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On the Hardness of Full Steiner Tree Problems
, 2014
"... Given a weighted graph G = (V,E) and a subset R of V, a Steiner tree in G is a tree which spans all vertices in R. The vertices in V \R are called Steiner vertices. A full Steiner tree is a Steiner tree in which each vertex of R is a leaf. The full Steiner tree problem is to find a full Steiner tree ..."
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Given a weighted graph G = (V,E) and a subset R of V, a Steiner tree in G is a tree which spans all vertices in R. The vertices in V \R are called Steiner vertices. A full Steiner tree is a Steiner tree in which each vertex of R is a leaf. The full Steiner tree problem is to find a full Steiner
Steiner tree problems with profits
 INFOR: Information Systems and Operational Research
, 2006
"... Abstract This is a survey of the Steiner tree problem with profits, a variation of the classical Steiner problem where, besides the costs associated with edges, there are also revenues associated with vertices. The relationships between these costs and revenues are taken into consideration when dec ..."
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Cited by 9 (0 self)
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Abstract This is a survey of the Steiner tree problem with profits, a variation of the classical Steiner problem where, besides the costs associated with edges, there are also revenues associated with vertices. The relationships between these costs and revenues are taken into consideration when
Packing Steiner Trees
"... Let T be a distinguished subset of vertices in a graph G. A TSteiner tree is a subgraph of G that is a tree and that spans T. Kriesell conjectured that G contains k pairwise edgedisjoint TSteiner trees provided that every edgecut of G that separates T has size ≥ 2k. When T = V (G) a TSteiner t ..."
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Let T be a distinguished subset of vertices in a graph G. A TSteiner tree is a subgraph of G that is a tree and that spans T. Kriesell conjectured that G contains k pairwise edgedisjoint TSteiner trees provided that every edgecut of G that separates T has size ≥ 2k. When T = V (G) a TSteiner
On MinPower Steiner Tree⋆
"... an edgeweighted undirected graph and a set of terminal nodes. The goal is to compute a mincost tree S which spans all terminals. In this paper we consider the minpower version of the problem (a.k.a. symmetric multicast), which is better suited for wireless applications. Here, the goal is to mini ..."
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as to support protocols with ack messages). Observe that we do not require that edge costs reflect Euclidean distances between nodes: this way we can model obstacles, limited transmitting power, nonomnidirectional antennas etc. Differently from its mincost counterpart, minpower Steiner tree is NPhard even
Preferred Direction Steiner Trees
"... Interconnect optimization for VLSI circuits has received wide attention. To model routing surfaces, multiple circuit layers are frequently abstracted as a single rectilinear plane, ignoring via costs, layer dependent routing costs, and congestion impact for routing in a particular direction. In this ..."
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Cited by 8 (0 self)
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. In this paper, we consider preferred direction multilayer routing, which more closely models practical applications. We adapt a well known rectilinear planar Steiner tree heuristic, resulting in a new method to construct low cost Steiner trees under a realistic model. Our implementation is fast and effective
The Steiner tree polytope and related polyhedra
, 1994
"... We consider the vertexweighted version of the undirected Steiner tree problem. In this problem, a cost is incurred both for the vertices and the edges present in the Steiner tree. We completely describe the associated polytope by linear inequalities when the underlying graph is seriesparallel. For ..."
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Cited by 31 (1 self)
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We consider the vertexweighted version of the undirected Steiner tree problem. In this problem, a cost is incurred both for the vertices and the edges present in the Steiner tree. We completely describe the associated polytope by linear inequalities when the underlying graph is series
Creating and Exploiting Flexibility in Steiner Trees
 IN PROC. ACM/IEEE DESIGN AUTOMATION CONFERENCE
, 2001
"... This paper presents the concept of flexibility  a geometric property associated with Steiner trees. Flexibility is related to the routability of the Steiner tree. We present an optimal algorithm which takes a Steiner tree and outputs a more flexible Steiner tree. Our experiments show that a net wi ..."
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Cited by 8 (3 self)
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This paper presents the concept of flexibility  a geometric property associated with Steiner trees. Flexibility is related to the routability of the Steiner tree. We present an optimal algorithm which takes a Steiner tree and outputs a more flexible Steiner tree. Our experiments show that a net
Creating and Exploiting Flexibility in Steiner Trees
 In Proc. ACM/IEEE Design Automation Conference
, 2001
"... This paper presents the concept of flexibility  a geometric property associated with Steiner trees. Flexibility is related to the routability of the Steiner tree. We present an optimal algorithm which takes a Steiner tree and outputs a more flexible Steiner tree. Our experiments show that a net wi ..."
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This paper presents the concept of flexibility  a geometric property associated with Steiner trees. Flexibility is related to the routability of the Steiner tree. We present an optimal algorithm which takes a Steiner tree and outputs a more flexible Steiner tree. Our experiments show that a net
On Directed Steiner Trees
 In 13th Annual ACMSIAM Symposium on Discrete Algorithms
, 2002
"... The directed Steiner tree problem is the following: given a directed graph G = (V; E) with weights on the edges, a set of terminals S ` V , and a root vertex r, find a minimum weight outbranching T rooted at r, such that all vertices in S are included in T . This problem is known to be NPhard. Rece ..."
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The directed Steiner tree problem is the following: given a directed graph G = (V; E) with weights on the edges, a set of terminals S ` V , and a root vertex r, find a minimum weight outbranching T rooted at r, such that all vertices in S are included in T . This problem is known to be NPhard
Local Improvement in Steiner Trees
 PROC. OF THE 3RD GREAT LAKES SYMP. ON VLSI
, 1993
"... Next to the traveling salesman problem, the Steiner problem is possibly the most mentioned NPcomplete problem in existence. This is due to the ease with which it can be stated (join a set of points with the smallest collection of connections) and its many, varied applications. For example, with a ..."
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Cited by 4 (0 self)
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, with a rectilinear metric, Steiner spanning trees are used in several phases of CAD for VLSI systems. Since this problem is NPcomplete [GJ77], most attempts at solving it have been heuristics based on paradigms such as minimal spanning tree modification, computational geometry, stochastic evolution
Results 11  20
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