Related papers: Improved Region-Growing and Combinatorial Algorith…
Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of…
The $k$-center problem is a central optimization problem with numerous applications for machine learning, data mining, and communication networks. Despite extensive study in various scenarios, it surprisingly has not been thoroughly…
Given an edge-weighted graph, how many minimum $k$-cuts can it have? This is a fundamental question in the intersection of algorithms, extremal combinatorics, and graph theory. It is particularly interesting in that the best known bounds…
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
Many large-scale optimization problems decompose into a master problem and scenario subproblems, a structure that can be exploited by Benders decomposition. In Benders decomposition, each iteration may generate many cuts from scenario…
Motivated by what is required for real-time path planning, the paper starts out by presenting sRMPD, a new recursive "local" planner founded on the key notion that, unless made necessary by an obstacle, there must be no deviation from the…
Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find…
Several important tasks in medical image analysis can be stated in the form of an optimization problem whose feasible solutions are connected subgraphs. Examples include the reconstruction of neural or vascular structures under…
We consider the rooted prize-collecting walks (PCW) problem, wherein we seek a collection $C$ of rooted walks having minimum prize-collecting cost, which is the (total cost of walks in $C$) + (total node-reward of nodes not visited by any…
In this paper, we study two important extensions of the classical minimum cut problem, called {\em Connectivity Preserving Minimum Cut (CPMC)} problem and {\em Threshold Minimum Cut (TMC)} problem, which have important applications in…
Characterization of joint probability distribution for large networks of random variables remains a challenging task in data science. Probabilistic graph approximation with simple topologies has practically been resorted to; typically the…
We give almost-linear-time algorithms for approximating rooted minimum cut and maximum arborescence packing in directed graphs, two problems that are dual to each other [Edm73]. More specifically, for an $n$-vertex, $m$-edge directed graph…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
Districting-and-routing is a strategic problem aiming to aggregate basic geographical units (e.g., zip codes) into delivery districts. Its goal is to minimize the expected long-term routing cost of performing deliveries in each district…
Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose…
In the $k$-Cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. Prior work on this problem gives, for all $h…
Data-analysis tasks often involve an iterative process, which requires refining previous solutions. For instance, when analyzing dynamic social networks, we may be interested in monitoring the evolution of a community that was identified at…
Most state-of-the-art motion segmentation algorithms draw their potential from modeling motion differences of local entities such as point trajectories in terms of pairwise potentials in graphical models. Inference in instances of minimum…
In this article, we develop a trust-region technique to find critical points of unconstrained set optimization problems with the objective set-valued map defined by finitely many twice continuously differentiable functions. The technique is…
The k-forest problem is a common generalization of both the k-MST and the dense-$k$-subgraph problems. Formally, given a metric space on $n$ vertices $V$, with $m$ demand pairs $\subseteq V \times V$ and a ``target'' $k\le m$, the goal is…