Multichannel Communication and Graph Vertex Labeling Problems
Berger-Wolf, Yonit
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https://hdl.handle.net/2142/81597
Description
Title
Multichannel Communication and Graph Vertex Labeling Problems
Author(s)
Berger-Wolf, Yonit
Issue Date
2002
Doctoral Committee Chair(s)
Edward M. Reingold
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
Depending on the type of data, error measure, and type of failure, the problem of designing these encoding schemes is equivalent to several classical problems in graph theory. For example, no-redundancy encodings that minimize maximum absolute error for complete loss of data correspond to the problem of bandwidth optimization of Hamming graphs (Cartesian products of cliques). The graph problem has been open since the 1960s. In this thesis, we demonstrate lower bounds and a nearly optimal solution to this problem. Using techniques developed for this solution, we give an algorithm for the wirelength optimization problem of grid graphs (products of paths) of arbitrary dimensions. This is the first constructive result for the product of more than two paths. In the communications setting, this problem is equivalent to designing no-redundancy encodings that minimize average error of a distance-1 type of medium failure. Similar techniques solved an unrelated graph edge isoperimetric problem. In addition, extending the algorithm to allow redundancy in the encoding improved the only previously known constructive result.
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