Related papers: Decomposable Submodular Function Minimization via …
Submodular function minimization (SFM) is a fundamental discrete optimization problem which generalizes many well known problems, has applications in various fields, and can be solved in polynomial time. Owing to applications in computer…
We devise a deterministic algorithm for minimum Steiner cut, which uses $(\log n)^{O(1)}$ maximum flow calls and additional near-linear time. This algorithm improves on Li and Panigrahi's (FOCS 2020) algorithm, which uses $(\log…
We present an $\tilde{O}\left(m^{\frac{10}{7}}U^{\frac{1}{7}}\right)$-time algorithm for the maximum $s$-$t$ flow problem and the minimum $s$-$t$ cut problem in directed graphs with $m$ arcs and largest integer capacity $U$. This matches…
This paper studies a variant of the minimum-cost flow problem in a graph with convex cost function where the demands at the vertices are functions depending on a one-dimensional parameter $\lambda$. We devise two algorithmic approaches for…
We present the first polynomial-time algorithm for computing a near-optimal \emph{flow}-expander decomposition. Given a graph $G$ and a parameter $\phi$, our algorithm removes at most a $\phi\log^{1+o(1)}n$ fraction of edges so that every…
We consider the problem of maximizing a non-negative submodular set function $f:2^N \rightarrow \mathbb{R}_+$ over a ground set $N$ subject to a variety of packing type constraints including (multiple) matroid constraints, knapsack…
For $n$-vertex $m$-edge graphs with integer polynomially-bounded costs and capacities, we provide a randomized parallel algorithm for the minimum cost flow problem with $\tilde O(m+n^ {1.5})$ work and $\tilde O(\sqrt{n})$ depth. On…
The proximal problem for structured penalties obtained via convex relaxations of submodular functions is known to be equivalent to minimizing separable convex functions over the corresponding submodular polyhedra. In this paper, we reveal a…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization (QDSFM), which allows to model a number of learning tasks on graphs and hypergraphs. The problem exhibits close ties to…
In this paper, we introduce a novel technique for constrained submodular maximization, inspired by barrier functions in continuous optimization. This connection not only improves the running time for constrained submodular maximization but…
This paper presents a framework that supports the implementation of parallel solutions for the widespread parametric maximum flow computational routines used in image segmentation algorithms. The framework is based on supergraphs, a special…
Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…
We give faster algorithms for weak expander decompositions and approximate max flow on undirected graphs. First, we show that it is possible to "warm start" the cut-matching game when computing weak expander decompositions, avoiding the…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in…
We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on $n$ vertices and $m$ edges using $\text{polylog}(n)$ calls to any maximum flow subroutine. Using the current best deterministic maximum flow…
In this paper we study the problem of minimizing a submodular function $f : 2^V \rightarrow \mathbb{R}$ that is guaranteed to have a $k$-sparse minimizer. We give a deterministic algorithm that computes an additive $\epsilon$-approximate…
We develop a framework for the distributed minimization of submodular functions. Submodular functions are a discrete analog of convex functions and are extensively used in large-scale combinatorial optimization problems. While there has…
The paper presents a dynamic solution method for dynamic minimum parametric networks flow. The solution method solves the problem for a special parametric dynamic network with linear lower bound functions of a single parameter. Instead…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…