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Improved Steiner Tree Approximation in Graphs
, 2000
"... The Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialtime heuristic with an approximation ratio approaching 1 + 2 1:55, which improves upon the previously bestknown approximation ..."
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Cited by 197 (8 self)
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The Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialtime heuristic with an approximation ratio approaching 1 + 2 1:55, which improves upon the previously bestknown approximation algorithm of [10] with performance ratio 1:59.
THE PRIMALDUAL METHOD FOR APPROXIMATION ALGORITHMS AND ITS APPLICATION TO NETWORK DESIGN PROBLEMS
"... The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent researc ..."
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Cited by 123 (7 self)
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The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent research applying the primaldual method to problems in network design.
Tighter Bounds for Graph Steiner Tree Approximation
 SIAM Journal on Discrete Mathematics
, 2005
"... Abstract. The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialln 3 time heuristic that achieves a bestknown approximation ratio of 1 + ≈ 1.55 for general graphs 2 and best ..."
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Cited by 66 (7 self)
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Abstract. The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialln 3 time heuristic that achieves a bestknown approximation ratio of 1 + ≈ 1.55 for general graphs 2 and bestknown approximation ratios of ≈ 1.28 for both quasibipartite graphs (i.e., where no two nonterminals are adjacent) and complete graphs with edge weights 1 and 2. Our method is considerably simpler and easier to implement than previous approaches. We also prove the first known nontrivial performance bound (1.5 · OPT) for the iterated 1Steiner heuristic of Kahng and Robins in quasibipartite graphs.
Efficient steiner tree construction based on spanning graphs
 IEEE Transactions ComputerAided Design
, 2004
"... Abstract—The Steiner Minimal Tree (SMT) problem is a very important problem in very large scale integrated computeraided design. Given points on a plane, an SMT connects these points through some extra points (called Steiner points) to achieve a minimal total length. Even though there exist many he ..."
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Cited by 23 (3 self)
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Abstract—The Steiner Minimal Tree (SMT) problem is a very important problem in very large scale integrated computeraided design. Given points on a plane, an SMT connects these points through some extra points (called Steiner points) to achieve a minimal total length. Even though there exist many heuristic algorithms for this problem, they have either poor performances or expensive running time. This paper records an implementation of an efficient SMT algorithm that has a worst case running time of ( log) and a performance close to that of the Iterated 1Steiner algorithm. The algorithm efficiently combines Borah et al.’s edge substitute concept with Zhou et al.’s spanning graph. Extensive experimental studies are conducted to compare it with other programs. Index Terms—Graph algorithms, routing, Steiner tree. I.
Minimum steiner tree construction
 In Alpert, C.J., Mehta, D.P. and Sapatnekar, S.S. (eds), The Handbook of Algorithms for VLSI Physical Design Automation
, 2009
"... In optimizing the area of Very Large Scale Integrated (VLSI) layouts, circuit interconnections should generally be realized with minimum total interconnect. This chapter addresses several variations of the corresponding fundamental Steiner minimal tree (SMT) problem, where a given set of pins is to ..."
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Cited by 2 (0 self)
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In optimizing the area of Very Large Scale Integrated (VLSI) layouts, circuit interconnections should generally be realized with minimum total interconnect. This chapter addresses several variations of the corresponding fundamental Steiner minimal tree (SMT) problem, where a given set of pins is to be connected using minimum total wirelength. Steiner trees are important in
Practical Approximations of Steiner Trees in Uniform Orientation Metrics
"... The Steiner minimum tree problem, which asks for a minimumlength interconnection of a given set of terminals in the plane, is one of the fundamental problems in Very Large Scale Integration (VLSI) physical design. Although advances in VLSI manufacturing technologies have introduced additional rout ..."
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The Steiner minimum tree problem, which asks for a minimumlength interconnection of a given set of terminals in the plane, is one of the fundamental problems in Very Large Scale Integration (VLSI) physical design. Although advances in VLSI manufacturing technologies have introduced additional routing objectives, minimum length continues to be the primary objective when routing noncritical nets, since the minimumlength
3A1 A Novel PerformanceDriven Topology Design Algorithm
"... Abstract — This paper presents a very efficient algorithm for performancedriven topology design for interconnects. Given a net, it first generates Atree1 topology using table lookup and netbreaking. Then a performancedriven postprocessing heuristic not restricting to Atree topology improves th ..."
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Abstract — This paper presents a very efficient algorithm for performancedriven topology design for interconnects. Given a net, it first generates Atree1 topology using table lookup and netbreaking. Then a performancedriven postprocessing heuristic not restricting to Atree topology improves the obtained topology by considering the sink positions, required time and load capacitance to achieve better timing. Experimental results show that our new technique can produce topologies with better timing and is hundreds of times faster than traditional approach. I.
Rio Design Automation
"... FLUTE [1, 2] is a very fast and accurate rectilinear Steiner minimal tree (RSMT) 1 algorithm particularly suitable for VLSI applications. It is optimal for nets up to degree 9 and is still very accurate for nets up to degree 30. However, for higher degree nets, the original FLUTE algorithm is not ef ..."
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FLUTE [1, 2] is a very fast and accurate rectilinear Steiner minimal tree (RSMT) 1 algorithm particularly suitable for VLSI applications. It is optimal for nets up to degree 9 and is still very accurate for nets up to degree 30. However, for higher degree nets, the original FLUTE algorithm is not effective. In this paper, we present an improvement of FLUTE which is more effective in handling nets with degree tens or more. The main idea is to partition a net according to a spanning tree into small subnets that can be handled effectively by the original FLUTE algorithm. Several novel techniques are proposed to partition a net into small subnets and to merge the Steiner trees for the subnets together. Some improvements of the original FLUTE algorithm, and a scheme to allow users to control the tradeoff between accuracy and runtime are also presented. We show experimentally that the resulting algorithm FLUTE3.0 achieves a much better accuracyruntime tradeoff than the original FLUTE algorithm for degree 30 or more. It produces better quality of result than the wellknown nearoptimal BI1S algorithm [3] in a runtime shorter than the highly scalable BGA algorithm [4]. FLUTE3.0 is also highly scalable. It can route a 3millionpin net in about 25 minutes. 1
Resilience Provisioning Mechanisms for IPCentric Optical Networks By
"... To accommodate the increasing volume of Internet traffic brought about by the growing user community and new enterprise applications, optical networks are being deployed at unprecedented rates. This trend is changing the fundamental way in which optical transport networks are being designed and oper ..."
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To accommodate the increasing volume of Internet traffic brought about by the growing user community and new enterprise applications, optical networks are being deployed at unprecedented rates. This trend is changing the fundamental way in which optical transport networks are being designed and operated. Traditional optical networks have been configured as static physical pipes to expand the transport capacity. In such a network, carriergrade network resilience is provided by the protection and restoration facility in the SONET (Synchronous Optical Network) / SDH (Synchronous Digital Hierarchy) “transport ” layer with the network topology mainly being ringbased. However, this solution has many limitations and cannot provide fast connection provisioning which is essential to the realisation of highvalue broadband services. Thus there are efforts to develop a new generation of dynamic reconfigurable optical networks with an IPcentric control plane. This research investigates how optical resilience could be efficiently provisioned in such an infrastructure. In addition, traditional optical networks have been deployed to meet the demands of