Comparing online algorithms for bin packing problems

Abstract

The relative worst-order ratio is a measure of the quality of online algorithms. In contrast to the competitive ratio, this measure compares two online algorithms directly instead of using an intermediate comparison with an optimal offline algorithm. In this paper, we apply the relative worst-order ratio to online algorithms for several common variants of the bin packing problem. We mainly consider pairs of algorithms that are not distinguished by the competitive ratio and show that the relative worst-order ratio prefers the intuitively better algorithm of each pair.

Online Bin Covering: Expectations vs. Guarantees

“…DNF was shown to be 1 2 -competitive in [2], and the same result for DH k was noted in [16]. For completeness, to show that this result is tight for a large class of algorithms, we define a reasonable algorithm to be one that closes bins as soon as they are covered, does not close bins before they are covered, and does not have more than a constant number of open bins at any point.…”

“…In [16], bin covering was analyzed, but using a version of the problem allowing items of size 1. We analyze the more commonly studied version for bin covering, where all items are strictly smaller than 1.…”

Online bin covering: Expectations vs. guarantees

“…Relative worst order analysis [4,5] has been applied to many problems; a recent list can be found in [15]. In [16], bin covering was analyzed, but using a version of the problem allowing items of size 1. We analyze the more commonly studied version for bin covering, where all items are strictly smaller than 1.…”

Relative Worst-Order Analysis: A Survey

“…We claim that GREEDY-FIT is obviously the better algorithm, but if the bin size is larger than approximately q 3 , ONE-BIN has a better competitive ratio than GREEDY-FIT [55]. However, according to RWOA, GREEDY-FIT is better [40].…”