Related papers: Interdicting Structured Combinatorial Optimization…
Combinatorial optimization problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral…
Submodular optimization generalizes many classic problems in combinatorial optimization and has recently found a wide range of applications in machine learning (e.g., feature engineering and active learning). For many large-scale…
We study a family of (potentially non-convex) constrained optimization problems with convex composite structure. Through a novel analysis of non-smooth geometry, we show that proximal-type algorithms applied to exact penalty formulations of…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every…
The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…
In the restricted assignment problem, the input consists of a set of machines and a set of jobs each with a processing time and a subset of eligible machines. The goal is to find an assignment of the jobs to the machines minimizing the…
We consider the max-cut and max-$k$-cut problems under graph-based constraints. Our approach can handle any constraint specified using monadic second-order (MSO) logic on graphs of constant treewidth. We give a $\frac{1}{2}$-approximation…
Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the…
In this paper, the monotone submodular maximization problem (SM) is studied. SM is to find a subset of size $\kappa$ from a universe of size $n$ that maximizes a monotone submodular objective function $f$. We show using a novel analysis…
Shortest path network interdiction is a combinatorial optimization problem on an activity network arising in a number of important security-related applications. It is classically formulated as a bilevel maximin problem representing an…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
In a widely-studied class of multi-parametric optimization problems, the objective value of each solution is an affine function of real-valued parameters. Then, the goal is to provide an optimal solution set, i.e., a set containing an…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
SSP reductions are a type of polynomial reductions that also preserve the solutions of the instances. This means there is a mapping from each solution in the original instance to one in the reduced instance, allowing direct deduction of an…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
This paper investigates a combinatorial optimization problem motived from a secure power network design application in [D\'{a}n and Sandberg 2010]. Two equivalent graph optimization formulations are derived. One of the formulations is a…