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10
Problems in Computational Geometry
 Packing and Covering
, 1974
"...  reproduced, stored In a retrieval system, or transmlt'ted, In any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the author. ..."
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Cited by 452 (2 self)
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 reproduced, stored In a retrieval system, or transmlt'ted, In any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the author.
VLSI cell placement techniques
 ACM Computing Surveys
, 1991
"... VLSI cell placement problem is known to be NP complete. A wide repertoire of heuristic algorithms exists in the literature for efficiently arranging the logic cells on a VLSI chip. The objective of this paper is to present a comprehensive survey of the various cell placement techniques, with emphasi ..."
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Cited by 74 (0 self)
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VLSI cell placement problem is known to be NP complete. A wide repertoire of heuristic algorithms exists in the literature for efficiently arranging the logic cells on a VLSI chip. The objective of this paper is to present a comprehensive survey of the various cell placement techniques, with emphasis on standard ce11and macro
Estimating Bounds for Quadratic Assignment Problems Associated with Hamming and Manhattan Distance Matrices based on Semidefinite Programming
, 2008
"... Quadratic assignment problems (QAPs) with a Hamming distance matrix for a hypercube or a Manhattan distance matrix for a rectangular grid arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems. In this paper we consider the is ..."
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Cited by 6 (2 self)
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Quadratic assignment problems (QAPs) with a Hamming distance matrix for a hypercube or a Manhattan distance matrix for a rectangular grid arise frequently from communications and facility locations and are known to be among the hardest discrete optimization problems. In this paper we consider the issue of how to obtain lower bounds for those two classes of QAPs based on semidefinite programming (SDP). By exploiting the data structure of the distance matrix B, we first show that for any permutation matrix X, the matrix Y = αE − XBX T is positive semidefinite, where α is a properly chosen parameter depending only on the associated graph in the underlying QAP and E = ee T is a rank one matrix whose elements have value 1. This results in a natural way to approximate the original QAPs via SDP relaxation based on the matrix splitting technique. Our new SDP relaxations have a smaller size compared with other SDP relaxations in the literature and can be solved efficiently by most open source SDP solvers. Experimental results show that for the underlying QAPs of size up to n=200, strong bounds can be obtained effectively.
An Investigation of Genetic Algorithms for Facility Layout Problems
 University of Edinburgh
, 1995
"... The Facility Layout Problem (FLP) concerns minimising total traffic cost between facilities in a particular location under given conditions including facility size and traffic between each pair of them. Because of its NPcompleteness, many suboptimal methods, which look for reasonably good solutions ..."
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Cited by 5 (0 self)
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The Facility Layout Problem (FLP) concerns minimising total traffic cost between facilities in a particular location under given conditions including facility size and traffic between each pair of them. Because of its NPcompleteness, many suboptimal methods, which look for reasonably good solutions, have been suggested. Although many papers exist which compare the performance of these methods with each other, the work is limited in the following ways: benchmark tests were done only on FLPs consisting of identical facilities; most of the algorithms being compared relied on deterministic approaches. Genetic Algorithms (GAs), which use a stochastic approach, have been used with some success for a number of NPcomplete problems, typically finding good answers but not necessarily the best. However, a range of other approaches, from traditional operations research to simulated annealing, are possible. Moreover, a GA itself can be varied in many ways. So, in this research project, not only t...
Graph Modeling for Quadratic Assignment Problem Associated with the Hypercube
, 2007
"... Abstract. In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at le ..."
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Cited by 3 (3 self)
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Abstract. In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs. Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n − 1) binary variables and O(n 3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.
New Convex Relaxations for Quadratic Assignment Problems
, 2008
"... Quadratic assignment problems (QAPs) are known to be among the hardest discrete optimization problems. Recent study shows that even obtaining a strong lower bound for QAPs is a computational challenge. In this paper, we first discuss how to construct new simple convex relaxations of QAPs based on va ..."
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Cited by 3 (2 self)
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Quadratic assignment problems (QAPs) are known to be among the hardest discrete optimization problems. Recent study shows that even obtaining a strong lower bound for QAPs is a computational challenge. In this paper, we first discuss how to construct new simple convex relaxations of QAPs based on various matrix splitting schemes. Then we introduce the socalled symmetric mappings that can be used to derive strong cuts for the proposed relaxation model. We show that the bounds based on the new models are comparable to the strongest bounds in the literature. Promising experimental results based on the new relaxations will be reported. Key words. Quadratic Assignment Problem (QAP), Semidefinite Programming
A Modified Simulated Annealing Algorithm for the Quadratic Assignment Problem
, 2003
"... Abstract. The quadratic assignment problem (QAP) is one of the wellknown combinatorial optimization problems and is known for its various applications. In this paper, we propose a modified simulated annealing algorithm for the QAP – MSAQAP. The novelty of the proposed algorithm is an advanced for ..."
