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Maximum Planar Subgraphs and Nice Embeddings: Practical Layout Tools
 ALGORITHMICA
, 1996
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Solving the Maximum Weight Planar Subgraph Problem by Branch and Cut
 PROCEEDINGS OF THE THIRD CONFERENCE ON INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION
, 1993
"... In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3 ..."
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Cited by 11 (1 self)
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In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3;3 , turn out to define facets of this polytope. We also present computational experience with a branch and cut algorithm for the above problem. Our approach is based on an algorithm which searches for forbidden substructures in a graph that contains a subdivision of K 5 or K 3;3 . These structures give us inequalities which are used as cutting planes.
A New Approximation Algorithm for Finding Heavy Planar Subgraphs
 ALGORITHMICA
, 1997
"... We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NPHard problem of finding a heaviest planar subgraph in an edgeweighted graph G. This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM ..."
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Cited by 9 (2 self)
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We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NPHard problem of finding a heaviest planar subgraph in an edgeweighted graph G. This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH had performance ratio exceeding 1=3, which is obtained by any algorithm that produces a maximum weight spanning tree in G. Based on the BermanRamaiyer Steiner tree algorithm, the new algorithm has performance ratio at least 1/3 + 1/72. We also show that if G is complete and its edge weights satisfy the triangle inequality, then the performance ratio is at least 3/8. Furthermore, we derive the first nontrivial performance ratio (7/12 instead of 1/2) for the NPHard MAXIMUM WEIGHT OUTERPLANAR SUBGRAPH problem.
ProximityBased Adjacency Determination for Facility Layout
"... We define a new model for adjacency subgraph selection for the facility layout problem based on proximity and present some heuristics for its solution. The new model presents a more realistic representation of the problem than previous ones in that departments which are nonadjacent yet "clo ..."
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Cited by 2 (0 self)
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We define a new model for adjacency subgraph selection for the facility layout problem based on proximity and present some heuristics for its solution. The new model presents a more realistic representation of the problem than previous ones in that departments which are nonadjacent yet "close" to each other are compensated in the determination of the optimal adjacency subgraph. Empirical results comparing the heuristics with the method of Leung [17] are reported.
Considering Production Uncertainty In Block Layout Design
, 1999
"... This paper presents a formulation of the facilities block layout problem which explicitly considers uncertainty in material handling costs by use of expected values and standard deviations of product forecasts. This formulation is solved using a genetic algorithm metaheuristic with a flexible ba ..."
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This paper presents a formulation of the facilities block layout problem which explicitly considers uncertainty in material handling costs by use of expected values and standard deviations of product forecasts. This formulation is solved using a genetic algorithm metaheuristic with a flexible bay construct of the departments and total facility area. It is shown that depending on the attitude of the decisionmaker towards uncertainty, the optimal layout can change significantly. Furthermore, designs can be optimized directly for robustness over a range of uncertainty that is prespecified by the user. Keywords  facilities, heuristics, optimisation, genetic algorithms, block layout, production uncertainty 1. Introduction Facility design problems generally involve the partition of a planar region into departments (work centers or cells) along with an aisle structure and a material handling system to link the departments. The primary objective of the design problem is to minimi...
BranchandBound Techniques for the Maximum Planar Subgraph Problem
, 1994
"... We present branchandbound algorithms for finding a maximum planar subgraph of a nonplanar graph. The problem has important applications in circuit layout, automated graph drawing, and facility layout. The algorithms described utilize heuristics to obtain an initial lower bound for the size of a ..."
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We present branchandbound algorithms for finding a maximum planar subgraph of a nonplanar graph. The problem has important applications in circuit layout, automated graph drawing, and facility layout. The algorithms described utilize heuristics to obtain an initial lower bound for the size of a maximum planar subgraph, then apply a sequence of fast preliminary tests for planarity to eliminate infeasible partial solutions. Computational experience is reported from testing the algorithms on a set of random nonplanar graphs and is encouraging. A bestfirst search technique is shown to be a practical approach to solving problems of moderate size. KEY WORDS: Maximum planar subgraph, branchandbound, planar graph, graph planarization, NPhard, planarity. C.R. CATEGORIES: F.2.2, G.2.2. 1
An improved convex optimization model for twodimensional facility layout
, 2006
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ..."
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Cited by 1 (1 self)
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I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public.
A Polynomial Time Randomized Parallel Approximation Algorithm for Finding Heavy Planar Subgraphs
, 2006
"... We provide an approximation algorithm for the Maximum Weight Planar Subgraph problem, the NPhard problem of finding a heaviest planar subgraph in an edgeweighted graph G. In the general case our algorithm has performance ratio at least 1/3 + 1/72 matching the best algorithm known so far, though in ..."
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We provide an approximation algorithm for the Maximum Weight Planar Subgraph problem, the NPhard problem of finding a heaviest planar subgraph in an edgeweighted graph G. In the general case our algorithm has performance ratio at least 1/3 + 1/72 matching the best algorithm known so far, though in several special cases we prove stronger results. In particular, we obtain performance ratio 2/3 (instead of 7/12) for the NPhard Maximum Weight Outerplanar Subgraph problem meeting the performance ratio of the best algorithm for the unweighted case. When the maximum weight planar subgraph is one of several special types of Hamiltonian graphs, we show performance ratios at least 2/5 and 4/9 (instead of 1/3 + 1/72), and 1/2 (instead of 4/9) for the unweighted case.
Graph Theoretic Based Heuristics For the Facility Layout Design Problems
"... The facility layout problem is concerned with determining the location of a number of facilities which optimizes a prescribed objective such as profit, cost, or distance. This problem arises in many applications; for example, in design of buildings and in plant layout design. The facility layout pro ..."
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The facility layout problem is concerned with determining the location of a number of facilities which optimizes a prescribed objective such as profit, cost, or distance. This problem arises in many applications; for example, in design of buildings and in plant layout design. The facility layout problem has been modeled as: a quadratic assignment problem; a quadratic set covering problem; a linear integer programming problem; a graph theoretic problem. Since this problem is NPcomplete, most approaches are heuristic in nature and based on graph theoretic concepts. Graph theoretically, when the objective is to maximize profit, the facility layout problem is to determine, in a given edge weighted graph G, a maximum weight planar subgraph. In this paper, we discuss a number of heuristics for this problem. The performance of the heuristics is established through a comparative analysis based on an extensive set of random test problems. 1. Introduction Typically the facility layout design ...