Width-Independence Beyond Linear Objectives: Distributed Fair Packing and Covering Algorithms
In network routing and resource allocation, $\alpha$-fair utility functions are concave objective functions used to model different notions of fairness in a single, generic framework. Different choices of the parameter $\alpha$ give rise to different notions of fairness, including max-min fairness ($\alpha = \infty$), proportional fairness ($\alpha=1$), and the unfair linear optimization ($\alpha = 0)$. In this work, we consider $\alpha$-fair resource allocation problems, defined as the maximization of $\alpha$-fair utility functions under packing constraints. We give improved distributed algorithms for constructing $\epsilon$-approximate solutions to such problems. Our algorithms are width-independent, i.e., their running time depends only poly-logarithmically on the largest entry of the constraint matrix, and closely matches the state-of-the-art guarantees for distributed algorithms for packing linear programs, i.e., for the case $\alpha = 0.$ The only previously known width-independent algorithms for $\alpha$-fair resource allocation, by Marasevic, Stein, and Zussman, obtained convergence times that exhibited much worse dependence on $\epsilon$ and $\alpha$ and relied on a less principled analysis. By contrast, our analysis leverages the Approximate Duality Gap framework of Diakonikolas and Orecchia to obtain better algorithms with a (slightly) simpler analysis. Finally, we introduce a natural counterpart of $\alpha$-fairness for minimization problems and motivate its usage in the context of fair task allocation. This generalization yields $\alpha$-fair covering problems, for which we provide the first width-independent nearly-linear-time approximate solvers by reducing their analysis to the $\alpha < 1$ case of the $\alpha$-fair packing problem.
NurtureToken New!

Token crowdsale for this paper ends in

Buy Nurture Tokens

Authors

Are you an author of this paper? Check the Twitter handle we have for you is correct.

Jelena Diakonikolas (add twitter)
Maryam Fazel (add twitter)
Lorenzo Orecchia (add twitter)
Ask The Authors

Ask the authors of this paper a question or leave a comment.

Read it. Rate it.
#1. Which part of the paper did you read?

#2. The paper contains new data or analyses that is openly accessible?
#3. The conclusion is supported by the data and analyses?
#4. The conclusion is of scientific interest?
#5. The result is likely to lead to future research?

Github
User:
None (add)
Repo:
None (add)
Stargazers:
0
Forks:
0
Open Issues:
0
Network:
0
Subscribers:
0
Language:
None
Youtube
Link:
None (add)
Views:
0
Likes:
0
Dislikes:
0
Favorites:
0
Comments:
0
Other
Sample Sizes (N=):
Inserted:
Words Total:
Words Unique:
Source:
Abstract:
None
08/08/18 05:54PM
14,517
2,535
Tweets
Nobody has tweeted about this paper.
Images
Related