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Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
A Heuristic Algorithm for the Rectilinear Steiner Arborescence Problem
 Engineering Optimization
, 1994
"... In this paper the following problem is considered: given a root node R in a mesh and a set D of nodes from the mesh, construct a shortestpath tree rooted at R that spans the set D and minimizes the number of links used. The problem is equivalent as finding a Steiner tree in a directed mesh in whic ..."
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Cited by 6 (0 self)
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in which all the links point away from the root node R. The problem of finding a Steiner tree in such grid has been known in the literature as the Rectilinear Steiner Arborescence (RSA) problem. Rao et. al [9] have proposed an efficient heuristic algorithm for a special case of this problem, in which all
On the Approximation of the Rectilinear Steiner Arborescence Problem in the Plane
, 2000
"... We give a polynomial time approximation scheme (PTAS) for the rectilinear Steiner arborescence problem in the plane. The result is obtained by modifying Arora's PTAS for Euclidean TSP. The previously best known result was a 2approximation algorithm. Keywords: Analysis of algorithms, subopt ..."
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Cited by 1 (0 self)
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We give a polynomial time approximation scheme (PTAS) for the rectilinear Steiner arborescence problem in the plane. The result is obtained by modifying Arora's PTAS for Euclidean TSP. The previously best known result was a 2approximation algorithm. Keywords: Analysis of algorithms
Wireless Communications
, 2005
"... Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University ..."
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Cited by 1129 (32 self)
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Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University
On the Construction of Optimal or NearOptimal Rectilinear Steiner Arborescence
, 1994
"... Given a set of nodes N lying on the first quadrant of the Euclidean Plane E 2 , the Rectilinear Minimum Steiner Arborescence (RMSA) problem is to find a shortestpath tree of the minimum length rooted at the origin, containing all nodes in N , and composed solely of horizontal and vertical arcs or ..."
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Given a set of nodes N lying on the first quadrant of the Euclidean Plane E 2 , the Rectilinear Minimum Steiner Arborescence (RMSA) problem is to find a shortestpath tree of the minimum length rooted at the origin, containing all nodes in N , and composed solely of horizontal and vertical arcs
Fast Optimal Algorithms for the Minimum Rectilinear Steiner Arborescence Problem
 in Proc. IEEE Int. Symp. on Circuits and Systems
, 1997
"... In this paper, we present two optimal algorithms for solving the Minimum Rectilinear Steiner Arborescence (MRSA) Problem. The first algorithm is a recursive branchandbound variant of the RSA heuristic by Rao et al. [14]. The second algorithm uses dynamic programming to avoid solving the same subpr ..."
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Cited by 5 (2 self)
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In this paper, we present two optimal algorithms for solving the Minimum Rectilinear Steiner Arborescence (MRSA) Problem. The first algorithm is a recursive branchandbound variant of the RSA heuristic by Rao et al. [14]. The second algorithm uses dynamic programming to avoid solving the same
A Polynomial Time Approximation Scheme for the Symmetric Rectilinear Steiner Arborescence Problem
, 2002
"... The Symmetric Rectilinear Steiner Arborescence (SRStA) problem is defined as follows: given a set of terminals in the positive quadrant of the plane, connect them using horizontal and vertical lines such that each terminal can be reached from the origin via a ymonotone path and the total length o ..."
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Cited by 4 (2 self)
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The Symmetric Rectilinear Steiner Arborescence (SRStA) problem is defined as follows: given a set of terminals in the positive quadrant of the plane, connect them using horizontal and vertical lines such that each terminal can be reached from the origin via a ymonotone path and the total length
Algorithms for the Steiner Problem in Networks
, 2003
"... The Steiner problem in networks is the problem of connecting a set of required vertices in a weighted graph at minimum cost. It is a classical N Phard problem with many important applications. For this problem we develop, implement and test several new techniques. On the side of lower bounds, we pr ..."
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The Steiner problem in networks is the problem of connecting a set of required vertices in a weighted graph at minimum cost. It is a classical N Phard problem with many important applications. For this problem we develop, implement and test several new techniques. On the side of lower bounds, we
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
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