Semi-Streaming Algorithms for Submodular Matroid Intersection

02/08/2021
by   Paritosh Garg, et al.
0

While the basic greedy algorithm gives a semi-streaming algorithm with an approximation guarantee of 2 for the unweighted matching problem, it was only recently that Paz and Schwartzman obtained an analogous result for weighted instances. Their approach is based on the versatile local ratio technique and also applies to generalizations such as weighted hypergraph matchings. However, the framework for the analysis fails for the related problem of weighted matroid intersection and as a result the approximation guarantee for weighted instances did not match the factor 2 achieved by the greedy algorithm for unweighted instances. Our main result closes this gap by developing a semi-streaming algorithm with an approximation guarantee of 2+ϵ for weighted matroid intersection, improving upon the previous best guarantee of 4+ϵ. Our techniques also allow us to generalize recent results by Levin and Wajc on submodular maximization subject to matching constraints to that of matroid-intersection constraints. While our algorithm is an adaptation of the local ratio technique used in previous works, the analysis deviates significantly and relies on structural properties of matroid intersection, called kernels. Finally, we also conjecture that our algorithm gives a (k+ϵ) approximation for the intersection of k matroids but prove that new tools are needed in the analysis as the used structural properties fail for k≥ 3.

READ FULL TEXT

page 1

page 2

page 3

page 4

07/15/2021

Streaming Submodular Maximization with Matroid and Matching Constraints

Recent progress in (semi-)streaming algorithms for monotone submodular f...
02/18/2021

Improved Multi-Pass Streaming Algorithms for Submodular Maximization with Matroid Constraints

We give improved multi-pass streaming algorithms for the problem of maxi...
06/17/2018

Greedy and Local Ratio Algorithms in the MapReduce Model

MapReduce has become the de facto standard model for designing distribut...
08/23/2020

Streaming Submodular Matching Meets the Primal-Dual Method

We study streaming submodular maximization subject to matching/b-matchin...
04/11/2022

Submodular Maximization Subject to Matroid Intersection on the Fly

Despite a surge of interest in submodular maximization in the data strea...
10/30/2018

Submodular Maximization Under A Matroid Constraint: Asking more from an old friend, the Greedy Algorithm

The classical problem of maximizing a submodular function under a matroi...
07/21/2021

Approximation by Lexicographically Maximal Solutions in Matching and Matroid Intersection Problems

We study how good a lexicographically maximal solution is in the weighte...