Martin Böhm

Online Colored Bin Packing

In the Colored Bin Packing problem a sequence of items of sizes up to \(1\) arrives to be packed into bins of unit capacity. Each item has one of \(c\ge 2\) 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.

Better Algorithms for Online Bin Stretching

Online Bin Stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as the optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin.

Online bin stretching with three bins

Online bin stretching is a semi-online variant of bin packing in which the algorithm has to use the same number of bins as an optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for online bin stretching with a stretching factor of

Online Chromatic Number is PSPACE-Complete

11/8 = 1.375

Online Packet Scheduling with Bounded Delay and Lookahead.

11/8=1.375 for three bins. Additionally, we present a lower bound of

On Packet Scheduling with Adversarial Jamming and Speedup

45/33 = 1.\overline{36}