Semi-online scheduling revisited

Online Bin Packing with Advice

“…Algorithm 2 shows the details of the reduction. The bin packing sequence starts with n 1 items of size 1 2 + ε min (in Algorithm 2, the variable "NumberOfLargeItems" is n 1 from the Binary Separation Problem). Any algorithm needs to open a bin for each of these n 1 items.…”

“…Other almost-online settings allow the online algorithms to repack some items or arrange for some pre-ordering of the items [22,27,23]. Along similar lines, the almost-online setting is studied for the related problem of scheduling; see [14,1,34], for example.…”

A Graph Theoretic Approach for Minimizing Storage Space using Bin Packing Heuristics

“…But it needs further investigations. Secondly, online partition problem or semi-online partition problem [28] can be applied to generate cliques with constrained weight of the vertex weighted graph. This concept can be used to tackle online or semi-online Bin Packing Problem but needs further detailed study.…”

Better Algorithms for Online Bin Stretching

“…Historically first is the study of ordered sequences with non-decreasing processing times [9]. Most closely related is the variant with known sum of all processing times studied in [12] and the currently best results are a lower bound of 1.585 and an algorithm with ratio 1.6, both from [1]. Note that this shows, somewhat surprisingly, that knowing the actual optimum gives a significantly bigger advantage to the online algorithm over knowing just the sum of the processing times (which, divided by m, is a lower bound on the optimum).…”

“…Input: an integer m, a stretching factor R, and a sequence of items I = i 1 Guarantee: there exists a packing of all items of the sequence I into m bins of capacity 1. Goal: Design an online algorithm with the stretching factor R as small as possible which packs all input sequences satisfying the guarantee.…”