Abstract
Bin packing problems, in which one is asked to pack items of various sizes into bins so as to optimize some given objective function, arise in a wide variety of contexts and have been studied extensively during the past ten years, primarily with the goal of finding fast “approximation algorithms” that construct near-optimal packings. Beginning with the classical one-dimensional bin packing problem first studied in the early 1970’s, we survey the approximation results that have been obtained for this problem and its many variants and generalizations, including recent (unpublished) work that reflects the currently most active areas of bin packing research. Our emphasis is on the worst-case performance guarantees that have been proved, but we also discuss work that has been done on expected performance and behavior “in practice,” as well as mentioning some of the many applications of these problems.
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