Improved Streaming Algorithms for Maximizing Monotone Submodular Functions under a Knapsack Constraint
In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in a streaming setting. In such a setting, elements arrive sequentially and at any point in time, and the algorithm can store only a small fraction of the elements that have arrived s...
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| Vydáno v: | Algorithmica Ročník 83; číslo 3; s. 879 - 902 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.03.2021
Springer Verlag |
| Témata: | |
| ISSN: | 0178-4617, 1432-0541 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in a streaming setting. In such a setting, elements arrive sequentially and at any point in time, and the algorithm can store only a small fraction of the elements that have arrived so far. For the special case that all elements have unit sizes (i.e., the cardinality-constraint case), one can find a
(
0.5
-
ε
)
-approximate solution in
O
(
K
ε
-
1
)
space, where
K
is the knapsack capacity (Badanidiyuru
et al.
KDD 2014). The approximation ratio is recently shown to be optimal (Feldman
et al.
STOC 2020). In this work, we propose a
(
0.4
-
ε
)
-approximation algorithm for the knapsack-constrained problem, using space that is a polynomial of
K
and
ε
. This improves on the previous best ratio of
0.363
-
ε
with space of the same order. Our algorithm is based on a careful combination of various ideas to transform multiple-pass streaming algorithms into a single-pass one. |
|---|---|
| ISSN: | 0178-4617 1432-0541 |
| DOI: | 10.1007/s00453-020-00786-4 |