Proceedings 32nd Annual Symposium of Foundations of Computer Science (1991)
San Juan, Puerto Rico
Oct. 1, 1991 to Oct. 4, 1991
P.W. Shor , AT&T Bell Lab., Murray Hill, NJ, USA
An O(n log n)-time online algorithm is given for packing items i.i.d. uniform on (0, 1) into bins of size 1 with expected wasted space Theta (n/sup 1/2/ log /sup 1/2/n). This matches the lowest bound that no online algorithm can achieve O(n/sup 1/2/ log /sup 1/2/ n) wasted space. It is done by analyzing another algorithm which involves putting balls into buckets online. The analysis of this second algorithm also gives bound on the stochastic rightward matching problem, which arises in analyzing not only the above online bin packing problem, but also a 2-D problem of packing rectangles into a half-infinite strip. The bounds on rightward matching thus give good bounds for the 2-D strip packing problem.
2-D strip packing problem, ball packing, rectangle packing, tight bounds, average-case online bin packing, online algorithm, expected wasted space, lowest bound, stochastic rightward matching problem, half-infinite strip
P. Shor, "How to pack better than best fit: tight bounds for average-case online bin packing,"  Proceedings 32nd Annual Symposium of Foundations of Computer Science(FOCS), San Juan, Puerto Rico, 1991, pp. 752-759.