Abstract
In this paper, we present an O(r 4 n) algorithm for the linear matroid parity problem. Our solution technique is to introduce a modest generalization, the non-simple parity problem, and identify an important subclass of non-simple parity problems called ‘easy’ parity problems which can be solved as matroid intersection problems. We then show how to solve any linear matroid parity problem parametrically as a sequence of ‘easy’ parity problems.
In contrast to other algorithmic work on this problem, we focus on general structural properties of dual solutions rather than on local primal structures. In a companion paper, we develop these ideas into a duality theory for the parity problem.
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Orlin, J.B., Vande Vate, J.H. Solving the linear matroid parity problem as a sequence of matroid intersection problems. Mathematical Programming 47, 81–106 (1990). https://doi.org/10.1007/BF01580854
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DOI: https://doi.org/10.1007/BF01580854