Online Vector Bin Packing and Hypergraph Coloring Illuminated: Simpler Proofs and New Connections Article Swipe
Yaqiao Li
,
Denis Pankratov
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2306.11241
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2306.11241
This paper studies the online vector bin packing (OVBP) problem and the related problem of online hypergraph coloring (OHC). Firstly, we use a double counting argument to prove an upper bound of the competitive ratio of $FirstFit$ for OVBP. Our proof is conceptually simple, and strengthens the result in Azar et. al. by removing the dependency on the bin size parameter. Secondly, we introduce a notion of an online incidence matrix that is defined for every instance of OHC. Using this notion, we provide a reduction from OHC to OVBP, which allows us to carry known lower bounds of the competitive ratio of algorithms for OHC to OVBP. Our approach significantly simplifies the previous argument from Azar et. al. that relied on using intricate graph structures. In addition, we slightly improve their lower bounds. Lastly, we establish a tight bound of the competitive ratio of algorithms for OHC, where input is restricted to be a hypertree, thus resolving a conjecture in Nagy-Gyorgy et. al. The crux of this proof lies in solving a certain combinatorial partition problem about multi-family of subsets, which might be of independent interest.
Related Topics
Concepts
Hypergraph
Mathematics
Mathematical proof
Competitive analysis
Upper and lower bounds
Combinatorics
Incidence matrix
Online algorithm
Partition (number theory)
Simple (philosophy)
Bin packing problem
Discrete mathematics
Conjecture
Computer science
Algorithm
Bin
Mathematical analysis
Node (physics)
Engineering
Geometry
Structural engineering
Philosophy
Epistemology
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2306.11241
- https://arxiv.org/pdf/2306.11241
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4381573200
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4381573200Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2306.11241Digital Object Identifier
- Title
-
Online Vector Bin Packing and Hypergraph Coloring Illuminated: Simpler Proofs and New ConnectionsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
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2023-06-20Full publication date if available
- Authors
-
Yaqiao Li, Denis PankratovList of authors in order
- Landing page
-
https://arxiv.org/abs/2306.11241Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2306.11241Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2306.11241Direct OA link when available
- Concepts
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Hypergraph, Mathematics, Mathematical proof, Competitive analysis, Upper and lower bounds, Combinatorics, Incidence matrix, Online algorithm, Partition (number theory), Simple (philosophy), Bin packing problem, Discrete mathematics, Conjecture, Computer science, Algorithm, Bin, Mathematical analysis, Node (physics), Engineering, Geometry, Structural engineering, Philosophy, EpistemologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.(OVBP) | 8 |
| abstract_inverted_index.allows | 91 |
| abstract_inverted_index.bounds | 97 |
| abstract_inverted_index.double | 23 |
| abstract_inverted_index.matrix | 70 |
| abstract_inverted_index.notion | 65 |
| abstract_inverted_index.online | 4, 15, 68 |
| abstract_inverted_index.relied | 120 |
| abstract_inverted_index.result | 47 |
| abstract_inverted_index.vector | 5 |
| abstract_inverted_index.Lastly, | 134 |
| abstract_inverted_index.bounds. | 133 |
| abstract_inverted_index.certain | 173 |
| abstract_inverted_index.defined | 73 |
| abstract_inverted_index.improve | 130 |
| abstract_inverted_index.notion, | 81 |
| abstract_inverted_index.packing | 7 |
| abstract_inverted_index.problem | 9, 13, 176 |
| abstract_inverted_index.provide | 83 |
| abstract_inverted_index.related | 12 |
| abstract_inverted_index.simple, | 43 |
| abstract_inverted_index.solving | 171 |
| abstract_inverted_index.studies | 2 |
| abstract_inverted_index.Firstly, | 19 |
| abstract_inverted_index.approach | 109 |
| abstract_inverted_index.argument | 25, 114 |
| abstract_inverted_index.coloring | 17 |
| abstract_inverted_index.counting | 24 |
| abstract_inverted_index.instance | 76 |
| abstract_inverted_index.previous | 113 |
| abstract_inverted_index.removing | 53 |
| abstract_inverted_index.slightly | 129 |
| abstract_inverted_index.subsets, | 180 |
| abstract_inverted_index.Secondly, | 61 |
| abstract_inverted_index.addition, | 127 |
| abstract_inverted_index.establish | 136 |
| abstract_inverted_index.incidence | 69 |
| abstract_inverted_index.interest. | 186 |
| abstract_inverted_index.intricate | 123 |
| abstract_inverted_index.introduce | 63 |
| abstract_inverted_index.partition | 175 |
| abstract_inverted_index.reduction | 85 |
| abstract_inverted_index.resolving | 157 |
| abstract_inverted_index.$FirstFit$ | 36 |
| abstract_inverted_index.algorithms | 103, 145 |
| abstract_inverted_index.conjecture | 159 |
| abstract_inverted_index.dependency | 55 |
| abstract_inverted_index.hypergraph | 16 |
| abstract_inverted_index.hypertree, | 155 |
| abstract_inverted_index.parameter. | 60 |
| abstract_inverted_index.restricted | 151 |
| abstract_inverted_index.simplifies | 111 |
| abstract_inverted_index.Nagy-Gyorgy | 161 |
| abstract_inverted_index.competitive | 33, 100, 142 |
| abstract_inverted_index.independent | 185 |
| abstract_inverted_index.strengthens | 45 |
| abstract_inverted_index.structures. | 125 |
| abstract_inverted_index.conceptually | 42 |
| abstract_inverted_index.multi-family | 178 |
| abstract_inverted_index.combinatorial | 174 |
| abstract_inverted_index.significantly | 110 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile |