1.1 Introduction
1.1.1 Organization of the chapter
1.2 Properties of multimodular functions
1.2.1 General properties
1.2.2 Multimodularity and convexity
1.3 The optimality of bracket policies for a single criterion
1.3.1 Upper Bounds
1.3.2 Lower Bounds
1.3.3 Optimality of the Bracket Sequences
1.4 The optimality of bracket policies for multiple criteria
1.5 Application of the optimization theorems
1.5.1 Applications in high-speed telecommunication systems
1.6 Clustering versus Smoothing
1.7 Appendix A: proof of Lemma 2
1.8 Appendix B: Proof of Lemma 5
1.9 Appendix C: average and weighted costs