Errata: `` Analysis of Several Task-Scheduling Algorithms for a Model of Multiprogramming Computer Systems''

Abstract

of the Los Alamos Scientific Laboratory, has discovered several errors in this paper. Although most of these were of a minor nature, he did discover a significant flaw m the proof of case 4, Theorem 4.5. The authors have dtscovered a vahd proof for case 4; unfortunately, the proof of case 7, Theorem 4.5, depended on the incorrect proof of case 4. A valid proof for case 7 has not yet emerged A bound for case 7 which has been proved is the general bound of 3 -3In from Theorem 3.1. The authors have not discovered a counterexample for case 7 and do conjecture that it remains vahd Complete errata correcting all known errors are avadable by contacting the authors at

Algorithms for on-line bin-packing problems with cardinality constraints

“…In the o -line version of the problem, Krause et al [6,7] introduced several approximation algorithms and showed that they all have an asymptotic worst-case performance ratio of 2. Very recent progress in this direction is due to Caprara et al [1], who present an asymptotic polynomial time approximation scheme for ordered vector packing problems, which include the (kBP) problem as a special case.…”

“…Krause et al [6,7] have also considered the on-line version. They investigate an adaptation of the (FF) algorithm to the cardinality constrained problem, denoted by (kFF), which packs a new item into the ÿrst possible bin that contains less than k items.…”

MILP-based approaches for a bin-packing problem with a fixed-plus-linear charge scheme

“…Each feasible solution for the cardinality-constrained bin-packing problem satisfies the condition of Theorem 1. Many algorithms have been proposed since the early work by [14] Krause et al (1977). Here, we adopt the technique presented by [13] Kellerer and Pferschy (1999).…”

“…For example, if 𝑟(𝑥 * ) < 𝑟(𝑥 * ), we can swap columns 1 and 2, that is, 𝑥 * * = 𝑥 * and 𝑥 * * = 𝑥 * . Note that 𝛿 * * is an optimal solution for BP and a feasible solution for constraints (14) Theorem 3 shows that there exists an error bound for 𝐴 . Thus, it suffices to solve IBP when 𝑍 * (𝐴 , 𝑘, 𝑣, |𝐴 |, ℎ) is small.…”

Online interval coloring with packing constraints

“…This problem was studied also in [17,10,4]. Cardinality constrained bin packing was first studied by Krause, Shen and Schwetman [18,19]. It was also studied in [3,8].…”