How to Navigate Through Obstacles -- Approximation Algorithms for Vertex- Connectivity Augmentation on the Cycle -- Constant Factor Approximation for Tracking Paths and Fault Tolerant Feedback Vertex Set -- An Improved Approximation Bound for Minimum Weight Dominating Set on Graphs of Bounded Arboricity -- Tight Inapproximability of Minimum Maximal Matching on Bipartite Graphs -- On b-Matchings and b-Edge Dominating Sets: A 2-Approximation Algorithm for the 4-Edge Dominating Set Problem -- The Traveling k-Median Problem: Approximating Optimal Network Coverage -- EPTAS for Load Balancing Problem on Parallel Machines with a Non-renewable Resource -- Several methods of analysis for cardinality constrained bin packing -- Leah Epstein Weighted completion time minimization for capacitated parallel machines -- Server Cloud Scheduling -- FIFO and Randomized Competitive Packet Routing Games -- Improved Online Algorithm for Fractional Knapsack in the Random Order Model -- Improved Online Algorithm for Fractional Knapsack in the Random Order Model -- Improved Analysis of Online Balanced Clustering -- Precedence-Constrained Covering Problems with Multiplicity Constraints -- Contention Resolution, Matrix Scaling and Fair Allocation.

This book constitutes the thoroughly refereed workshop post-proceedings of the 19th International Workshop on Approximation and Online Algorithms, WAOA 2021, held in September 2021. Due to COVID-19 pandemic the conference was held virtually. The 16 revised full papers presented in this book were carefully reviewed and selected from 31 submissions. The papers focus on the design and analysis of algorithms for online and computationally hard problems.