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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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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
Presented to
, 2000
"... This thesis gives improved approximation algorithms and heuristics for several NPhard problems arising in the global routing phase of physical VLSI design. In each of these problems interconnection topologies must be specified for nets consisting of a source and multiple sink terminals. Different o ..."
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This thesis gives improved approximation algorithms and heuristics for several NPhard problems arising in the global routing phase of physical VLSI design. In each of these problems interconnection topologies must be specified for nets consisting of a source and multiple sink terminals. Different optimization objectives are used, depending on the functionality of the nets. We address the singlenet routing problem under three of the most important objectives: minimizing length, skew, and number of buffers. We also address a multinet global buffered routing problem in which a large number of nets must be routed simultaneously using only buffers located in a given set of regions, each with prescribed capacity. The problem of finding a minimumlength interconnection of a net using only horizontal and vertical wires, the so called rectilinear Steiner tree (RST) problem, has long been one of the fundamental problems in the field of electronic design automation. In this thesis we give a new RST heuristic which has at its core a recent 3/2 approximation algorithm of Rajagopalan and Vazirani for the metric Steiner tree problem on quasibipartite graphs— these are graphs that do not contain edges connecting pairs of Steiner vertices. Our new RST
Approximation Algorithms for VLSI Routing
, 2000
"... This thesis gives improved approximation algorithms and heuristics for several NPhard problems arising in the global routing phase of physical VLSI design. In each of these problems interconnection topologies must be specified for nets consisting of a source and multiple sink terminals. Different o ..."
Abstract
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This thesis gives improved approximation algorithms and heuristics for several NPhard problems arising in the global routing phase of physical VLSI design. In each of these problems interconnection topologies must be specified for nets consisting of a source and multiple sink terminals. Different optimization objectives are used, depending on the functionality of the nets. We address the singlenet routing problem under three of the most important objectives: minimizing length, skew, and number of buffers. We also address a multinet global buffered routing problem in which a large number of nets must be routed simultaneously using only buffers located in a given set of regions, each with prescribed capacity. The problem of finding a minimumlength interconnection of a net using only horizontal and vertical wires, the so called rectilinear Steiner tree (RST) problem, has long been one of the fundamental problems in the field of electronic design automation. In this thesis we give a new RST heuristic which has at its core a recent 3/2 approximation algorithm of Rajagopalan and Vazirani for the metric Steiner tree problem on quasibipartite graphs— these are graphs that do not contain edges connecting pairs of Steiner vertices. Our new RST
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.
Approximation Algorithms for the SingleSink Edge Installation Problems and Other Graph Problems
, 2004
"... vi LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv CHAPTER ..."
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vi LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv CHAPTER 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