Online Strip Packing with Polynomial Migration

Online bin covering with limited migration

“…A number of different scenarios to loosen the strict requirement of irreversibility -called semi-online scenarios -have been developed over time in order to find algorithms that achieve good competitive ratios for some of the scenarios with bounded reversibility. In the last few years, the concept of the migration factor has been studied intensively [3,10,11,12,13,16,19,21,22]. Roughly speaking, a migration factor of β allows to reverse a total size of β • s(o) decisions, where s(o) denotes the size of the newly arrived object o.…”

“…This notion of reversibility is very natural, as it guarantees that a small object can only lead to small changes in the solution structure. Furthermore, algorithms with bounded migration factor often show a very clear-cut tradeoff between their migration and the competitive ratio: Many algorithms in this setting have a bounded migration factor which can be defined as a function f (ε) (growing with 1 ε ) and a small competitive ratio g(ε) (growing with ε), where the functions f and g can be defined for all ε > 0 [3,10,13,16,19,21,22]. Such algorithms are called robust, as the amount of reversibility allowed only depends on the solution guarantee that one wants to achieve.…”

Online Bin Covering with Limited Migration

“…A number of different scenarios to loosen the strict requirement of irreversibilitycalled semi-online scenarios -have been developed over time in order to find algorithms that achieve good competitive ratios for some of the scenarios bounded reversibility. In the last few years, the concept of the migration factor has been studied intensively [4,11,12,13,14,17,20,22,23]. Roughly speaking, a migration factor of β allows to reverse a total size of β • s(o) decisions, where s(o) denotes the size of the newly arrived object o.…”

“…This notion of reversibility is very natural, as it guarantees that a small object can only lead to small changes in the solution structure. Furthermore, algorithms with bounded migration factor often show a very clear-cut tradeoff between their migration and the competitive ratio: Many algorithms in this setting have a bounded migration factor which can be defined as a function f (ε) (growing with 1 ε ) and a small competitive ratio g(ε) (growing with ε), where the functions f and g can be defined for all ε > 0 [4,11,14,17,20,22,23]. Such algorithms are called robust, as the amount of reversibility allowed only depends on the solution guarantee that one wants to achieve.…”

“…Many different problems have been studied in online and semi-online scenarios, but two problems that have been considered in nearly every scenario are classic scheduling problems: The bin packing problem and the makespan minimization problem. Both of these problems have been studied intensively in the migration model [4,11,13,14,20,22,23]. Both of these problems also have corresponding dual maximization variants.…”