This volume contains the papers presented at the 10th International Workshopon Approximation Algorithms for Combinatorial Optimization Problems(APPROX 2007) and the 11th International Workshop on Randomization andComputation (RANDOM 2007), which took place concurrently at PrincetonUniversity, on August 20–22, 2007. APPROX focuses on algorithmic and complexityissues surrounding the development of efficient approximate solutionsto computationally difficult problems.