Results 11  20
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24
Small degree outbranchings
, 2001
"... Using a suitable orientation, we give a short proof of a result of Czumaj and Strothmann [3]: Every 2edgeconnected graph G contains a spanning tree T with the property that dT (v) ≤ dG(v)+3 for every vertex v. 2 Trying to find an analogue of this result in the directed case, we prove that every 2 ..."
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Using a suitable orientation, we give a short proof of a result of Czumaj and Strothmann [3]: Every 2edgeconnected graph G contains a spanning tree T with the property that dT (v) ≤ dG(v)+3 for every vertex v. 2 Trying to find an analogue of this result in the directed case, we prove that every 2arcstrong digraph D has an outbranching B such that d + d+
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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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
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
Improved Approximation Algorithms for SingleTiered Relay Placement ∗
, 2015
"... We consider the problem of SingleTiered Relay Placement with Basestations, which takes as input a set S of sensors and a set B of basestations described as points in a normed space (M,d), and real numbers 0 < r ≤ R. The objective is to place a minimum cardinality set Q of wireless relay nodes t ..."
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We consider the problem of SingleTiered Relay Placement with Basestations, which takes as input a set S of sensors and a set B of basestations described as points in a normed space (M,d), and real numbers 0 < r ≤ R. The objective is to place a minimum cardinality set Q of wireless relay nodes that connects S and B according to the following rules. The sensors in S can communicate within distance r, relay nodes in Q can communicate within distance R, and basestations are considered to have an infinite broadcast range. Together the sets S, B, and Q induce an undirected graph G = (V,E) defined as follows: V = S ∪ B ∪ Q and E = {uvu, v ∈ B} ∪ {uvu ∈ Q and v ∈ Q ∪ B and d(u, v) ≤ R} ∪ {uvu ∈ S and v ∈ S ∪ Q ∪ B and d(u, v) ≤ r}. Then Q connects S and B when this induced graph is connected. In the case of the
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 ..."
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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.