This volume contains the papers presented at the 12th International Wo- shop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2009) and the 13th International Workshop on Randomization and Computation (RANDOM 2009), which took place concurrently at the HP - ditorium in UC Berkeley, USA, during August 21-23, 2009. APPROX focuses on algorithmic and complexity issues surrounding the development of e?cient approximate solutions to computationally di?cult problems, and was the 12th in the series after Aalborg (1998), Berkeley (1999), Saarbru ]cken (2000), Ber- ley (2001), Rome (2002), Princeton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), Princeton (2007), and Boston (2008). RANDOM is concerned with applications of randomness to computational and combinatorial problems, and was the 13th workshop in the series following Bologna (1997), Barcelona (1998), Berkeley(1999), Geneva(2000), Berkeley(2001), Harvard(2002), Prin- ton (2003), Cambridge (2004), Berkeley (2005), Barcelona (2006), Princeton (2007), and Boston (2008). Topics of interest for APPROX and RANDOM are: design and analysis of approximation algorithms, hardness of approximation, small space algorithms, sub-linear time algorithms, streaming algorithms, embeddings and metric space methods, mathematicalprogrammingmethods, combinatorialproblemsingraphs andnetworks, gametheory, markets, andeconomicapplications, geometricpr- lems, packing, covering, scheduling, approximate learning, design and analysis of online algorithms, randomized complexity theory, pseudorandomness and - randomization, randomcombinatorialstructures, randomwalks/Markovchains, expander graphs and randomness extractors, probabilistic proof systems, err- correctingcodes, average-caseanalysis, propertytesting, computationallearning theory, and other applications of approximation and randomness. The volume contains 25 contributed papers, selected by the APPROX Program Committee out of 56 submissions, and 28 contributed papers, selected by the RANDOM Program Committee out of 57 submissions.