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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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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
Wireless network design via 3decompositions
 Inf. Process. Lett
"... We consider some network design problems with applications for wireless networks. The input for these problems is a metric space (X,d) and a finite subset U ⊆ X of terminals. In the Steiner Tree with Minimum Number of Steiner Points (STMSP) problem, the goal is to find a minimum size set S ⊆ X − U o ..."
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We consider some network design problems with applications for wireless networks. The input for these problems is a metric space (X,d) and a finite subset U ⊆ X of terminals. In the Steiner Tree with Minimum Number of Steiner Points (STMSP) problem, the goal is to find a minimum size set S ⊆ X − U of points so that the unitdisc graph of S + U is connected. Let ∆ be the smallest integer so that for any finite V ⊆ X for which the unitdisc graph is connected, this graph contains a spanning tree with maximum degree ≤ ∆. The best known approximation ratio for STMSP was ∆ − 1 [10]. We improve this ratio to ⌊( ∆ + 1)/2 ⌋ + 1 + ε. In the Minimum Power Spanning Tree (MPST) problem, V = X is finite, and the goal is to find a “range assignment ” {p(v) : v ∈ V} on the nodes so that the edge set {uv ∈ E: d(uv) ≤ min{p(u),p(v)}} contains a spanning tree, and ∑ v∈V p(v) is minimized. We consider a particular case {0,1}MPST of MPST when the distances are in {0,1}; here the goal is to find a minimum size set S ⊆ V of ”active ” nodes so that the graph (V,E0 + E1(S)) is connected, where E0 = {uv: d(uv) = 0}, and E1(S) is the set the edges in E1 = {uv: d(uv) = 1} with both endpoints in S. We will show that the (5/3+ε)approximation scheme for MPST of [1] achieves a ratio 3/2 for {0,1}distances. This answers an open question posed in [9].
An efficient lowdegree RMST algorithm for VLSI/ULSI physical design
 in Lecture Notes in Computer Science (LNCS) 3254—Integrated Circuit and System Design
, 2004
"... Abstract. Motivated by very/ultra large scale integrated circuit (VLSI/ULSI) physical design applications, we study the construction of rectilinear minimum spanning tree (RMST) with its maximum vertex degree as the constraint. Given a collection of n points in the plane, we firstly construct a graph ..."
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Abstract. Motivated by very/ultra large scale integrated circuit (VLSI/ULSI) physical design applications, we study the construction of rectilinear minimum spanning tree (RMST) with its maximum vertex degree as the constraint. Given a collection of n points in the plane, we firstly construct a graph named the boundeddegree neighborhood graph (BNG). Based on this framework, we propose an O(n log n) algorithm to construct a 4BDRMST (RMST with maximum vertex degree ≤ 4). This is the first 4BDRMST algorithm with such a complexity, and experimental results show that the algorithm is significantly faster than the existing 4BDRMST algorithms. 1
New lower bounds for the Hadwiger numbers of l_p balls for p < 2
, 1996
"... In this note we derive an asymptotic lower bound for the size of constant weight binary codes that is exponential in the code length, if both the minimum distance and the weight grow in proportion to the code length. ..."
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In this note we derive an asymptotic lower bound for the size of constant weight binary codes that is exponential in the code length, if both the minimum distance and the weight grow in proportion to the code length.
E cient Minimum Spanning Tree Construction
"... Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least (n 2) time. More e cie ..."
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Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least (n 2) time. More e cient approaches nd a minimum spanning tree only among edges in the Delaunay triangulation of the points. However, Delaunay triangulation is not well de ned in rectilinear distance. In this paper, we rst establish a framework for minimum spanning tree construction which is based on a general concept of spanning graphs. A spanning graph is a natural de nition and not necessarily a Delaunay triangulation. Based on this framework, we then design an O(n log n) sweepline algorithm to construct a rectilinear minimum spanning tree without using Delaunay triangulation. 1