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This book constitutes the refereed proceedings of the International Workshop on Approximation Algorithms for Combinatorical Optimization, APPROX'98, held in conjunction with ICALP'98 in Aalborg, Denmark, in July 1998.The volume presents 14 revised full papers together with three invited papers selected from 37 submissions. The papers address the design and analysis of approximation algorithms, inapproximability results, on-line problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and various applications.