Abstract
This chapter presents definitions, relevant properties, and examples of submodular functions, which will be built on in subsequent sections. Techniques for constructing submodular functions and proving submodularity are described. The concept of a matroid, which generalizes the concept of matrix rank, is introduced. The matroid rank, basis, and closure are presented along with examples and proofs of needed properties. The matroid dual and union constructions are reviewed.
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© 2016 Springer International Publishing Switzerland
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Clark, A., Alomair, B., Bushnell, L., Poovendran, R. (2016). Submodular Functions and Matroids. In: Submodularity in Dynamics and Control of Networked Systems. Communications and Control Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-26977-1_1
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DOI: https://doi.org/10.1007/978-3-319-26977-1_1
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-26977-1
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