F. K. Hwang, D. S. Richards, and P. Winter. The Steiner Tree Problem. North-Holland, Amsterdam, 1992. Home/Search Document Not in Database Summary Related Articles Check |
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The Rectilinear Steiner Arborescence Problem is NP-Complete - Chen (2000) (5 citations) (Correct)
....for example [1, 2] However, it is still a major open problem in VLSI whether the RSA problem can be solved in polynomial time. For completeness, previous results on the complexity of rectilinear trees are listed in Table 1. More information can be found in the book by Hwang, Richards and Winter [9]. Table 1: Complexity of rectilinear trees. Arborescence Tree Steiner NP complete [5] Spanning O(n log n) 14] O(n log n) 8] 2 NP Completeness 2.1 Overall Strategy We assume the readers are familiar with the general concept of NP completeness [6] The decision version of the Rectilinear Steiner ....
F.K.Hwang,D.S.Richards,andP.Winter,The Steiner Tree Problem, North-Holland, Amsterdam, 1992.
A Flexible Multicast Routing Protocol For Group Communication - Aggarwal, Paul, al. (2000) (Correct)
....is O(IDlIVI 2) to determine our heuristic Steiner trees [3] These heuristics are guaranteed to produce a tree whose cost is within twice that of the Steiner minimal tree. Thus, although finding a Steiner minimal tree is difficult, it is fairly straightforward to find heuristic Steiner trees. See [21,40] for interesting surveys on such problems. Ad hoc cen tered trees that use reasonable heuristics for finding good shared trees may also be useful and are supported by our notion of Application Assisted Routing. In the rest of this paper, we will use the term CO Steiner tree to mean an ....
F.K. Hwang, D.S. Richards, Steiner tree problems, Networks 22 (1992) 55 89.
The Local Steiner Problem in Normed Planes - Swanepoel (Correct)
....of Pretoria, Pretoria 0002, South Africa. E mail: konrad math.up.ac.za 1.2 The Local Steiner Problem The Steiner problem is the problem of nding an SMT if it exists (or all SMTs) for a given set of points in a metric space. The problem was probably rst stated by Jarn k and K ossler in 1934 [14], the (inaccurate) name of the problem originated in [6] and the term Steiner minimal tree in [12] The Steiner problem in the rectilinear (taxicab) plane and in the geometry is important in certain aspects of VLSI layout [16] See also [19, 20, 21, 22, 23] for recent work in the geometry. ....
....(taxicab) plane and in the geometry is important in certain aspects of VLSI layout [16] See also [19, 20, 21, 22, 23] for recent work in the geometry. The Steiner problem has rst been considered in the rectilinear plane by Hanan [13] and in general normed planes by Cockayne [5] See [14, 4, 17] for surveys on the Steiner problem and the related FermatTorricelli (or Fermat Weber) problem. Also, see [15] for a study of the Steiner problem in Riemannian spaces. Conceptually, there are two aspects to the Steiner problem: the rst is searching through all candidate Steiner trees, the second ....
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F. K. Hwang, D. S. Richards, and P. Winter, The Steiner tree problem, Ann. Discrete Math., vol. 53, North-Holland, Amsterdam, 1992.
Variable Neighborhood Search - Hansen, Mladenovic (1997) (22 citations) (Correct)
....a minimum weighted subtree of G which spans all terminal nodes. The solution X and corresponding tree are called Steiner nodes and Steiner minimum tree respectively. Application can be found in many areas, such as telecommunication network design, computational biology, VLSI design, etc. see e.g. [90] for a survey) In [108] and later in [125] two types of neighborhoods, i.e. node based (N) 2) and path based (P) 134] are successfully used for solving SPG as in VND. For example, the average of improvement over a constructive initial solution on 454 instances was 10.24 for the N P ....
F.K. Hwang, D.S. Richards and P. Winter. The Steiner tree problem, North-Holland, Amsterdam, 1992.
Creating and Exploiting Flexibility in Rectilinear.. - Bozorgzadeh, Kastner.. (Correct)
....topology does not change (see Figure 3) Similarly in graph G(T ) the degree of vertices is bounded by 4. If the Steiner point p has edge degree of 4, it is called cross point. T point is a node with degree 3 in which one of incident edges is perpendicular to the other two incident edges. In [2], Hwang et al. define two different transformations for rectilinear Steiner trees: flipping and sliding. Each transformation maps one such tree to another without moving the positions of the terminals and without increasing the length of the tree. Depending on the direction of transformation, ....
