Independence and port oracles for matroids, with an application to computational learning theory
 Collette R. Coullard,
 Lisa Hellerstein
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Given a matroidM with distinguished elemente, aport oracie with respect toe reports whether or not a given subset contains a circuit that containse. The first main result of this paper is an algorithm for computing anebased ear decomposition (that is, an ear decomposition every circuit of which contains elemente) of a matroid using only a polynomial number of elementary operations and port oracle calls. In the case thatM is binary, the incidence vectors of the circuits in the ear decomposition form a matrix representation forM. Thus, this algorithm solves a problem in computational learning theory; it learns the class ofbinary matroid port (BMP) functions with membership queries in polynomial time. In this context, the algorithm generalizes results of Angluin, Hellerstein, and Karpinski [1], and Raghavan and Schach [17], who showed that certain subclasses of the BMP functions are learnable in polynomial time using membership queries. The second main result of this paper is an algorithm for testing independence of a given input set of the matroidM. This algorithm, which uses the ear decomposition algorithm as a subroutine, uses only a polynomial number of elementary operations and port oracle calls. The algorithm proves a constructive version of an early theorem of Lehman [13], which states that the port of a connected matroid uniquely determines the matroid.
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 Title
 Independence and port oracles for matroids, with an application to computational learning theory
 Journal

Combinatorica
Volume 16, Issue 2 , pp 189208
 Cover Date
 19960601
 DOI
 10.1007/BF01844845
 Print ISSN
 02099683
 Online ISSN
 14396912
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 05 B 35
 68 T 05
 68 Q 20
 68 Q 25
 Industry Sectors
 Authors

 Collette R. Coullard ^{(1)}
 Lisa Hellerstein ^{(2)}
 Author Affiliations

 1. Department of Industrial Engineering and Management Sciences, Northwestern University, 60208, Evanston, IL, USA
 2. Department of Electrical Engineering and Computer Science, 60208, Evanston, IL, USA