This book constitutes the joint refereed proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and the 10th International Workshop on Randomization and Computation, RANDOM 2006, held in Barcelona, Spain, in August 2006.

The 44 revised full papers presented were carefully reviewed and selected from 105 submissions. Among the topics covered are design and analysis of approximation algorithms, hardness of approximation problems, small spaces and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, game theory, network design and routing, packing and covering, scheduling, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness, derandomization, random combinatorial structures, Markov chains, prohabalistic proof systems, error-correcting codes, etc.

Thisvolumecontainsthe66contributedpapersandabstractsofthethreeinvited lecturespresentedatthe11thAnnualEuropeanSymposiumonAlgorithms(ESA 2003), held in Budapest, September 16-19, 2003. The papers in each section of the proceedings are arranged alphabetically. The three distinguished invited ' speakers were Bernard Chazelle, Roberto Tamassia, and Eva Tardos. Forthesecondtime,ESAhadtwotracks,withseparateprogramcommittees, which dealt respectively with: The design and mathematical analysis of algorithms (the "Design and Analysis" track); Real-world applications, engineering, and experimental analysis of al- rithms (the "Engineering and Applications" track). Previous ESAs were held at Bad Honnef, Germany (1993); Utrecht, The Neth- lands (1994); Corfu, Greece (1995); Barcelona, Spain (1996); Graz, Austria (1997); Venice, Italy (1998); Prague, Czech Republic (1999); Saarbruc .. ken, Ger- ? many (2000); Arhus, Denmark (2001), and Rome, Italy (2002). The predecessor to the Engineering and Applications track of ESA was the annual Workshop on Algorithm Engineering (WAE). Previous WAEs were held in Venice, Italy (1997), Saarbruc .. ken, Germany (1998), London, UK (1999), Saarbruc .. ken, Ger- ? many (2000), Arhus, Denmark (2001), and Rome, Italy (2002) . The proceedings of the previous ESAs were published as Springer-Verlag's LNCS volumes 726, 855, 979, 1284, 1461, 1643, 1879, 2161, and 2461. The p- ceedings of the WAEs from 1999 onwards were published as Springer-Verlag's LNCS volumes 1668, 1982, and 2141.