Windows scheduling as a restricted version of bin packing

Abstract

Given is a sequence of n positive integers w 1

Online Multi-dimensional Dynamic Bin Packing of Unit-Fraction Items

“…2. When the new item is T(≤ 1 3 , 1 2 ) or T(≤ 1 3 , 1) and the bin contains T(≤ 1 3 , ≤ 1 3 )-item, we divide the bin into two compartments, one with width 1 3 and the other 2 3 and both with height 1. We reserve the small compartment for the new item and try to repack the existing items in the large compartment using Steinberg's algorithm.…”

“…Bar-Noy et al [2] initiated the study of the unit fraction bin packing problem, a restricted version where all sizes of items are of the form 1 k , for some integer k. The problem was motivated by the window scheduling problem [1,2]. Another related problem is for power fraction items, where sizes are of the form 1 2 k , for some integer k. Bin packing with other restricted form of item sizes includes divisible item sizes [8] (where each possible item size can be divided by the next smaller item size) and discrete item sizes [6] (where possible item sizes are {1/k, 2/k, · · · , j/k} for some 1 ≤ j ≤ k).…”

Windows scheduling of arbitrary-length jobs on multiple machines

“…In a way, bin packing is the fractional version of windows scheduling while windows scheduling imposes another restriction on the packing. The relationship between these two problems and their off-line and the on-line cases were considered in Bar-Noy et al (2007).…”

“…Since a restricted version of the optimal windows scheduling problem is NP-hard even for one machine , 2007Feinberg et al 2002), we look for approximate solutions. A natural lower bound to the windows scheduling problem is the total width of the jobs.…”

“…Previous results for the windows scheduling problem considered either the case of one machine with unit-length jobs (the pinwheel problem, Holte et al 1989Holte et al , 1992, or the case of unit-length jobs with multiple machines (BarNoy and Ladner 2003;Bar-Noy et al 2007), or the case of one machine with arbitrary-length jobs (the generalized pinwheel problem, Baruah and Lin 1998;Feinberg et al 2002;Feinberg and Curry 2005). This paper considers the generalized windows scheduling problem of multiple machines with arbitrary-length jobs.…”