Geodesic
On the problem of maximizing a modular function in the geometric lattice
The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 1, pp. 2-13

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The problem of maximizing a modular set function on order ideal in the finite geometric lattice is considered. Possibility of generalizing the Rado–Edmonds theorem is studied. A performance guarantee of the greedy algorithm generalizing the known Jenkyns–Korte–Hausmann bound for the problem of maximizing an additive function on independence system is obtained.
Keywords: modular function; geometric lattice; order ideal; $L$-matroid; greedy algorithm; performance guarantee. 
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V. A. Baransky; M. Yu. Vyplov; V. P. Il'ev. On the problem of maximizing a modular function in the geometric lattice. The Bulletin of Irkutsk State University. Series Mathematics, Tome 6 (2013) no. 1, pp. 2-13. http://geodesic.mathdoc.fr/item/IIGUM_2013_6_1_a0/