Streaming Submodular Maximization under Matroid Constraints

Feldman, Moran; Liu, Paul; Norouzi-Fard, Ashkan; Svensson, Ola; Zenklusen, Rico

doi:10.48550/arxiv.2107.07183

Cited by 1 publication

(1 citation statement)

References 23 publications

(55 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Often, the algorithm makes one (single) pass if it is allowed to visit the stream once. Indeed, single-streaming algorithms have been proposed for the submodular problem with a variety of constraints, such as knapsack [18,19] , matroid [20,21] , and a more general independence system [22][23][24] . In other cases, the algorithms are allowed to visit the input multiple times, which are summarized as multi-pass streaming algorithms.…”

Section: Related Workmentioning

confidence: 99%

Approximating ($m_{B},m_{P}$)-Monotone BP Maximization and Extensions

Yang

Gao

Han

et al. 2023

Tsinghua Sci. Technol.

View full text Add to dashboard Cite

The paper proposes the optimization problem of maximizing the sum of suBmodular and suPermodular (BP) functions with partial monotonicity under a streaming fashion. In this model, elements are randomly released from the stream and the utility is encoded by the sum of partial monotone suBmodular and suPermodular functions.The goal is to determine whether a subset from the stream of size bounded by parameter k subject to the summarized utility is as large as possible. In this work, a threshold-based streaming algorithm is presented for the BP maximization that attains a ..1 Ä/=.2 Ä/ O."//-approximation with O.1=" 4 log 3 .1="/ log..2 Ä/k=.1 Ä/ 2 // memory complexity, where Ä denotes the parameter of supermodularity ratio. We further consider a more general model with fair constraints and present a greedy-based algorithm that obtains the same approximation. We finally investigate this fair model under the streaming fashion and provide a ..1 Ä/ 4 =.2 2Ä C Ä 2 / 2 O."//-approximation algorithm.

show abstract