D S ] 17 D ec 2 01 2 Online Bin Packing with Advice ⋆

We consider the online bin packing problem under the advice c omplexity model where the “online constraint” is relaxed and a algorithm receives partial information about the future requests. We provide t ght upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. In a theoretical setting in which there is no restrictio n n items sizes, we show thatn log OPT−o(n log OPT) bits of advice are necessary to achieve an optimal packing, wheren is the length of the sequence and O PT is the cost of an optimal packing. This matches the natural upper bound of n l g OPT bits up to additive lower order terms and is in that sense optimal. In a more practical setting in which there are a constant number of m distinct items, we show that (m − 3) log n − O (1) bits of advice are necessary and m log n bits are sufficient to achieve an optimal packing. We also introduce an alg orithm that, when provided withlog n bits of advice, achieves a competitive ratio of 3/2 for the general problem. This algorithm is simple and is expected to find real-world applications. We introduce another algorithm that receives 2n+ o(n) bits of advice and achieves a competitive ratio of 4/3. Finally, we provide a lower bound argument that implies that advice of linear size is required for a n algorithm to achieve a competitive ratio better than 5/4.