Contributors Introduction Lucas Bordeaux, Youssef Hamadi and Pushmeet Kohli Part I. Graphical Structure: 1. Treewidth and hypertree width Georg Gottlob, Gianluigi Greco and Francesco Scarcello 2. Perfect graphs and graphical modeling Tony Jebara Part II. Language Restrictions: 3. Submodular function maximization Andreas Krause and Daniel Golovin 4. Tractable valued constraints Peter G. Jeavons and Stanislav Zivny 5. Tractable knowledge representation formalisms Adnan Darwiche Part III. Algorithms and their Analysis: 6. Tree-reweighted message passing Vladimir Kolmogorov 7. Tractable optimization in machine learning Suvrit Sra 8. Approximation algorithms Mohit Singh and Kunal Talwar 9. Kernelization methods for fixed-parameter tractability Fedor V. Fomin and Saket Saurabh Part IV. Tractability in Some Specific Areas: 10. Efficient submodular function minimization for computer vision Pushmeet Kohli 11. Towards practical graph-based, iteratively decoded channel codes: insights through absorbing sets Lara Dolecek Part V. Heuristics: 12. SAT solvers Joao Marques-Silva and Ines Lynce 13. Tractability and modern satisfiability modulo theories solvers Nikolaj Bjorner and Leonardo de Moura.