Abstract

The tight asymptotic approximation ratio of the classical bin packing algorithm called First Fit was known for many years, also in the parameterized case, when any item has size of at most 1/d, where d is integer. But the tight absolute bound was found only recently, and only for d=1. Here we give the tight absolute approximation ratio of First Fit for any d≥2. In fact, we do more. For any value of OPT (the number of bins in an optimum solution) we determine that exactly how large FF (the number of bins created by First Fit) can be in the worst case.The proof is very simple, since we can apply the lower bound construction of case d=1, in a slightly modified form.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.