Invited Talks -- Online Packet Switching -- Approximation Algorithms for Mixed Fractional Packing and Covering Problems -- Regular Papers -- Minimum Sum Multicoloring on the Edges of Planar Graphs and Partial k-Trees -- Online Bin Packing with Resource Augmentation -- A PTAS for Delay Minimization in Establishing Wireless Conference Calls -- This Side Up! -- Approximation Algorithm for Directed Multicuts -- Improved Bounds for Sum Multicoloring and Scheduling Dependent Jobs with Minsum Criteria -- Approximation Algorithms for Spreading Points -- More Powerful and Simpler Cost-Sharing Methods -- Approximation Schemes for Deal Splitting and Covering Integer Programs with Multiplicity Constraints -- Priority Algorithms for Graph Optimization Problems -- Pricing Network Edges to Cross a River -- Submodular Integer Cover and Its Application to Production Planning -- Stochastic Online Scheduling on Parallel Machines -- A -Approximation Algorithm for Biconnecting a Graph with a Given Hamiltonian Path -- Order-Preserving Transformations and Greedy-Like Algorithms -- Off-line Admission Control for Advance Reservations in Star Networks -- Joint Base Station Scheduling -- Universal Bufferless Routing -- Strong Colorings of Hypergraphs -- Deterministic Monotone Algorithms for Scheduling on Related Machines -- Better Bounds for Minimizing SONET ADMs.The 2nd Workshop on Approximation and Online Algorithms (WAOA 2004) focused on the design and analysis of algorithms for online and computationally hard problems. Both kinds of problems have a large number of applications arising from a variety of ?elds. WAOA 2004 took place in Bergen, Norway, from September 14 to September 16, 2004. The workshop was part of the ALGO 2004 event which also hosted ESA, WABI, IWPEC, and ATMOS. TopicsofinterestsforWAOA2004were:applicationstogametheory,appr- imation classes, coloring and partitioning, competitive analysis, computational ?nance, cuts and connectivity, geometric problems, inapproximability results, mechanism design, network design, routing, packing and covering, paradigms, randomization techniques, and scheduling problems. In response to our call we received 47 submissions. Each submission was reviewed by at least 3 referees, who judged the paper on originality, quality, and consistency with the topics of the conference. Based on the reviews, the Program Committee selected 21 papers. This volume contains the 21 selected papers and the two invited talks given by Yossi Azar and Klaus Jansen. We thank all the authors who submitted papers to the workshop and we also kindly thank the local organizers of ALGO 2004.