Online Colored Bin Packing
Martin B\"ohm, Ji\v{r}\'i Sgall, Pavel Vesel\'y

TL;DR
This paper studies the colored bin packing problem, providing optimal algorithms for zero-size items and competitive algorithms for general sizes, while analyzing classical algorithms' limitations.
Contribution
It introduces asymptotically optimal algorithms for colored bin packing with zero and general item sizes, and proves limitations of classical algorithms.
Findings
Optimal 1.5-competitive algorithm for zero-size items based on color discrepancy.
Asymptotically 3.5-competitive algorithm for items of unrestricted sizes.
Classical algorithms like First Fit, Best Fit, Worst Fit are not constant competitive.
Abstract
In the Colored Bin Packing problem a sequence of items of sizes up to arrives to be packed into bins of unit capacity. Each item has one of colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most bins and we show a matching lower bound of for any value of . In particular, the absolute ratio of our algorithm is and this is optimal. For items of unrestricted sizes we give an asymptotically -competitive algorithm. When the…
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Taxonomy
TopicsOptimization and Packing Problems · Optimization and Search Problems · Advanced Manufacturing and Logistics Optimization
