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# Approximation algorithms for packing and scheduling problems

## Research and Teaching Output of the MIT Community

 dc.contributor.advisor Michael X. Goemans and Andreas S. Schulz. en_US dc.contributor.author Correa, José Rafael, 1975- en_US dc.contributor.other Massachusetts Institute of Technology. Operations Research Center. en_US dc.date.accessioned 2005-06-02T18:23:11Z dc.date.available 2005-06-02T18:23:11Z dc.date.copyright 2004 en_US dc.date.issued 2004 en_US dc.identifier.uri http://hdl.handle.net/1721.1/17720 dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004. en_US dc.description Includes bibliographical references (p. 149-161). en_US dc.description.abstract In this thesis we consider three combinatorial optimization problems. Specifically, we study packing and scheduling questions of relevance in several areas of operations research, including interconnection networks and switch scheduling, VLSI design, and processor scheduling. The first chapter studies a natural edge-coloring question arising from the problem of scheduling packets through an interconnection network. The theoretical model we consider can be seen as a weighted extension of Konig's theorem that states that the minimum number of colors needed to color all edges of a bipartite graph equals the maximum vertex degree. For the weighted generalization, a longstanding open question is to determine the minimum number of colors as a function of n, the maximum total weight adjacent to any vertex. Our main contribution is to show that 2.557n + o(n) colors are sufficient, improving upon earlier work. In the second chapter, we consider the following variant of the classical bin-packing problem: Place a given list of rectangles into the minimum number of unit square bins. In the restricted case where all rectangles are squares, we design an algorithm with an asymptotic performance guarantee arbitrarily close to optimal. In the general case, we give an algorithm that outputs a near-optimal solution, provided it is allowed to use slightly larger bins. Moreover, we extend these algorithmic ideas to handle a number of multidimensional packing problems, obtaining best-known results for several of these. en_US dc.description.abstract (cont.) Finally, in the third chapter, we discuss a standard sequencing problem, namely, scheduling precedence-constrained jobs on a single machine to minimize the sum of weighted completion times. We look at the problem from a polyhedral perspective, obtaining, as one of our main results, a generalization of a classical result by Sidney. This new insight allows us to reason that all known 2-approximation algorithms behave similarly. Furthermore, we present a new integer programming model that suggests a strong connection between the scheduling problem and the vertex cover problem. en_US dc.description.statementofresponsibility by José Rafael Correa. en_US dc.format.extent 161 p. en_US dc.format.extent 6124424 bytes dc.format.extent 10998617 bytes dc.format.mimetype application/pdf dc.format.mimetype application/pdf dc.language.iso eng en_US dc.publisher Massachusetts Institute of Technology en_US dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 dc.subject Operations Research Center. en_US dc.title Approximation algorithms for packing and scheduling problems en_US dc.type Thesis en_US dc.description.degree Ph.D. en_US dc.contributor.department Massachusetts Institute of Technology. Operations Research Center. en_US dc.identifier.oclc 56430193 en_US
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