Explore the dynamic field of Combinatorial Optimization with this essential handbook. Discover how discrete optimization problems, fundamental to operations research, computer science, and applied mathematics, shape diverse applications. From communication networks and VLSI design to scheduling and computational biology, this supplement volume B delves into the mathematical formulation of optimization challenges and their discreteness. Trace the historical roots in linear programming, a cornerstone with wide-ranging applications in resource allocation, production planning, and finance. Understand the impact of groundbreaking algorithms like the ellipsoid method and interior point approaches, and see how they inform solutions for NP-hard problems and specific cases like matching and maximum flow. An indispensable resource for researchers and practitioners seeking to master the intricacies of combinatorial optimization.