The complexity of finding two disjoint paths with min-max objective function

Li, Chung‐Lun; McCormick, Thomas S.; Simich-Levi, David

doi:10.1016/0166-218x(90)90024-7

Cited by 130 publications

(91 citation statements)

References 6 publications

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“…The algorithm is obtained by extending the Li's algorithm [9] to find two disjoint paths on acyclic directed graphs for MIN-MAX objectiveh.…”

Section: Pseudo-polynomial-time Algorithm For Acyclic Directed Graphsmentioning

confidence: 99%

“…Suurballe and Tarjan provided different treatment, and presented algorithms that are more efficient [18] [19]. Li et al proved that all four versions of the problem of finding two disjoint paths such that the length of the longer path is minimized (called the MIN-MAX 2-Path Problem) are strongly NP-complete [9]. They also considered a generalized MIN-SUM problem (which we call the G-MIN-SUM e -Path Problem) assuming that each edge is associated with e different lengths.…”

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confidence: 99%

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Finding Two Disjoint Paths in a Network with Normalized α + -MIN-SUM Objective Function

Yang

Zheng

2005

Algorithms and Computation

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“…The algorithm is obtained by extending the Li's algorithm [9] to find two disjoint paths on acyclic directed graphs for MIN-MAX objectiveh.…”

Section: Pseudo-polynomial-time Algorithm For Acyclic Directed Graphsmentioning

confidence: 99%

mentioning

confidence: 99%

Finding Two Disjoint Paths in a Network with Normalized α + -MIN-SUM Objective Function

Yang

Zheng

2005

Algorithms and Computation

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“…For instance, the Min-Sum problem mentioned earlier, in which the objective is to minimize the sum of the costs of the two paths can be solved using a polynomial time algorithm called SPP [4], [5]. Unlike Min-Sum, the Min-Max problem, whose objective is to minimize the length of the longer one of the two paths was proved to be NPC [9], [10]. However, as far as we know, no existing work has addressed what we call the Min-Min problem, in which the objective is to minimize the length of the shorter one of the two paths.…”

Section: Computational Complexity Of Various Problemsmentioning

confidence: 99%

“…Many problems related to finding a pair of link or node disjoint paths in single cost networks have been studied [4], [5], [9]- [11]. For instance, the Min-Sum problem mentioned earlier, in which the objective is to minimize the sum of the costs of the two paths can be solved using a polynomial time algorithm called SPP [4], [5].…”

Section: Computational Complexity Of Various Problemsmentioning

confidence: 99%

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On finding disjoint paths in single and dual link cost networks

Chen

Xiong

et al.

Ieee Infocom 2004

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Abstract-Finding a disjoint path pair is an important component in survivable networks. Since the traffic is carried on the active (working) path most of the time, it is useful to find a disjoint path pair such that the length of the shorter path (to be used as the active path) is minimized. In this paper, we first address such a Min-Min problem. We prove that this problem is NP-complete in either single link cost (e.g. dedicated backup bandwidth) or dual link cost (e.g. shared backup bandwidth) networks. In addition, it is NP-hard to obtain a k-approximation to the optimal solution for any k > 1. Our proof is extended to another open question regarding the computational complexity of a restricted version of the Min-Sum problem in an undirected network with ordered dual cost links (called MSOD problem). To solve the Min-Min problem efficiently, we introduce a novel concept called conflicting link set which provides insights into the so-called trap problem, and develop a divide-and-conquer strategy. The result is an effective heuristic for the Min-Min problem called COLE, which can outperform other approaches in terms of both the optimality and running time. We also apply COLE to the MSOD problem to efficiently provide shared path protection and conduct comprehensive performance evaluation as well as comparison of various schemes for shared path protection. We show that COLE not only processes connection requests much faster than existing ILP based approaches but also achieves a good balance among the AP length, bandwidth efficiency and recovery time.

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Disjoint Paths in Networks

Iqbal

Kuipers

2015

Wiley Encyclopedia of Electrical and Electronics Engineering

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This article provides the basic concepts, complexity analysis, and discussions on the disjoint paths problem. The disjoint paths problem has a wide range of applications across various network types, particularly in providing a more reliable service to network traffic. Traffic that can make use of disjoint paths is more robust to the effect of network node or link failures. This article also covers many different variants of the disjoint paths problem, namely, the availability‐based disjoint paths problem, the maximally disjoint paths problem, the domain‐disjoint paths problem, the shared risk link group (SRLG)‐disjoint paths problem, the region‐disjoint paths problem, and the disjoint path pairs problem.

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The complexity of finding two disjoint paths with min-max objective function

Cited by 130 publications

References 6 publications

Finding Two Disjoint Paths in a Network with Normalized α + -MIN-SUM Objective Function

Finding Two Disjoint Paths in a Network with Normalized α + -MIN-SUM Objective Function

On finding disjoint paths in single and dual link cost networks

Disjoint Paths in Networks

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