The Optimal Linear Arrangement Problem
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The Optimal Linear Arrangement Problem
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Author : Steven B. Horton
language : en
Publisher:
Release Date : 1997
The Optimal Linear Arrangement Problem written by Steven B. Horton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Algorithms categories.
Trees And The Optimal Linear Arrangement Problem
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Author : Pramod R. Surve
language : en
Publisher:
Release Date : 2003
Trees And The Optimal Linear Arrangement Problem written by Pramod R. Surve and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Contributions To The Minimum Linear Arrangement Problem
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Author : Hanna Seitz
language : en
Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
Release Date : 2010
Contributions To The Minimum Linear Arrangement Problem written by Hanna Seitz and has been published by Sudwestdeutscher Verlag Fur Hochschulschriften AG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
The Minimum Linear Arrangement problem consists in finding an ordering of the nodes of a weighted graph, such that the sum of the weighted edge lengths is minimized. We report on the usefulness of a new model within a branch-and-cut-and-price algorithm for solving Minimum Linear Arrangement problems to optimality. The key idea is to introduce binary variables d_{ijk}, that are equal to 1 if nodes i and j have distance k in the permutation. We present formulations for complete and for sparse graphs and explain the realization of a branch-and-cut-and-price algorithm. Furthermore, its different settings are discussed and evaluated. To the study of the theoretical aspects concerning the Minimum Linear Arrangement problem, we contribute a characterization of a relaxation of the corresponding polyeder.
Optimal Linear Arrangement And Optimal Linear Ordering
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Author : D. Adolphson
language : en
Publisher:
Release Date : 1974
Optimal Linear Arrangement And Optimal Linear Ordering written by D. Adolphson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Linear orderings categories.
Consider a set of n pins and a required number of wire connections between each pair of the pins. The problem is to put the n pins into n holes such that the total wire length is a minimum. The holes are all in a line with adjacent holes at unit distance apart. The authors can abstract the pins and wire connections as a graph G with n nodes and numbers associated with the arcs. For an arbitrary G, a lower bound is established on the total wire length. If G is a rooted tree, an algorithm is presented which requires O(n log n) operations. (Modified author abstract).
Minimum Linear Arrangement Of Trees
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Author :
language : en
Publisher:
Release Date : 2002
Minimum Linear Arrangement Of Trees written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
In the minimum linear arrangement problem one is given a graph, and wishes to assign distinct integers to the vertices of the graph so that the sum of the differences (in absolute value) across the edges of the graph is minimized. This problem is known to be NP-complete for the class of all graphs, but polynomial for special classes of graphs, one of which is the class of trees. For trees on n vertices, algorithms of time complexity O(n2.2) and O(n1.6) were given by Shiloach in 1979 and Chung in 1983 respectively, with no improvement since then. In this thesis, we present a linear-time algorithm for finding the optimal embedding among those embeddings which have no "crossings," and we describe a C++ implementation of that algorithm as well as Shiloach's algorithm which we make available to the research community.
New Approximation Techniques For Some Ordering Problems
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Author : Carnegie-Mellon University. Computer Science Dept
language : en
Publisher:
Release Date : 1997
New Approximation Techniques For Some Ordering Problems written by Carnegie-Mellon University. Computer Science Dept and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computational complexity categories.
Abstract: "We describe O(log n) times optimal approximation algorithms for the NP-hard graph optimization problems of minimum linear arrangement, minimum containing interval graph, and minimum storage-time product. This improves on the O(log n log log n) approximation bounds provided in a previous paper by Even, Naor, Scheiber and Rao. Our techniques are based on using spreading metrics (as in Even, Naor, Rao, and Scheiber) to define a cost estimate for a problem. In this paper, we develop a recursion where at each level we identify cost which, if incurred, yields a reduction in the spreading metric cost estimates for the resulting subproblems. Specifically, we give a strategy where the cost of solving a problem at a recursive level is C plus the cost of solving the subproblems, and where the spreading metric cost estimate on the subproblem(s) is reduced by at least [omega](C/log n). This ensures that the resulting solution has cost at most O(log n) times the original spreading metric cost estimate. We note that this is an existentially tight bound on the relationship between the spreading metric cost estimates and the true optimal values for these problems. For planar graphs, we combine a structural theorem of Klein, Plotkin and Rao, with our new recursion and standard divide-and-conquer techniques to show that the spreading metric cost estimates are within an O(log log n) factor of the cost of the optimal solution for the minimum linear arrangement and the minimum containing interval graph problems."
