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The primary activities supported by the grant during the reporting period include a new result showing the hardness of the single-source robust network design and an invitation to include this in the special issue devoted to selected papers in FOCS 2005. A summer intern was hosted, Andrew McGregor from UPenn, who worked with Shepherd on recognizing Hilbert Bases and other theoretical topics in Math Programming. A visit was also supported for Gianpaolo Oriolo (Rome), which resulted in some new joint work on robust network design. In addition, there was a week visit from Seffi Naor (Technicion). Travel supported during this period includes trips by Shepherd to UPenn to work with Sanjeev Khanna and C. Chekuri on the mutlicommodity flow problem. This work has resulted in the FOCS 2005 paper, which in addition was invited into a special issue of selected papers. Conferences attended were the 2004 APPROX/RANDOM (Chekuri) and CORC 4th Optimization Day (Shepherd).