....excluding the ones belonging to Ps , Ms , and Fs . For an example of a movable set, see Figure 10. The movable set is a subtree with 4 leaves and two internal nodes. It is similar to definition of full component in Steiner tree. Full component is defined as a subtree with leaves of terminals [2]. However, in a movable set, the leaves need not to be the terminals. Corollary 2: If the leaves of subtree of movable component are the terminals, the movable set is a full rectilinear Steiner component with 4 nodes. B. Algorithm Figure 9 shows 4 different movable sets (s; Es) The movable ....
F. K. Hwang, D. S. Richards, and P. Winter. "The Steiner Tree Problem". Annals of Discrete Mathematics 53, North-Holland, pp. 203-282, 1992.
An Efficient Algorithm For Shortest Path Multicast.. - Mokbel, El-Haweet.. (2000) (Correct)
....all destinations. Generally, there are two types of such a tree, the Steiner tree and the shortest path tree. Steiner tree or groupshared tree tends to minimize the total cost of the resulting tree, this is an NP Complete problem. Number of heuristics to this problem can be found in (Winter 1987; Hwang and Richards 1992). Shortest path tree or source based tree tends to minimize the cost of each path from source to any destination, this can be achieved in polynomial time by using one of the two famous algorithms of Bellman (Bellman 1957) and Dijkstra (Dossey et al. 1993) and pruning the undesired links. Recently, ....
Hwang, F. and D. Richards 1992. "Steiner Tree Problems", Networks, vol. 22, no. 1, pp
Appia: Formalization of Its Topology Assignment Problem - Peh (1998) (Correct)
....it takes to find the optimal solution. Constraint programming may be a viable alternative, since it prunes the search space more efficiently. 5.3 Steiner Trees Steiner trees may be another well known problem which we can map Appia problem to. A good starting point for exploring steiner trees is (Hwang,Richards and Winter, 1992) and (Winter, 1987) Analysis and algorithms for degree constrained steiner treees are available, but they do not fully address Appia s problem either. It may be fruitful to pursue this. 5.4 Degree constrained multicasting This is an idea I came upon, but had no time to pursue. The idea is that ....
F. K. Hwang, D. S. Richards, P. Winter, "The Steiner Tree Problem", Annals of Discrete Mathematics 53, North-Holland, 1992.
Position-Based Multicast Routing for Mobile Ad-Hoc Networks - Mauve, Füßler, Widmer, Lang (2003) (4 citations) (Correct)
....possible. If the topology of the network is known, a distribution tree that optimizes the first criterion can be obtained by combining the shortest paths to the destinations. Wherever these paths diverge, the packet is split. The second criterion is optimized by so called Steiner trees (see e.g. [23]) which connect source and destinations with the minimum possible number of hops. A formulation of the Steiner problem for wireless networks where packets are broadcast to neighboring nodes is given in [24] However, with position based routing, routing decisions are based solely on local ....
F. K. Hwang, D. S. Richards, and P. Winter, "The Steiner tree problem," Annals of discrete mathematics, vol. 53, 1992.
New Algorithms for Multicast Routing in Real Time Networks - Mokbel (1999) (Correct)
....minimum spanning tree problem which can be solved in polynomial time O(N ) Because of the exponential time of finding the optimal Steiner tree for multicast problem, several heuristics have been introduced to get near optimal solution. An exhaustive survey of these heuristics can be found in [11,12]. The most famous heuristic is the one proposed in [13] and it is called KMB algorithm. More recent heuristics can be found in Widyono [7] where he proposed four different heuristics for delay constrained Steiner tree problem. 2.3.2 Constrained Steiner Tree Problem With the rapid evolution of ....
F. Hwang and D. Richards, "Steiner Tree Problems", Networks, vol. 22, no. 1, pp 55-89, January 1992.
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F. K. Hwang, D. S. Richards, and P. Winter. The Steiner Tree Problem. North-Holland, Amsterdam, 1992.
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Published in the IEEE INFOCOM 94 Proceedings, Toronto.. - Ciro Noronha Jr (Correct)
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An Overview of Quality-of-Service Routing for the Next.. - Chen, Nahrstedt (1998) (122 citations) (Correct)
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F. K. Hwang and D. S. Richards. Steiner tree problems. Networks, 22:55--89, 1992.
Hybrid Local Search for the Steiner Problem in Graphs - de Aragao, Ribeiro, Uchoa.. (2001) (Correct)
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Hwang, F., Richards, D. & Winter, P. (1992) The Steiner Tree Problem (North-Holland, Amsterdam), pp. 37-49.
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F. K. Hwang, D. S. Richards, and P. Winter, "The Steiner tree problem," in Annals of Discrete Mathematics. Amsterdam, The Netherlands: North-Holland, 1992, vol. 53, pp. 203--282.
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F. Hwang, D. Richards, Steiner tree problems, Networks 22 (1992) 55--89.
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