Quasi M-convex and L-convex functions: quasiconvexity in discrete optimization

Authors:
Kazuo Murota;Akiyoshi Shioura
Affiliations:
Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan;Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
Venue:
Discrete Applied Mathematics - Submodularity
Year:
2003

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Abstract

We introduce two classes of discrete quasiconvex functions, called quasi M- and L-convex functions, by generalizing the concepts of M- and L-convexity due to Murota (Adv. Math. 124 (1996) 272) and (Math. Programming 83 (1998) 313). We investigate the structure of quasi Mand L-convex functions with respect to level sets, and show that various greedy algorithms work for the minimization of quasi M- and L-convex functions.