An algorithm for weighted fractional matroid matching

Authors:
Dion Gijswijt;Gyula Pap
Affiliations:
CWI and Department of Mathematics, Leiden University, Netherlands;MTA-ELTE Egerváry Research Group on Combinatorial Optimization, Department of Operations Research, Eötvös Loránd University, Pázmány Péter sétány, 1/C, ...
Venue:
Journal of Combinatorial Theory Series B
Year:
2013

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Abstract

Let M be a matroid on ground set E with rank function r. A subset l@?E is called a line when r(l)@?{1,2}. Given a finite set L of lines in M, a vector x@?R"+^L is called a fractional matching when @?"l"@?"Lx"la(F)"l=Q, a maximum weight fractional matching. A simple reference to the equivalence of separation and optimization does not lead to such an algorithm, since no direct method for polynomial time separation is known for this polytope.