This book constitutes the proceedings of the 31st International Workshop on Combinatorial Algorithms which was planned to take place in Bordeaux, France, during June 8-10, 2020. Due to the COVID-19 pandemic the conference changed to a virtual format. The 30 full papers included in this book were carefully reviewed and selected from 62 submissions. They focus on algorithms design for the myriad of combinatorial problems that underlie computer applications in science, engineering and business.