Dynamic averaging load balancing on cycles

D.-A. Alistarh, G. Nadiradze, A. Sabour, in:, 47th International Colloquium on Automata, Languages, and Programming, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.

Download
OA 2020_LIPIcs_Alistarh.pdf 782.99 KB

Conference Paper | Published | English

Scopus indexed
Department
Series Title
LIPIcs
Abstract
We consider the following dynamic load-balancing process: given an underlying graph G with n nodes, in each step t≥ 0, one unit of load is created, and placed at a randomly chosen graph node. In the same step, the chosen node picks a random neighbor, and the two nodes balance their loads by averaging them. We are interested in the expected gap between the minimum and maximum loads at nodes as the process progresses, and its dependence on n and on the graph structure. Variants of the above graphical balanced allocation process have been studied previously by Peres, Talwar, and Wieder [Peres et al., 2015], and by Sauerwald and Sun [Sauerwald and Sun, 2015]. These authors left as open the question of characterizing the gap in the case of cycle graphs in the dynamic case, where weights are created during the algorithm’s execution. For this case, the only known upper bound is of 𝒪(n log n), following from a majorization argument due to [Peres et al., 2015], which analyzes a related graphical allocation process. In this paper, we provide an upper bound of 𝒪 (√n log n) on the expected gap of the above process for cycles of length n. We introduce a new potential analysis technique, which enables us to bound the difference in load between k-hop neighbors on the cycle, for any k ≤ n/2. We complement this with a "gap covering" argument, which bounds the maximum value of the gap by bounding its value across all possible subsets of a certain structure, and recursively bounding the gaps within each subset. We provide analytical and experimental evidence that our upper bound on the gap is tight up to a logarithmic factor.
Publishing Year
Date Published
2020-06-01
Proceedings Title
47th International Colloquium on Automata, Languages, and Programming
Volume
168
Article Number
7
Conference
ICALP: International Colloquium on Automata, Languages, and Programming
Conference Location
Virtual, Online; Germany
Conference Date
2020-07-08 – 2020-07-11
ISSN
IST-REx-ID

Cite this

Alistarh D-A, Nadiradze G, Sabour A. Dynamic averaging load balancing on cycles. In: 47th International Colloquium on Automata, Languages, and Programming. Vol 168. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.ICALP.2020.7
Alistarh, D.-A., Nadiradze, G., & Sabour, A. (2020). Dynamic averaging load balancing on cycles. In 47th International Colloquium on Automata, Languages, and Programming (Vol. 168). Virtual, Online; Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.ICALP.2020.7
Alistarh, Dan-Adrian, Giorgi Nadiradze, and Amirmojtaba Sabour. “Dynamic Averaging Load Balancing on Cycles.” In 47th International Colloquium on Automata, Languages, and Programming, Vol. 168. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.ICALP.2020.7.
D.-A. Alistarh, G. Nadiradze, and A. Sabour, “Dynamic averaging load balancing on cycles,” in 47th International Colloquium on Automata, Languages, and Programming, Virtual, Online; Germany, 2020, vol. 168.
Alistarh D-A, Nadiradze G, Sabour A. 2020. Dynamic averaging load balancing on cycles. 47th International Colloquium on Automata, Languages, and Programming. ICALP: International Colloquium on Automata, Languages, and Programming , LIPIcs, vol. 168.
Alistarh, Dan-Adrian, et al. “Dynamic Averaging Load Balancing on Cycles.” 47th International Colloquium on Automata, Languages, and Programming, vol. 168, 7, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.ICALP.2020.7.
All files available under the following license(s):
Main File(s)
File Name
Access Level
OA Open Access
Date Uploaded
2020-08-25
MD5 Checksum
ec8475b5bf3f24453c3a879e6ab45f16


Export

Marked Publications

Open Data IST Research Explorer

Sources

arXiv 2003.09297

Search this title in

Google Scholar
ISBN Search