness of the feasibility variant is an open question.…”

Section: B Hard Already On Eulerian Graphsmentioning

confidence: 99%

“…For bidirected cactus graphs of constant capacity, the ordered waypoint routing problem can be optimally solved in polynomial time [22]. Bounded Treewidth Graphs II.…”

Section: A Exact Polynomial-time Algorithmsmentioning

confidence: 99%

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Charting the Algorithmic Complexity of Waypoint Routing

Amiri¹,

Foerster

Jacob

et al. 2018

SIGCOMM Comput. Commun. Rev.

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Modern computer networks support interesting new routing models in which traffic flows from a source s to a destination t can be flexibly steered through a sequence of waypoints, such as (hardware) middleboxes or (virtualized) network functions (VNFs), to create innovative network services like service chains or segment routing. While the benefits and technological challenges of providing such routing models have been articulated and studied intensively over the last years, much less is known about the underlying algorithmic traffic routing problems. This paper shows that the waypoint routing problem features a deep combinatorial structure, and we establish interesting connections to several classic graph theoretical problems. We find that the difficulty of the waypoint routing problem depends on the specific setting, and chart a comprehensive landscape of the computational complexity. In particular, we derive several NPhardness results, but we also demonstrate that exact polynomialtime algorithms exist for a wide range of practically relevant scenarios.

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“…Lastly, for the case that all edges have a capacity of at least two and s = t, a direct connection of WRP to the subset traveling salesman problem (TSP) can be made [32]. In the subset TSP, the task is to find a shortest closed walk that visits a given subset of the vertices [39].…”

Section: Related Workmentioning

confidence: 99%

Walking Through Waypoints

Amiri¹,

Foerster²,

Schmid³

2017

Preprint

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We initiate the study of a fundamental combinatorial problem: Given a capacitated graph G = (V, E), find a shortest walk ("route") from a source s ∈ V to a destination t ∈ V that includes all vertices specified by a set W ⊆ V : the waypoints. This waypoint routing problem finds immediate applications in the context of modern networked distributed systems. Our main contribution is an exact polynomial-time algorithm for graphs of bounded treewidth. We also show that if the number of waypoints is logarithmically bounded, exact polynomial-time algorithms exist even for general graphs. Our two algorithms provide an almost complete characterization of what can be solved exactly in polynomial-time: we show that more general problems (e.g., on grid graphs of maximum degree 3, with slightly more waypoints) are computationally intractable.

show abstract

A Walk in the Clouds: Routing Through VNFs on Bidirected Networks

Cited by 6 publications

References 33 publications

Walking Through Waypoints

Walking Through Waypoints

Charting the Algorithmic Complexity of Waypoint Routing

Walking Through Waypoints

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