List of accepted papers for APPROX 2007: Maximum gradient embeddings and monotone clustering Manor Mendel and Assaf Naor On the approximation resistance of a random predicate Johan Hastad Almost exact matchings Raphael Yuster Parity and contraction in planar graph embeddings Amit Chakrabarti, James Lee and Justin Vincent Coarse differentiation and multi-flows in planar graphs James Lee and Prasad Raghavendra An optimal bifactor approximation algorithm for the metric uncapacitated facility location problem Jaroslaw Byrka Packing and covering delta-hyperbolic spaces by balls Victor Chepoi and Bertrand Estellon Approximation Algorithms for the Traveling Repairman and Speeding Deliveryman Problems with Unit-Time Windows Greg Frederickson and Barry Wittman Approximation algorithms and hardness for domination with propagation Ashkan Aazami and Michael Stilp Stochastic Steiner Tree with Non-Uniform Inflation Anupam Gupta, MohammadTaghi Hajiaghayi and Amit Kumar Poly-logarithmic Approximation Algorithms for Directed Vehicle Routing Problems Viswanath Nagarajan and R Ravi Soft Edge Coloring Chadi Kari, Yoo-Ah Kim, Seungjoon Lee, Alexander Russell and Min-ho Shin Increasing the Span of Stars Ning Chen, Roee Engelberg, C. Thach Nguyen, Prasad Raghavendra, Atri Rudra and Gyanit Singh Improved approximation ratios for traveling salesperson tours and paths in directed graphs Uriel Feige and Mohit Singh Two Randomized Mechanisms for Combinatorial Auctions Shahar Dobzinski Hardness of Embedding Metric Spaces of Equal Size Subhash Khot and Rishi Saket Optimal Resource Augmentations for Online Knapsack Kazuo Iwama and Guochuan Zhang Approximation Algorithms for the Max-Min Allocation problem Ashok Kumar Ponnuswami and Subhash Khot Integrality gaps of semidefinite programs for Vertex Cover and relations to $\ell_1$ embeddability of negative type metrics Hamed Hatami, Avner Magen and Evangelos Markakis Encouraging Cooperation in Sharing Supermodular Costs Andreas S. Schulz and Nelson Uhan Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems Ilias Diakonikolas and Mihalis Yannakakis A Knapsack Secretary Problem with Applications Moshe Babaioff, Nicole Immorlica, David Kempe and Robert Kleinberg