A new problem of degree-constrained Euclidean Steiner minimal tree is discussed, which is quite useful in several fields. Although it is slightly different from the traditional degree-constrained minimal spanning tree...A new problem of degree-constrained Euclidean Steiner minimal tree is discussed, which is quite useful in several fields. Although it is slightly different from the traditional degree-constrained minimal spanning tree, it is also NP-hard. Two intelligent algorithms are proposed in an attempt to solve this difficult problem. Series of numerical examples are tested, which demonstrate that the algorithms also work well in practice.展开更多
In this paper,Steiner minimal trees for point sets with special structure are studied. These sets consist of zigzag lines and equidistant points lying on them.
The rectilinear Steiner minimal tree （RSMT） problem is one of the fundamental problems in physical design, especially in routing, which is known to be NP-complete. This paper presents an algorithm, called ACO-Steine...The rectilinear Steiner minimal tree （RSMT） problem is one of the fundamental problems in physical design, especially in routing, which is known to be NP-complete. This paper presents an algorithm, called ACO-Steiner, for RSMT construction based on ant colony optimization （ACO）. An RSMT is constructed with ants＇ movements in Hanan grid, and then the constraint of Hanan grid is broken to accelerate ants＇ movements to improve the performance of the algorithm. This algorithm has been implemented on a Sun workstation with Unix operating system and the results have been compared with the fastest exact RSMT algorithm, GeoSteiner 3.1 and a recent heuristic using batched greedy triple construction （BGTC）. Experimental results show that ACO-Steiner can get a short running time and keep the high performance. Furthermore, it is Mso found that the ACO-Steiner can be easily extended to be used to some other problems, such as rectilinear Steiner minimal tree avoiding obstacles, and congestion reduction in global routing.展开更多
This paper considers the Steiner Minimal Tree （SMT） problem in the rectilinear and octilinear planes. The study is motivated by the physical design of VLSI： The rectilinear case corresponds to the currently used M-...This paper considers the Steiner Minimal Tree （SMT） problem in the rectilinear and octilinear planes. The study is motivated by the physical design of VLSI： The rectilinear case corresponds to the currently used M-architecture, which uses either horizontal or vertical routing, while the octilinear case corresponds to a new routing technique, X-architecture, that is based on the pervasive use of diagonal directions. The experimental studies show that the X-architecture demonstrates a length reduction of more than 10-20%. In this paper, we make a theoretical study on the lengths of SMTs in these two planes. Our mathematical analysis confirms that the length reduction is significant as the previous experimental studies claimed, but the reduction for three points is not as significant as for two points. We also obtain the lower and upper bounds on the expected lengths of SMTs in these two planes for arbitrary number of points.展开更多
Through the combination of the minimum energy principle in physics and the Steiner minimal tree (SMT) theory in geometry,this paper proves a universal law for lipid nanotube networks (LNNs):at stable equilibrium state...Through the combination of the minimum energy principle in physics and the Steiner minimal tree (SMT) theory in geometry,this paper proves a universal law for lipid nanotube networks (LNNs):at stable equilibrium state,the network of three-way lipid nanotube junctions is equivalent to a SMT.Besides,an arbitrary (usually non-equilibrium) network of lipid nanotube junctions may fission into a SMT through diffusions and dynamic self-organizations of lipid molecules.Potential applications of the law to the micromanipulations of LNNs are presented.展开更多
基金the National Natural Science Foundation of China (70471065)the Shanghai Leading Academic Discipline Project (T0502).
文摘A new problem of degree-constrained Euclidean Steiner minimal tree is discussed, which is quite useful in several fields. Although it is slightly different from the traditional degree-constrained minimal spanning tree, it is also NP-hard. Two intelligent algorithms are proposed in an attempt to solve this difficult problem. Series of numerical examples are tested, which demonstrate that the algorithms also work well in practice.
基金Supported by NSF of China(1 970 1 0 2 8) and National973Fundamental Research Project
文摘In this paper,Steiner minimal trees for point sets with special structure are studied. These sets consist of zigzag lines and equidistant points lying on them.
基金This work was partially supported by the National Natural Science Foundation of China （NSFC） under Grant No. 60373012, and the Specialized Research Fund for the Doctoral Program of Higher Education （SRFDP） of China under Grant No. 20050003099. Some preliminary results of this work were presented at IEEE International Conference on Communications, Circuits and Systems （ICCCAS）, Chengdu, China, 2004.
文摘The rectilinear Steiner minimal tree （RSMT） problem is one of the fundamental problems in physical design, especially in routing, which is known to be NP-complete. This paper presents an algorithm, called ACO-Steiner, for RSMT construction based on ant colony optimization （ACO）. An RSMT is constructed with ants＇ movements in Hanan grid, and then the constraint of Hanan grid is broken to accelerate ants＇ movements to improve the performance of the algorithm. This algorithm has been implemented on a Sun workstation with Unix operating system and the results have been compared with the fastest exact RSMT algorithm, GeoSteiner 3.1 and a recent heuristic using batched greedy triple construction （BGTC）. Experimental results show that ACO-Steiner can get a short running time and keep the high performance. Furthermore, it is Mso found that the ACO-Steiner can be easily extended to be used to some other problems, such as rectilinear Steiner minimal tree avoiding obstacles, and congestion reduction in global routing.
基金the National Natural Science Foundation of China under Grant Nos.10401038,60373012 and 70221001the Key Project of Chinese Ministry of Education under Grant No.106008
文摘This paper considers the Steiner Minimal Tree （SMT） problem in the rectilinear and octilinear planes. The study is motivated by the physical design of VLSI： The rectilinear case corresponds to the currently used M-architecture, which uses either horizontal or vertical routing, while the octilinear case corresponds to a new routing technique, X-architecture, that is based on the pervasive use of diagonal directions. The experimental studies show that the X-architecture demonstrates a length reduction of more than 10-20%. In this paper, we make a theoretical study on the lengths of SMTs in these two planes. Our mathematical analysis confirms that the length reduction is significant as the previous experimental studies claimed, but the reduction for three points is not as significant as for two points. We also obtain the lower and upper bounds on the expected lengths of SMTs in these two planes for arbitrary number of points.
基金supported by the National Natural Science Foundation of China(Grant Nos. 10872114,11072125)the Natural Science Foundation of Jiangsu Province(Grant No. BK2008370)
文摘Through the combination of the minimum energy principle in physics and the Steiner minimal tree (SMT) theory in geometry,this paper proves a universal law for lipid nanotube networks (LNNs):at stable equilibrium state,the network of three-way lipid nanotube junctions is equivalent to a SMT.Besides,an arbitrary (usually non-equilibrium) network of lipid nanotube junctions may fission into a SMT through diffusions and dynamic self-organizations of lipid molecules.Potential applications of the law to the micromanipulations of LNNs are presented.
