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An APTAS for Bin Packing with Clique-graph Conflicts [article]

Ilan Doron-Arad, Ariel Kulik, Hadas Shachnai
2021 arXiv   pre-print
This problem, known as bin packing with clique-graph conflicts, has natural applications in storing file replicas, security in cloud computing and signal distribution.  ...  Our main result is an asymptotic polynomial time approximation scheme (APTAS) for the problem, improving upon the best known ratio of 2. particular, for any instance I and a fixed ∈ (0,1), the items are  ...  Indeed, GBP is the special case where the conflict graph is a union of cliques. Thus, GBP is also known as bin packing with clique-graph conflicts (see Section 1.2).  ... 
arXiv:2011.04273v6 fatcat:2ay62rfv45fz5gjukgxw6y5fnm

Multi-dimensional Packing with Conflicts [chapter]

Leah Epstein, Asaf Levin, Rob van Stee
2007 Lecture Notes in Computer Science  
We study the multi-dimensional version of the bin packing problem with conflicts.  ...  . , n} with sides s1, s2, . . . , sn ∈ [0, 1] and a conflict graph G = (V, E).  ...  An improved 1.75-approximation for bipartite conflict graphs was achieved by applying the algorithm of [12] on inputs with large enough values of opt, while finding better solutions for inputs with small  ... 
doi:10.1007/978-3-540-74240-1_25 fatcat:nyhnndbelbfdjiaihmoc6lacba

Two-dimensional packing with conflicts

Leah Epstein, Asaf Levin, Rob van Stee
2008 Acta Informatica  
We study the two-dimensional version of the bin packing problem with conflicts.  ...  . , n} with sides s 1 , s 2 . . . , s n ∈ [0, 1] and a conflict graph G = (V, E).  ...  An interesting research direction would be to find whether an Asymptotic Polynomial Time Approximation Scheme (APTAS) exists for some square packing with conflicts, for some class of (non-empty) conflict  ... 
doi:10.1007/s00236-007-0067-7 fatcat:5rcq7atkzzgcxes2fobtxjfgke

Towards Bin Packing (preliminary problem survey, models with multiset estimates) [article]

Mark Sh. Levin
2016 arXiv   pre-print
A special attention is targeted to the following versions of bin packing problems: (a) problem with multiset estimates of items, (b) problem with colored items (and some close problems).  ...  The paper described a generalized integrated glance to bin packing problems including a brief literature survey and some new problem formulations for the cases of multiset estimates of items.  ...  Robust APTAS (for classical bin packing) [99] 3.11.  ... 
arXiv:1605.07574v1 fatcat:inhdwvq6kzhzrad5uv4qo27ami

A multidimensional colored packing approach for network slicing with dedicated protection

Hicham Lesfari, Frederic Giroire, Giuseppe Di Lena, Chidung Lac
2021 2021 IEEE Global Communications Conference (GLOBECOM)  
A novel approach based on an extension of bin packing is proposed. We perform a comprehensive evaluation in terms of performance under realworld ISP networks along with synthetic traces.  ...  We show that our methods can calculate rapidly efficient solutions for large instances.  ...  In order to solve the COLOURED-BIN-PACKING, we leverage upon efficient algorithms for the bin packing tailored for a certain class of graphs.  ... 
doi:10.1109/globecom46510.2021.9685460 fatcat:xajgobpg4bgczcbrqkrkiycegm

An Asymptotic PTAS for Batch Scheduling with Nonidentical Job Sizes to Minimize Makespan [chapter]

Yuzhong Zhang, Zhigang Cao
Lecture Notes in Computer Science  
Finally, we thank Xi'an Jiaotong University and NSF of China for the support and local organizers and colleagues for their assistance.  ...  We thank all the people who made this meeting possible: the authors for submitting papers, the Program Committee members and external referees (listed in the proceedings) for their excellent work, and  ...  We develop an improved parameterized algorithm for the problem based on a deeper and more careful analysis on the structures of bipartite graphs.  ... 
doi:10.1007/978-3-540-73556-4_7 fatcat:qundndqypvgupglzb3iv4yhe7m