Semi-streaming Algorithms for Submodular Matroid Intersection

Valuated Matroid Intersection II: Algorithms

Based on the optimality criteria established in Part I, we show a primal-type cyclecanceling algorithm and a primal-dual-type augmenting algorithm for the valuated independent assignment problem: Given a bipartite graph G = (V , V −;A) with arc weight w : A → R and matroid valuations ω and ω− on V + and V − respectively, find a matching M(⊆ A) that maximizes ∑ {w(a) | a ∈ M}+ ω(∂M) + ω−(∂−M), w...

Streaming Algorithms for Submodular Function Maximization

We consider the problem of maximizing a nonnegative submodular set function f : 2N → R+ subject to a p-matchoid constraint in the single-pass streaming setting. Previous work in this context has considered streaming algorithms for modular functions and monotone submodular functions. The main result is for submodular functions that are non-monotone. We describe deterministic and randomized algor...

Exact and Approximation Algorithms for Weighted Matroid Intersection

In this paper, we propose new exact and approximation algorithms for the weighted matroid intersection problem. Our exact algorithm is faster than previous algorithms when the largest weight is relatively small. Our approximation algorithm delivers a (1 − ε)-approximate solution with a running time significantly faster than most known exact algorithms. The core of our algorithms is a decomposit...

Matroid Intersection

Last lecture we covered matroid intersection, and defined matroid union. In this lecture we review the definitions of matroid intersection, and then show that the matroid intersection polytope is TDI. This is Chapter 41 in Schrijver’s book. Next we review matroid union, and show that unlike matroid intersection, the union of two matroids is again a matroid. This material is largely contained in...

Efficient Algorithms for a Family of Matroid Intersection Problems