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1. A LINEAR PROGRAMMING ANALYSIS OF PAPER RECYCLING.

Author

Glassey, C. Roger and Gupta, Virendra K.

Subjects
PAPER recycling, LINEAR statistical models, RECYCLED products, MATHEMATICAL models, LINEAR programming, RECYCLING research, PAPER industry & the environment, WASTE management research, PAPER
Abstract

A simple linear model is constructed for production, use and recycling of various paper and related products. This model is used to estimate the maximum feasible recycling rate given the current state of pulp and paper technology. Parametric linear programming is used to investigate the effect of the efficiency of collecting, sorting and transporting waste paper on the fraction recycled. [ABSTRACT FROM AUTHOR]

Published
1974
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2. A new algorithm for the maximum weighted stable set problem in claw-free graphs

Author

Gianpaolo Oriolo, Ugo Pietropaoli, Gautier Stauffer, Dipartimento di Ingegneria dell'Impresa [Roma], Università degli Studi di Roma Tor Vergata [Roma], Reformulations based algorithms for Combinatorial Optimization (Realopt), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Combinatorial optimization, Computer science, 0211 other engineering and technologies, 02 engineering and technology, Polynomials, 01 natural sciences, Domain decomposition methods, Scheduling algorithms, Matching problems, Chordal graph, Polynomial-time algorithms, Longest path, ComputingMilieux_MISCELLANEOUS, decomposition theorems, 021103 operations research, Quasi-line graphs, Mathematical programming, Integer programming, Longest path problem, Graph, Modular decomposition, 010201 computation theory & mathematics, (algorithmic) complexity, Auxiliary graphs, Claw-free graphs, Mathematical transformations, Set theory, Settore MAT/09 - Ricerca Operativa, Algorithm, Algorithms, Optimization, Paper, Aerospace applications, Boolean functions, Combinatorial mathematics, Curve fitting, Dynamic programming, Evolutionary algorithms, Farm buildings, Graph theory, Linear programming, Nonlinear programming, Polynomial approximation, Reduction, Trees (mathematics), General (CO), graph reductions, international conferences, New algorithm, Polynomial-time, Reduction tools, Running in, time bound, 0102 computer and information sciences, Combinatorics, Indifference graph, Pathwidth, Cograph, [INFO]Computer Science [cs], Graph coloring, Time complexity, Discrete mathematics, 1-planar graph, Vertex (geometry), Independent set
Abstract

In this paper, we introduce two powerful graph reductions for the maximum weighted stable set (mwss) in general graphs. We show that these reductions allow to reduce the mwss in claw-free graphs to the mwss in a class of quasi-line graphs, that we call bipolar-free. For this latter class, we provide a new algorithmic decomposition theorem running in polynomial time. We then exploit this decomposition result and our reduction tools again to transform the problem to either a single matching problem or a longest path computation in an acyclic auxiliary graph (in this latter part we use some results of Pulleyblank and Shepherd [10]). Putting all the pieces together, the main contribution of this paper is a new polynomial time algorithm for the mwss in claw-free graphs. A rough analysis of the complexity of this algorithm gives a time bound of O(n6), where n is the number of vertices in the graph, and which we hope can be improved by a finer analysis. Incidentally, we prove that the mwss problem can be solved efficiently for any class of graphs that admits a "suitable" decomposition into pieces where the mwss is easy.

Published
2008