Online Bin Packing with Advice

TL;DR

This paper explores the advice complexity in online bin packing, establishing bounds on advice needed for optimal solutions and presenting algorithms with competitive ratios of 3/2 and 4/3+epsilon based on advice size.

Contribution

It provides tight bounds on advice complexity for optimal packing and introduces new algorithms with specific advice requirements and competitive ratios.

Findings

An algorithm with log n + o(log n) advice achieves a 3/2 competitive ratio.

An algorithm with 2n + o(n) advice achieves a 4/3+epsilon competitive ratio.

Linear advice is necessary to surpass a 9/8 competitive ratio.

Abstract

We consider the online bin packing problem under the advice complexity model where the 'online constraint' is relaxed and an algorithm receives partial information about the future requests. We provide tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. We also introduce an algorithm that, when provided with log n + o(log 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 + {\epsilon}. Finally, we provide a lower bound argument that implies that advice of linear size is required for an algorithm to achieve a competitive ratio better than 9/8.