We investigate a new optimization problem involving minimizing the Ratio of two Submodular (RS) functions. We argue that this problem occurs naturally in several real world applications. We then show the connection between this problem and several related problems including minimizing the difference between submodular functions (Iyer & Bilmes, 2012b; Narasimhan & Bilmes, 2005), and to submodula...

We describe an O(nh min{log U, n log n}) capacity scaling algorithm for the minimum cost submodular flow problem. Our algorithm modifies and extends the Edmonds–Karp capacity scaling algorithm for minimum cost flow to solve the minimum cost submodular flow problem. The modification entails scaling a relaxation parameter δ. Capacities are relaxed by attaching a complete directed graph with unifo...

We study the problem of optimal flexibility capacity portfolio selection by introducing a new notion of submodularity for correspondences, which extends the classical notion of submodular functions. In particular, we prove that the correspondence that maps flexible resources to the set of demands that they can process is submodular, and use the properties of submodular correspondences to compar...

We consider an application of the minimum-norm-point algorithm to submodular function minimization. Although combinatorial polynomial algorithms for submodular function minimization (SFM) have recently been obtained, there still remain (open) problems of reducing the complexity of the SFM algorithms and of constructing a practically fast SFM algorithms. We show some possible approach to the pro...

This paper presents a faster algorithm for the M-convex submodular flow problem, which is a generalization of the minimum-cost flow problem with an M-convex cost function for the flow-boundary, where an M-convex function is a nonlinear nonseparable discrete convex function on integer points. The algorithm extends the capacity scaling approach for the submodular flow problem by Fleischer, Iwata ...

This paper presents an efficient algorithm for minimizing a certain class of submodular functions that arise in analysis of multiclass queueing systems. In particular, the algorithm can be used for testing whether a given multiclass M/M/1 system achieves a required average performance by an appropriate control policy. With the aid of the topological sweeping method for line arrangement, our alg...

It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show—arguably, surprisingly—that invoking the classical greedy algorithm O( √ k)-times leads to the (currently) fastest deterministic algorithm, called REPEATEDGREEDY, for maximizing a general submodular funct...