A Simple PTAS for the Dual Bin Packing Problem and Advice Complexity of Its Online Version
Allan Borodin, Denis Pankratov, Amirali Salehi-Abari

TL;DR
This paper introduces a simple polynomial-time approximation scheme (PTAS) for the dual bin packing problem and investigates the advice complexity of its online version, providing both upper and lower bounds.
Contribution
It presents a simple offline PTAS for dual bin packing and adapts it to an online setting with advice complexity bounds, advancing understanding of advice requirements.
Findings
A simple online algorithm with advice approximates dual bin packing within 1+ε.
A PTAS for dual bin packing is simpler to state and analyze than previous ones.
Lower bounds show that for unbounded item sizes, advice complexity is linear in input size.
Abstract
Recently, Renault (2016) studied the dual bin packing problem in the per-request advice model of online algorithms. He showed that given advice bits for each input item allows approximating the dual bin packing problem online to within a factor of . Renault asked about the advice complexity of dual bin packing in the tape-advice model of online algorithms. We make progress on this question. Let be the maximum bit size of an input item weight. We present a conceptually simple online algorithm that with total advice approximates the dual bin packing to within a factor. To this end, we describe and analyze a simple offline PTAS for the dual bin packing problem. Although a PTAS for a more general problem was known prior to our work (Kellerer 1999, Chekuri and Khanna 2006), our PTAS is arguably simpler…
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Taxonomy
TopicsOptimization and Packing Problems · Advanced Manufacturing and Logistics Optimization · Optimization and Search Problems