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Abstract. The quadratic assignment problem (QAP) is one of the wellknown combinatorial optimization problems and is known for its various applications. In this paper, we propose a modified simulated annealing algorithm for the QAP – MSAQAP. The novelty of the proposed algorithm is an advanced formula of calculation of the initial and final temperatures, as well as an original cooling schedule with oscillation, i.e., periodical decreasing and increasing of the temperature. In addition, in order to improve the results obtained, the simulated annealing algorithm is combined with a tabu search approach based algorithm. We tested our algorithm on a number of instances from the library of the QAP instances – QAPLIB. The results obtained from the experiments show that the proposed algorithm appears to be superior to earlier versions of the simulated annealing for the QAP. The power of MSAQAP is also corroborated by the fact that the new best known solution was found for the one of the largest QAP instances – THO150. Key words: heuristics, local search, simulated annealing, quadratic assignment problem. 1.
PARALLEL ALGORITHMS FOR PLACEMENT AND ROUTING IN VLSI DESIGN
, 1991
"... The computational requirements for high quality synthesis, analysis, and verification of VLSI designs have rapidly increased with the fast growing complexity of these designs. Research in the past has focused on the development of heuristic algorithms, special purpose hardware accelerators, or paral ..."
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Cited by 2 (0 self)
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The computational requirements for high quality synthesis, analysis, and verification of VLSI designs have rapidly increased with the fast growing complexity of these designs. Research in the past has focused on the development of heuristic algorithms, special purpose hardware accelerators, or parallel algorithms for the numerous design tasks to decrease the tirn,e required for solution. In this thesis, we propose two new parallel algorithms for two VLSI synthesis tasks, standard cell placement and global routing. The first algorithm, a parallel algorithm for global routing, uses hierarchical techniques to decompose the routing problem into independent routing subproblems that are solved in parallel. Results are then presented which compare the routing quality to the results of other published global routers and which evaluate the speedups attained. The second algorithm, a parallel algorithm for cell placement and global routing, hierarchically integrates a quadrisection placement algorithrr{, a bisection placement algorithm, and the previous global routing algorithm. Unique partitioning techniques are used to decompose the various stages of the algorithm into independent tasks which can be evaluated in parallel. Finally, we present results which evaluate the various algorithm alternatives and compare the algorithm performance to other placement programs, and we present measurements on the parallel speedups available.
ZeroChange Netlist Transformations: A New Technique for Placement Benchmarking
"... In this paper we introduce the concept of zerochange netlist transformations to (1) quantify the suboptimality of existing placers on artificially constructed instances, and (2) “partially ” quantify the suboptimality of placers on synthesized netlists from arbitrary netlists by giving lower bounds ..."
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In this paper we introduce the concept of zerochange netlist transformations to (1) quantify the suboptimality of existing placers on artificially constructed instances, and (2) “partially ” quantify the suboptimality of placers on synthesized netlists from arbitrary netlists by giving lower bounds to the suboptimality gap. Given a netlist and its placement from a placer, we formally define a class of netlist transformations that synthesize a different netlist from the given netlist but yet the new netlist has the same HalfPerimeter Wire Length (HPWL) on the given placement. Furthermore, and more importantly, the optimal HPWL value of the new netlist is no less than that of the original netlist. By applying our transformations and reexecuting the placer, we can interpret any deviation in HPWL as a lower bound to the gap from the optimal HPWL value of the new synthesized netlist. Our transformations allow us to (1) increase the cardinality of hyperedges, (2) reduce the number of hyperedges, and (3) increase the number of twopin edges, while maintaining the placement HPWL constant. We also develop methods that apply zerochange netlist transformations to synthesize netlists having typical netlist statistics. Furthermore, we extend our approach to estimate suboptimality of other metrics such as rectilinear minimumspanning tree (RMST) and minimumSteiner tree. Using these transformations, the suboptimality of some of the existing academic placers (FengShui [35], Capo [4], mPL [10], Dragon
A New Relaxation Framework for Quadratic Assignment Problems based on Matrix Splitting
, 2010
"... Quadratic assignment problems (QAPs) are known to be among the hardest discrete optimization problems. Recent study shows that even obtaining a strong lower bound for QAPs is a computational challenge. In this paper, we first discuss how to construct new simple convex relaxations of QAPs based on va ..."
Abstract
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Quadratic assignment problems (QAPs) are known to be among the hardest discrete optimization problems. Recent study shows that even obtaining a strong lower bound for QAPs is a computational challenge. In this paper, we first discuss how to construct new simple convex relaxations of QAPs based on various matrix splitting schemes. Then we introduce the socalled symmetric mappings that can be used to derive strong cuts for the proposed relaxation model. We show that the bounds based on the new models are comparable to some strong bounds in the literature. Promising experimental results based on the new relaxations will be reported.