A practical algorithm for the minimum rectilinear steiner tree

Ma, Jun; Yang, Bo; Ma, Shuping

doi:10.1007/bf02951931

Cited by 5 publications

(5 citation statements)

References 3 publications

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“…It shows that, with the increase of CNE resin content in the cured resin systems, the cracks on the fracture surfaces of the cured resins gradually changed from relatively coarse to relatively fine and dense. Meanwhile, the morphology of the surfaces gradually changed from a ladder shape with linear expansion to a disordered pattern with highs and lows 49 . The stress whitening phenomenon was seen to exist in the stress fringe fracture, which absorbs part of the tensile stress and makes crack propagation more difficult 50,51 .…”

Section: Resultsmentioning

confidence: 99%

Synthesis of star‐shaped epoxy resin with excellent mechanical properties using triazine as a skeleton

Qiao,

Ji,

Zhao

et al. 2024

J of Applied Polymer Sci

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The high‐performance development of advanced resin matrix composites has resulted in higher requirements for the mechanical strength and toughness of epoxy resin matrices. However, enhancing the toughness of the epoxy resin while maintaining its mechanical strength remains a considerable challenge. In this study, we utilized triazine rings as the skeleton, and introduced flexible chain segments and other forces into the polymer cross‐linked network to fabricate a star‐shaped epoxy resin (CNE) with exceptional mechanical properties. Benefiting from its meticulously designed rigid‐flexible integrated structure, after curing by 4,4′‐diaminodiphenylmethane (DDM), it demonstrated outstanding mechanical properties. The storage modulus of CNE/DDM was measured at up to 5.48 GPa; moreover, its tensile modulus and strength went as high as 5.04 GPa and 134.72 MPa respectively, and it also exhibited an elongation at break of up to 3.35%. The mechanical properties of CNE/DDM are far superior to those of AFG‐90 (N,N‐diglycidyl‐4‐glycidyloxyaniline)/DDM. Over all, the findings of this study thus provide an effective synthesis pathway toward achieving epoxy resins with high modulus, strength, and toughness.

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Section: Resultsmentioning

confidence: 99%

Synthesis of star‐shaped epoxy resin with excellent mechanical properties using triazine as a skeleton

Qiao,

Ji,

Zhao

et al. 2024

J of Applied Polymer Sci

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“…The size of BS did not vary significantly after the acid treatment, as shown in Figure 3c,d. A high diameter‐to‐thickness ratio in the polymer‐based composites can play a strong reinforcing role, which can significantly improve the impact strength of the resulting composites 30,31 …”

Section: Resultsmentioning

confidence: 99%

Enhanced thermal stability and impact strength of phenolic formaldehyde resin using acid‐treated basalt scales

Tang

Jin

et al. 2022

J of Applied Polymer Sci

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In this study, phenolic formaldehyde (PF) resin-based composites were prepared using basalt scale (BS) as a reinforcing agent via a melting-blending method. The BS surface was treated with hydrochloric acid, and the surface properties were characterized using thermal field-emission scanning electron microscopy, Fourier-transform infrared, X-ray photoelectron spectrometry, and energy-dispersive X-ray spectroscopy. Moreover, the influence of acidtreated BS (H-BS) content on the thermal properties, flexural properties, impact strength, and morphology of PF/H-BS composites was investigated. The thermal stability and glass transition temperature of the composites increased significantly with the increasing H-BS content. The impact strength tests indicated that the impact strength of the composite with 15 wt% H-BS was 0.66 kJ/m 2 , which is 153% higher than that of pristine PF. The scanning electron microscopy results indicated that the PF/H-BS composites exhibit rough morphology with numerous microcracks.

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“…It is hoped that future researchers will continue to explore the rectilinear Steiner book problem and optimise the algorithm for application in real production [9].…”

Section: Discussionmentioning

confidence: 99%

Algorithm design and simulation of Rectilinear Steiner Tree problems based on concrete class Line

Ma¹,

Li²,

Chen³

et al. 2021

Proceedings of the 8th EAI International Conference on Green Energy and Networking, GreeNets 2021, June 6-7, 2021, Dalian, Peop

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This graduation thesis mainly focuses on the specific RST, namely the Minimum Rectilinear Steiner tree, to study and improve the algorithm, and finally simulation and output results. Steiner tree problem belongs to combinatorial optimization discipline and is NP-hard problem. Over the past three centuries, many mathematicians have extended and extended this problem, making the steiner tree tree problem further developed. This paper mainly deals with a sub-problem of steiner tree, the Minimum Rectilinear Steiner tree problem. In this paper, based on dynamic programming, a classical technique to solve the steiner tree problem, two algorithms, L-MRST and Z-MRST, are proposed to construct the Minimum Rectilinear Steiner tree on a plane. Both algorithms use point data discretization for pre-tree preparation. However, in the same solution mode, the algorithm l-mrst directly iterates on the current subtree to build the final tree. The algorithm zmrst preprocesses the feasible z-layout standby of all points and enumerates all possible layouts when traversing the nodes. This algorithm increases the algorithm complexity, but the results are obviously optimized. Experimental results also bear this out. For the Minimum Rectilinear Steiner tree problem, the two algorithms in this paper have their own advantages and disadvantages, which can help VLSI problem to some extent, and can effectively optimize the large-scale wire network routing problem. The next research direction about the line steiner tree is also proposed.

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A practical algorithm for the minimum rectilinear steiner tree

Cited by 5 publications

References 3 publications

Synthesis of star‐shaped epoxy resin with excellent mechanical properties using triazine as a skeleton

Synthesis of star‐shaped epoxy resin with excellent mechanical properties using triazine as a skeleton

Enhanced thermal stability and impact strength of phenolic formaldehyde resin using acid‐treated basalt scales

Algorithm design and simulation of Rectilinear Steiner Tree problems based on concrete class Line

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