By Evripidis Bampis, Ola Svensson
This publication constitutes the completely refereed post-workshop lawsuits of the twelfth overseas Workshop on Approximation and on-line Algorithms, WAOA 2014, held in Wrocław, Poland, in September 2014 as a part of ALGO 2014.
The 22 revised complete papers awarded have been conscientiously reviewed and chosen from forty nine submissions. They hide quite a lot of issues equivalent to coloring and partitioning, aggressive research, community layout, packing and overlaying, paradigms for layout and research of approximation and on-line algorithms, randomization suggestions, real-world purposes, and scheduling problems.
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Additional info for Approximation and Online Algorithms: 12th International Workshop, WAOA 2014, Wrocław, Poland, September 11-12, 2014, Revised Selected Papers
Lemma 1. For any packing of a valid instance into m bins A of any size, we have w(A) ≤ 0 and v(A) ≤ 0. First Phase. During the ﬁrst phase, our algorithm maintains the invariant that only bins of the following types exist. See Fig. 1 for an illustration of the types of the bins. E Empty bins: bins that have no item. G Complete bins: all bins A that have w(A) ≥ 0 and s(A) ≥ 12; H Huge-item bins: all bins A that contain a huge item (plus possibly some other items) and have s(A) < 12; L One large-item bin: a bin containing only a single large item; M One medium-item bin: a bin A with s(A) ≤ 13 and only medium items; T One tiny bin: a bin with s(A) ≤ 3; R Regular bins: all other bins with s(A) ∈ (3, 6]; First-phase algorithm: Let e be the number of empty bins and r the number of regular bins.
Semi on-line algorithms for the partition problem. Oper. Res. Lett. 21, 235–242 (1997) 11. : The performance of a memory allocation algorithm. cz Abstract. In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of c ≥ 2 colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy.
WAOA 2014, LNCS 8952, pp. 23–34, 2015. 1007/978-3-319-18263-6 3 24 M. B¨ ohm et al. The problem has been revisited recently, with both lower bound improvements and new eﬃcient algorithms. 57 and Gabay et al. 53. 4. On the lower bound side, the lower bound 4/3 of  was surpassed only for the case of three bins by Gabay et al. , who show a lower bound of 19/14, using an extensive computer search. Our Contributions. In Sect. 5. We build on the techniques of [7,9] who designed two-phase algorithms where the ﬁrst phase tries to ﬁll some bins close to R − 1 and achieve a ﬁxed ratio between these bins and empty bins, while the second phase uses the bins in blocks of ﬁxed size and analyzes each block separately.