New Approximation Techniques For Some Ordering Problems
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Author : Carnegie Mellon University. Computer Science Department
language : en
Publisher:
Release Date : 1997
New Approximation Techniques For Some Ordering Problems written by Carnegie Mellon University. Computer Science Department and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computational complexity categories.
Abstract: "We describe O(log n) times optimal approximation algorithms for the NP-hard graph optimization problems of minimum linear arrangement, minimum containing interval graph, and minimum storage-time product. This improves on the O(log n log log n) approximation bounds provided in a previous paper by Even, Naor, Scheiber and Rao. Our techniques are based on using spreading metrics (as in Even, Naor, Rao, and Scheiber) to define a cost estimate for a problem. In this paper, we develop a recursion where at each level we identify cost which, if incurred, yields a reduction in the spreading metric cost estimates for the resulting subproblems. Specifically, we give a strategy where the cost of solving a problem at a recursive level is C plus the cost of solving the subproblems, and where the spreading metric cost estimate on the subproblem(s) is reduced by at least [omega](C/log n). This ensures that the resulting solution has cost at most O(log n) times the original spreading metric cost estimate. We note that this is an existentially tight bound on the relationship between the spreading metric cost estimates and the true optimal values for these problems. For planar graphs, we combine a structural theorem of Klein, Plotkin and Rao, with our new recursion and standard divide-and-conquer techniques to show that the spreading metric cost estimates are within an O(log log n) factor of the cost of the optimal solution for the minimum linear arrangement and the minimum containing interval graph problems."
Proceedings Of The Ninth Annual Acm Siam Symposium On Discrete Algorithms
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Author : Howard Karloff
language : en
Publisher: SIAM
Release Date : 1998-01-01
Proceedings Of The Ninth Annual Acm Siam Symposium On Discrete Algorithms written by Howard Karloff and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
This symposium is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics.
Combinatorial Optimization And Applications
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Author : Andreas Dress
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-25
Combinatorial Optimization And Applications written by Andreas Dress and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-25 with Computers categories.
Running to almost 400 pages, and featuring more than 40 papers, this work on combinatorial optimization and applications will be seen as an important addition to the literature. It constitutes the refereed proceedings of the first International Conference on Combinatorial Optimization and Applications, COCOA 2007, held in Xi'an, China in August of that year. The 29 revised full papers presented together with 8 invited papers and 2 invited presentations were carefully reviewed and selected from 114 submissions and cover both theoretical issues and practical applications.
The Quadratic Assignment Problem
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Author : E. Cela
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
The Quadratic Assignment Problem written by E. Cela and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The quadratic assignment problem (QAP) was introduced in 1957 by Koopmans and Beckmann to model a plant location problem. Since then the QAP has been object of numerous investigations by mathematicians, computers scientists, ope- tions researchers and practitioners. Nowadays the QAP is widely considered as a classical combinatorial optimization problem which is (still) attractive from many points of view. In our opinion there are at last three main reasons which make the QAP a popular problem in combinatorial optimization. First, the number of re- life problems which are mathematically modeled by QAPs has been continuously increasing and the variety of the fields they belong to is astonishing. To recall just a restricted number among the applications of the QAP let us mention placement problems, scheduling, manufacturing, VLSI design, statistical data analysis, and parallel and distributed computing. Secondly, a number of other well known c- binatorial optimization problems can be formulated as QAPs. Typical examples are the traveling salesman problem and a large number of optimization problems in graphs such as the maximum clique problem, the graph partitioning problem and the minimum feedback arc set problem. Finally, from a computational point of view the QAP is a very difficult problem. The QAP is not only NP-hard and - hard to approximate, but it is also practically intractable: it is generally considered as impossible to solve (to optimality) QAP instances of size larger than 20 within reasonable time limits.