On the complexity of vertex-disjoint length-restricted path problems

Bley, Andreas

doi:10.1007/s00037-003-0179-6

Cited by 26 publications

(36 citation statements)

References 14 publications

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“…Guruswami et al [2003] show that the edge-disjoint 6-length-bounded s-t-paths problem is MAX SN P-hard, and for any length-bound they give an O( √ m)-approximation algorithm, where m denotes the number of edges. Bley [2003] proves that both the node-and the edge-disjoint maximum 5-length-bounded s-t-paths problem are APX -complete. For directed networks, Guruswami et al [2003] show that the problem is N P-hard to approximate within a factor of n 1 2 −ǫ , for any ǫ > 0; n denotes the number of nodes.…”

Section: Introductionmentioning

confidence: 92%

Length-Bounded Cuts and Flows

Baier

Erlebach

Hall

et al. 2006

Automata, Languages and Programming

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For a given number L, an L-length-bounded edge-cut (node-cut, resp.) in a graph G with source s and sink t is a set C of edges (nodes, resp.) such that no s-t-path of length at most L remains in the graph after removing the edges (nodes, resp.) in C. An L-length-bounded flow is a flow that can be decomposed into flow paths of length at most L. In contrast to the classical flow theory, we describe instances for which the minimum L-length-bounded edge-cut (node-cut, resp.) is Θ(n 2/3 )-times (Θ( √ n)-times, resp.) larger than the maximum L-length-bounded flow, where n denotes the number of nodes; this is the worst case. We show that the minimum length-bounded cut problem is N P-hard to approximate within a factor of 1.1377 for L ≥ 5 in the case of nodecuts and for L ≥ 4 in the case of edge-cuts. We also describe algorithms with approximation ratio O(min{L, n/L}) ⊆ O( √ n) in the node case and O(min{L, n 2 /L 2 , √ m}) ⊆ O(n 2/3 ) in the edge case, where m denotes the number of edges. Concerning L-length-bounded flows, we show that in graphs with unit-capacities and general edge lengths it is N P-complete to decide whether there is a fractional length-bounded flow of a given value. We analyze the structure of optimal solutions and present further complexity results.

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Section: Introductionmentioning

confidence: 92%

Length-Bounded Cuts and Flows

Baier

Erlebach

Hall

et al. 2006

Automata, Languages and Programming

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“…If failures are expected to occur only sporadically (and in case of 1 : 1 protection), then it may be desirable to minimize the weight of the primary (shorter) path (min-min objective), which also leads to an NP-hard problem [109]. The min-max and minmin disjoint paths problems could be considered as extreme cases of the bounded disjoint paths problem, which was shown to be NP-hard [110] and later proven to be APX-hard by Bley [111] (the graph structure referred to as lobe that was used by Itai et al [110] to prove NP-completeness has since often been used to prove that other disjoint paths problems are NP-complete, e.g., [112][113][114]). Finding widest disjoint paths can easily be done by pruning "low-capacity" links from the graph and finding disjoint paths.…”

Section: Min-min Disjoint Paths Problemmentioning

confidence: 99%

An Overview of Algorithms for Network Survivability

Kuipers

2012

ISRN Communications and Networking

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Network survivability-the ability to maintain operation when one or a few network components fail-is indispensable for present-day networks. In this paper, we characterize three main components in establishing network survivability for an existing network, namely, (1) determining network connectivity, (2) augmenting the network, and (3) finding disjoint paths. We present a concise overview of network survivability algorithms, where we focus on presenting a few polynomial-time algorithms that could be implemented by practitioners and give references to more involved algorithms.

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“…The MLBDP problem was proven to be NP-complete for b ≥ 5 by Itai et al in [13] and later proven to be APX-hard 2 for b ≥ 5 by Bley in [3].…”

Section: Theoremmentioning

confidence: 99%

Impairment-aware path selection and regenerator placement in translucent optical networks

Kuipers

Beshir

Orda

et al. 2010

The 18th IEEE International Conference on Network Protocols

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Abstract-Physical impairments, such as noise and signal distortions, negatively affect the quality of information transfer in optical networks. The effect of physical impairments predominantly augments with distance and bit rate of the signal to the point that it becomes detrimental to the information transfer. To reverse the effect of physical impairments, the signal needs to be regenerated at nodes that have regeneration capabilities. Regenerators are costly and are, therefore, usually only sparsely placed in the network, in which case it is referred to as a translucent network. This paper deals with two problems in translucent networks, namely: (1) how to incorporate impairment awareness in the routing algorithms, and (2) how many regenerators to place inside the network and where. We propose exact and heuristic algorithms for impairment-aware path selection and, through simulations, show that our heuristic T IARA is computationally efficient and performs very close to our exact algorithm EIARA. Subsequently, we propose a greedy algorithm for placing regenerators that, contrary to previous proposals, is suitable for multiple impairment metrics, has polynomial complexity for a single impairment metric, and is cheaper in terms of the number of regenerators needed.

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On the complexity of vertex-disjoint length-restricted path problems

Cited by 26 publications

References 14 publications

Length-Bounded Cuts and Flows

Length-Bounded Cuts and Flows

An Overview of Algorithms for Network Survivability

Impairment-aware path selection and regenerator placement in translucent optical networks

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