This paper explores two fundamental concepts: branch width and weak ultrafilter. Branch
width is a significant graph width parameter that measures the degree of connectivity in a …

Motivated by concave cost combinatorial optimization problems, we study the following
mixed integer nonlinear set: P={(w, x)∈ R×{0, 1} n: w≥ f (a′ x), e′ x≤ k} where f: R→ R is …

Symmetric submodular functions are an important family of submodular functions capturing
many interesting cases, including cut functions of graphs and hypergraphs. Maximization of …

Symmetric submodular maximization is an important class of combinatorial optimization
problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm …

Numerous problems in machine learning and computer vision are discrete. As a
complicating factor, they often involve large data sets and higher-order interactions between …

Abstract We consider the Knapsack Covering problem subject to a matroid constraint. In this
problem, we are given an universe U of n items where item i has attributes: a cost c (i) and a …

We show that Karger's randomized contraction method (SODA 93) can be adapted to
multiobjective global minimum cut problems with a constant number of edge or node budget …

The problem of finding a global minimum cut in an undirected graph is fundamental to
combinatorial optimization. It has numerous applications including network reliability …

We address counting and optimization variants of multicriteria global min-cut and size-
constrained min-k-cut in hypergraphs. For an r-rank n-vertex hypergraph endowed with t …

In this paper we consider the problem of finding the {\em densest} subset subject to {\em co-
matroid constraints}. We are given a {\em monotone supermodular} set function $ f $ defined …