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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
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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
Lowdegree minimal spanning trees in normed spaces
, 2006
"... We give a complete proof that in any finitedimensional normed linear space a finite set of points has a minimal spanning tree in which the maximum degree is bounded above by the strict Hadwiger number of the unit ball, i.e., the largest number of unit vectors such that the distance between any two ..."
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We give a complete proof that in any finitedimensional normed linear space a finite set of points has a minimal spanning tree in which the maximum degree is bounded above by the strict Hadwiger number of the unit ball, i.e., the largest number of unit vectors such that the distance between any two is larger than 1. 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.
Relay Placement Approximation Algorithms for kConnectivity in Wireless Sensor Networks*
"... ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, ..."
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ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical,
Approximation Algorithms for the SingleSink Edge Installation Problems and Other Graph Problems
, 2004
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