Non UBC
DSpace
Udwani, Rajan
2019-07-17T09:10:01Z
2019-01-17T16:11
We consider the problem of multi-objective maximization of monotone submodular functions subject to cardinality constraint, often formulated as $\max_{|A|=k}\min_{i\in\{1,\dots,m\}}f_i(A)$. While it is widely known that greedy methods work well for a single objective, the problem becomes much harder with multiple objectives. In fact, Krause et al.\ (2008) showed that when the number of objectives $m$ grows as the cardinality $k$ i.e., $m=\Omega(k)$, the problem is inapproximable (unless $P=NP$). We focus on the case where the number of objectives is super-constant yet much smaller than the cardinality of the chosen set. We propose the first constant factor algorithms for this regime, including one with the best achievable asymptotic guarantee and also a more practical nearly linear time algorithm. Experiments on synthetic data show that a heuristic based on our more practical and fast algorithm outperforms existing heuristics.
https://circle.library.ubc.ca/rest/handle/2429/71026?expand=metadata
42.0
video/mp4
Author affiliation: Columbia University
Banff (Alta.)
10.14288/1.0379889
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Postdoctoral
BIRS Workshop Lecture Videos (Banff, Alta)
Mathematics
Operations research, mathematical programming
Computer science
Applied computer science
Multi-objective Maximization of Monotone Submodular Functions with Cardinality Constraint
Moving Image
http://hdl.handle.net/2429/71026