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Highly scalable algorithms for rectilinear and octilinear Steiner trees
 In Proc. Asian and South Pacific Design Automation Conf
, 2003
"... problem, which asks for a minimumlength interconnection of a given set of terminals in the rectilinear plane, is one of the fundamental problems in electronic design automation. Recently there has been renewed interest in this problem due to the need for highly scalable algorithms able to handle ne ..."
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Cited by 29 (3 self)
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problem, which asks for a minimumlength interconnection of a given set of terminals in the rectilinear plane, is one of the fundamental problems in electronic design automation. Recently there has been renewed interest in this problem due to the need for highly scalable algorithms able to handle nets with tens of thousands of terminals. In this paper we give a practical � heuristic for computing nearoptimal rectilinear Steiner trees based on a batched version of the greedy triple contraction algorithm of Zelikovsky [21]. Experiments conducted on both random and industry testcases show that our heuristic matches or exceeds the quality of best known RSMT heuristics, e.g., on random instances with more than 100 terminals our heuristic improves over the rectilinear minimum spanning tree by an average of 11%. Moreover, our heuristic has very well scaling runtime, e.g., it can route a 34kterminals net extracted from a real design in less than 25 seconds compared to over 86 minutes needed by the edgebased heuristic of Borah, Owens, and Irwin [3]. Since our heuristic is graphbased, it can be easily modified to handle practical considerations such as routing obstacles, preferred directions, via costs, and octilinear routing – indeed, experimental results show only a small factor increase in runtime when switching from rectilinear to octilinear routing. I.
FOARS: FLUTE based obstacleavoiding rectilinear Steiner tree construction
 In Proc. of ISPD
, 2010
"... Obstacleavoiding rectilinear Steiner minimal tree (OARSMT) construction is becoming one of the most sought after problems in modern design flow. In this paper we present FOARS, an algorithm to route a multiterminal net in the presence of obstacles. FOARS is a top down approach which includes parti ..."
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Cited by 6 (1 self)
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Obstacleavoiding rectilinear Steiner minimal tree (OARSMT) construction is becoming one of the most sought after problems in modern design flow. In this paper we present FOARS, an algorithm to route a multiterminal net in the presence of obstacles. FOARS is a top down approach which includes partitioning the initial solution into subproblems and using obstacle aware version of Fast Lookup Table based Wirelength Estimation (OAFLUTE) at a lower level to generate an OAST followed by recombining them with some backend refinement. To construct an initial connectivity graph FOARS uses a novel obstacleavoiding spanning graph (OASG) algorithm which is a generalization of Zhou’s spanning graph algorithm without obstacle [1]. FOARS has a run time complexity of O(nlog n). Our experimental results
The MST of Symmetric Disk Graphs (in Arbitrary Metric Spaces) is Light
, 2011
"... Consider an npoint metric space M = (V, δ), and a transmission range assignment r: V → R + that maps each point v ∈ V to the disk of radius r(v) around it. The symmetric disk graph (henceforth, SDG) that corresponds to M and r is the undirected graph over V whose edge set includes an edge (u, v) if ..."
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Consider an npoint metric space M = (V, δ), and a transmission range assignment r: V → R + that maps each point v ∈ V to the disk of radius r(v) around it. The symmetric disk graph (henceforth, SDG) that corresponds to M and r is the undirected graph over V whose edge set includes an edge (u, v) if both r(u) and r(v) are no smaller than δ(u, v). SDGs are often used to model wireless communication networks. AbuAffash, Aschner, Carmi and Katz (SWAT 2010, [1]) showed that for any npoint 2dimensional Euclidean space M, the weight of the MST of every connected SDG for M is O(log n) · w(MST(M)), and that this bound is tight. However, the upper bound proof of [1] relies heavily on basic geometric properties of constantdimensional Euclidean spaces, and does not extend to Euclidean spaces of superconstant dimension. A natural question that arises is whether this surprising upper bound of [1] can be generalized for wider families of metric spaces, such as highdimensional Euclidean spaces. In this paper we generalize the upper bound of AbuAffash et al. [1] for Euclidean spaces of any dimension. Furthermore, our upper bound extends to arbitrary metric spaces and, in particular, it applies to any of the normed spaces ℓp. Specifically, we demonstrate that for any npoint metric space M, the weight of the MST of every connected SDG for M is O(log n) · w(MST(M)).
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
ISPD: FOARS: FLUTE Based ObstacleAvoiding Rectilinear Steiner Tree Construction
"... In this paper, we present an algorithm called FOARS for obstacleavoiding rectilinear Steiner minimal tree (OARSMT) construction. FOARS applies a topdown approach which first partitions the set of pins into several subsets uncluttered by obstacles. Then an obstacleavoiding Steiner tree is generat ..."
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In this paper, we present an algorithm called FOARS for obstacleavoiding rectilinear Steiner minimal tree (OARSMT) construction. FOARS applies a topdown approach which first partitions the set of pins into several subsets uncluttered by obstacles. Then an obstacleavoiding Steiner tree is generated for each subset by an obstacle aware version of the rectilinear Steiner minimal tree (RSMT) algorithm FLUTE. Finally, the trees are merged and refined to form the OARSMT. To guide the partitioning of pins, we propose a novel algorithm to construct a linearsized obstacleavoiding spanning graph (OASG) which guarantees to contain a rectilinear minimum spanning tree if there is no obstacle. Experimental results show that FOARS is among the best algorithms in terms of both wirelength and runtime for testcases both with and without obstacles.
A Study on Approximation Algorithms for Constructing Rectilinear Steiner Trees
"... Abstract — The Steiner tree problem is one of the complex, combinatorial optimization problems in the graph theory literature. Solving Steiner tree problem is of great importance since its application includes VLSI physical design, routing, wire length estimation etc. The variant of the Steiner tree ..."
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Abstract — The Steiner tree problem is one of the complex, combinatorial optimization problems in the graph theory literature. Solving Steiner tree problem is of great importance since its application includes VLSI physical design, routing, wire length estimation etc. The variant of the Steiner tree called Rectilinear Steiner tree is used in the various phases of VLSI design and finding the Minimum Rectilinear Steiner tree is the problem that is in much research. Since the problem is NPhard, a lot of research is focused in designing good heuristics and approximation algorithms. This paper is a brief study on the different approximation and heuristic algorithms for solving Rectilinear Steiner tree problem.