This book constitutes the proceedings of the 13th International Workshop on Frontiers in Algorithmics, FAW 2019, held in Sanya, China, in April/May 2019. The 15 full papers presented in this volume were carefully reviewed and selected from 21 submissions. The workshop provides a focused forum on current trends of research on algorithms, discrete structures, and their applications, and brings together international experts at the research frontiers in these areas to exchange ideas and to present significant new results.