Algorithms and Data Structures for an Expanded Family of Matroid Intersection Problems

Efficient Algorithms for a Family of Matroid Intersection Problems

Algebraic Structures and Algorithms for Matching and Matroid Problems (Preliminary Version)

Basic path-matchings, introduced by Cunningham and Geelen (FOCS 1996), are a common generalization of matroid intersection and non-bipartite matching. The main results of this paper are a new algebraic characterization of basic path-matching problems and an algorithm for constructing basic path-matchings in Õ(nω) time, where n is the number of vertices and ω is the exponent for matrix multiplic...

ar X iv : c s . D S / 06 01 02 6 v 1 9 Ja n 20 06 Algebraic Structures and Algorithms for Matching and Matroid Problems ( Preliminary Version ) Nicholas

Basic path-matchings, introduced by Cunningham and Geelen (FOCS 1996), are a common generalization of matroid intersection and non-bipartite matching. The main results of this paper are a new algebraic characterization of basic path-matching problems and an algorithm for constructing basic path-matchings in Õ(nω) time, where n is the number of vertices and ω is the exponent for matrix multiplic...

Parallel Complexity for Matroid Intersection and Matroid Parity Problems

Let two linear matroids have the same rank in matroid intersection. A maximum linear matroid intersection (maximum linear matroid parity set) is called a basic matroid intersection (basic matroid parity set), if its size is the rank of the matroid. We present that enumerating all basic matroid intersections (basic matroid parity sets) is in NC, provided that there are polynomial bounded basic m...

Solving the Linear Matroid Parity Problem as a Sequence of Matroid Intersection Problems

In this paper, we present an O(r 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 parametr...