Hamiltonian paths and cycles pass through prescribed edges in the balanced hypercubes

Cheng, Dongqin

doi:10.1016/j.dam.2019.02.033

Cited by 13 publications

(4 citation statements)

References 23 publications

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“…When all the locations are interlinked, the procedure will get back to the starting point. This method could be summarised in multiple steps, as seen in [47].…”

Section: Design Of Modelsmentioning

confidence: 99%

Modelling Distribution Routes in City Logistics by Applying Operations Research Methods

Stopka¹

2022

PROMTT

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The article focuses on the up-to-date subject from the practical as well as scientific point of view. It specifically discusses a proposal of an approach concerning transport or distribution problems in the range of city logistics and investigates possibilities to use opted operations research methods in this particular area. Specific suggestions lie first and foremost in using selected tools of operations research (i.e. a set of methods concerning vehicle routing problem) to model multiple variants of distribution paths from a determined hub to multiple spokes in order to minimise the overall travelled distance in an urban area. As far as the very research goes, to define distribution paths to supply multiple logistics objects in the range of city logistics, ensuing methods are step by step used: Clarke-Wright algorithm, Mayer algorithm and the nearest neighbour algorithm. The article consists of a conceptual section, describing the relevant theory as well as data and methods used, the practical part and the section encompassing an assessment of the key findings, along with the discussion. A suitable combination of adequate operations research methods and their application to city logistics issues is where an innovative solution of this research lies.

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“…When all the locations are interlinked, the procedure will get back to the starting point. This method could be summarised in multiple steps, as seen in [47].…”

Section: Design Of Modelsmentioning

confidence: 99%

Modelling Distribution Routes in City Logistics by Applying Operations Research Methods

Stopka¹

2022

PROMTT

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“…The optimization of transport networks, among others, includes addressing the distribution tasks-pick-up and delivery problem-using mathematical (Operations Research) methods. According to Cheng [1], Hamiltonian circuits have a crucial role in terms of optimization tasks, especially in addressing distribution tasks where each vertex (customer, supplier, logistics center and so forth) needs to be visited just once. To address this problem, a number of conditions have been defined that the graph must adhere to including the Hamiltonian circuit [2].…”

Section: Literature Reviewmentioning

confidence: 99%

Optimization of the Pick-Up and Delivery Technology in a Selected Company: A Case Study

et al. 2022

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This article deals with pick-up and delivery activities in a selected company that focuses on the distribution of products in the gastronomic sector of the market and suggests how to make the present approach more efficient. The introductory part of the article clarifies the meanings of basic concepts related to the issue of optimizing the logistics processes in the company. The crucial goal is to analyze the existing pick-up and delivery technology and then, in the application part of the article, to propose adequate measures in the context of streamlining these activities with their technical and economic evaluation. An analysis of current delivery routes, which are used for the distribution of gastronomic products, is first performed. Thereafter, the routes are optimized with the aim of minimizing the total distance traveled by using the Operations Research methods, namely: the Hungarian method, Vogel approximation method, nearest neighbor method and the Routin route planner which is based on a principle of the Greedy algorithm. At the end of the article, a technical and economical evaluation of the findings is discussed, wherein the individual results of optimization through selected methods are first compared and then, new optimized routes are selected.

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“…As a complementary to fault-tolerant embedding problem, Dvořák [11] proposed the prescribed embedding problem which requires that the embedded paths and cycles pass through a given number of prescribed edges. Following Dvořák's work, prescribed embedding problems were studied in literatures (see, for example, [3,6,10,20] and references therein). A set {u, v} of two vertices in a graph G is compatible to a given linear forest L of G if none of the paths in L has u or v as internal vertices or both of them as end vertices.…”

Section: Introductionmentioning

confidence: 99%

“…A set {u, v} of two vertices in a graph G is compatible to a given linear forest L of G if none of the paths in L has u or v as internal vertices or both of them as end vertices. A bipartite graph G is k-prescribed hamiltonian laceable if G admits a hamiltonian path between u and v passing through any prescribed linear forest L with at most k edges provided that {u, v} is compatible to L. Cheng [10] investigated prescribed hamiltonian laceability of balanced hypercubes and she obtained the following.…”

Section: Introductionmentioning

confidence: 99%

Optimal edge fault-tolerant-prescribed hamiltonian laceability of balanced hypercubes

Song¹,

Yang²

2022

Preprint

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Aims: Try to prove the n-dimensional balanced hypercube BHn is (2n − 2)-fault-tolerant-prescribed hamiltonian laceability. Methods: Prove it by induction on n. It is known that the assertation holds for n ∈ {1, 2}. Assume it holds for n − 1 and prove it holds for n, where n ≥ 3. If there are 2n − 3 faulty links and they are all incident with a common node, then we choose some dimension such that there is one or two faulty links and no prescribed link in this dimension; Otherwise, we choose some dimension such that the total number of faulty links and prescribed links does not exceed 1. No matter which case, partition BHn into 4 disjoint copies of BHn−1 along the above chosen dimension. Results: On the basis of the above partition of BHn, in this manuscript, we complete the proof for the case that there is at most one faulty link in the above chosen dimension.

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Hamiltonian paths and cycles pass through prescribed edges in the balanced hypercubes

Cited by 13 publications

References 23 publications

Modelling Distribution Routes in City Logistics by Applying Operations Research Methods

Modelling Distribution Routes in City Logistics by Applying Operations Research Methods

Optimization of the Pick-Up and Delivery Technology in a Selected Company: A Case Study

Optimal edge fault-tolerant-prescribed hamiltonian laceability of balanced hypercubes

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