On the minimum routing cost clustered tree problem

Lin, Chen-Wan; Wu, Bang Ye

doi:10.1007/s10878-016-0026-8

Cited by 21 publications

(24 citation statements)

References 22 publications

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“…We then prove in Section 4 the

NP

‐completeness of the feasibility problem associated to

IDPC

‐

DU

(Theorem 1), implying that

IDPC

‐

DU

is not even approximable in polynomial time (Proposition 1). We point out that such complexity results have been independently proved in (see Section 3, Theorem 2), but via a different polynomial reduction technique. On the other hand, the dynamic programming algorithm presented in Section 5 is Fixed Parameter Tractable in the number of domains

| D |

(Lemma 2), suggesting that the computational bottleneck for

IDPC

‐

DU

is indeed

| D |

.…”

Section: Introductionmentioning

confidence: 84%

“…However, the literature does not provide algorithmic solutions for rainbow path computation, while it focuses on the characterization of the rainbow connection number (being the minimum number of colors needed to rainbow color the graph itself, that is, such that there exists a rainbow path between each pair of nodes; see, e.g., for a survey). The complexity properties of

IDPC

‐

DU

have already been studied in (see Section 3, Theorem 2). In this article we independently prove the NP‐hardness and the inapproximability of

IDPC

‐

DU

by using different techniques than those in .…”

Section: Related Workmentioning

confidence: 99%

“…The complexity properties of

IDPC

‐

DU

have already been studied in (see Section 3, Theorem 2). In this article we independently prove the NP‐hardness and the inapproximability of

IDPC

‐

DU

by using different techniques than those in .…”

Section: Related Workmentioning

confidence: 99%

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Domain clustering for inter‐domain path computation speed‐up

et al. 2017

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We consider a multi‐domain network scenario and we study the Inter‐Domain Path Computation problem under the Domain Uniqueness constraint (IDPC‐DU), that is, a path cannot visit a domain twice. It is known that hierarchical Path Computation Element (h‐PCE) architecture, that is commonly used to solve IDPC‐DU, shows poor scalability with respect to the number of domains. For this reason, we devise a new domain clustering concept allowing one to artificially reduce the number of domains in an offline phase, in order to solve IDPC‐DU with lower complexity at run‐time. More specifically, we first prove the NP‐completeness of the feasibility problem associated with IDPC‐DU and the inapproximability of IDPC‐DU itself. Yet, we show that the number of domains is the real computational bottleneck for the solution of IDPC‐DU. Then we provide a necessary and sufficient condition for a domain clustering to be proper, that is, without loss of optimality. Such a condition can be verified offline on the inter‐domain graph. We finally show via numerical experiments the impact of the inter‐domain treewidth on the computational speed‐up brought by proper clustering.

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“…We then prove in Section 4 the

NP

‐completeness of the feasibility problem associated to

IDPC

‐

DU

(Theorem 1), implying that

IDPC

‐

DU

| D |

(Lemma 2), suggesting that the computational bottleneck for

IDPC

‐

DU

is indeed

| D |

.…”

Section: Introductionmentioning

confidence: 84%

IDPC

‐

DU

have already been studied in (see Section 3, Theorem 2). In this article we independently prove the NP‐hardness and the inapproximability of

IDPC

‐

DU

by using different techniques than those in .…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Domain clustering for inter‐domain path computation speed‐up

et al. 2017

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“…The experimental results demonstrate the effectiveness of the proposed algorithm, partially on large instances. [12].Among those mentioned problems, CluMRCT is one of the most newly investigated problems. This problem has been formally formulated in [12].…”

mentioning

confidence: 99%

“…[12].Among those mentioned problems, CluMRCT is one of the most newly investigated problems. This problem has been formally formulated in [12]. Concretely, consider a connected, undirected graph G = (V , E, w) with nonnegative edge length function w :A spanning tree T of G is a clustered spanning tree if T can be cut into k subtrees by eliminating k − 1 edges such that each subtree is a spanning tree for only one cluster.…”

mentioning

confidence: 99%

Multifactorial Evolutionary Algorithm For Clustered Minimum Routing Cost Problem

Trung

Thanh

Hieu

et al. 2019

Proceedings of the Tenth International Symposium on Information and Communication Technology - SoICT 2019

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Minimum Routing Cost Clustered Tree Problem (CluMRCT) is applied in various fields in both theory and application. Because the CluMRCT is NP-Hard, the approximate approaches are suitable to find the solution for this problem. Recently, Multifactorial Evolutionary Algorithm (MFEA) has emerged as one of the most efficient approximation algorithms to deal with many different kinds of problems. Therefore, this paper studies to apply MFEA for solving CluMRCT problems. In the proposed MFEA, we focus on crossover and mutation operators which create a valid solution of CluM-RCT problem in two levels: first level constructs spanning trees for graphs in clusters while the second level builds a spanning tree for connecting among clusters. To reduce the consuming resources, we will also introduce a new method of calculating the cost of CluMRCT solution. The proposed algorithm is experimented on numerous types of datasets. The experimental results demonstrate the effectiveness of the proposed algorithm, partially on large instances. [12].Among those mentioned problems, CluMRCT is one of the most newly investigated problems. This problem has been formally formulated in [12]. Concretely, consider a connected, undirected graph G = (V , E, w) with nonnegative edge length function w :A spanning tree T of G is a clustered spanning tree if T can be cut into k subtrees by eliminating k − 1 edges such that each subtree is a spanning tree for only one cluster. The CluMRCT problem focuses on the routing cost, which is the sum of shortest path distance between any pairs of vertices given a clustered spanning tree T . The CluMRCT problem is finding on graph G a clustered spanning tree T having the minimum routing cost. One practical realization of this problem is in computer network application where the communication terminals are vertices, and they are partitioned into many clusters. The communication between those terminals are restricted within a cluster and only a few terminals can be connected to another cluster for maximizing efficiency and other security concerns. Solving CluMRCT is equivalent to facilitate the network architecture that consumes the minimum peer-to-peer communication resources.

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The resource constrained clustered shortest path tree problem: Mathematical formulation and Branch&Price solution algorithm

et al. 2022

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In this article, the Resource Constrained Clustered Shortest Path Tree Problem is defined. It generalizes the classic Resource Constrained Shortest Path Tree Problem since it is defined on an undirected, complete and weighted graph whose set of nodes is partitioned into clusters. The aim is then to find a shortest path tree respecting some resource consumption constraints and inducing a connected subgraph within each cluster. The main support and motivation for studying this problem are related, among the others, to the design of telecommunication networks, and to Disaster Operations Management. In this work, we present a path‐based formulation for the problem, addressing the case of local resource constraints, that is, resource constraints on single paths. For its resolution, a Branch&Price algorithm featuring a Column Generation approach with Multiple Pricing Scheme is devised. A comprehensive computational study is conducted, comparing the proposed method with the results achieved by the CPLEX solver, adopted to solve the mathematical model. The numerical results underline that the Branch&Price algorithm outperforms CPLEX, both in terms of solution cost and time.

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On the minimum routing cost clustered tree problem

Cited by 21 publications

References 22 publications

Domain clustering for inter‐domain path computation speed‐up

Domain clustering for inter‐domain path computation speed‐up

Multifactorial Evolutionary Algorithm For Clustered Minimum Routing Cost Problem

The resource constrained clustered shortest path tree problem: Mathematical formulation and Branch&Price solution algorithm

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