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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…
In this paper, we introduce a new model to study network reliability with node failures. This model, strongly connected node reliability, is the directed variant of node reliability and measures the probability that the operational vertices…
The future of main memory appears to lie in the direction of new technologies that provide strong capacity-to-performance ratios, but have write operations that are much more expensive than reads in terms of latency, bandwidth, and energy.…
Reeb graphs are simple topological descriptors with applications in many areas like topological data analysis and computational geometry. Despite their prevalence, visualization of Reeb graphs has received less attention. In this paper, we…
We show that the problem of counting perfect matchings remains #P-complete even if we restrict the input to very dense graphs, proving the conjecture in [5]. Here "dense graphs" refer to bipartite graphs of bipartite independence number…
DC power flow approximations are ubiquitous in the electricity industry. However, these linear approximations fail to capture important physical aspects of power flow, such as the reactive power and voltage magnitude, which are crucial in…
An enhanced label propagation (LP) method called GraphHop was proposed recently. It outperforms graph convolutional networks (GCNs) in the semi-supervised node classification task on various networks. Although the performance of GraphHop…
Power diagrams, a type of weighted Voronoi diagrams, have many applications throughout operations research. We study the problem of power diagram detection: determining whether a given finite partition of $\mathbb{R}^d$ takes the form of a…
Natural Language Processing (NLP) provides highly effective tools for interpreting and handling human language, offering a broad spectrum of applications. In this paper, we address a classic combinatorial problem -- finding graph partitions…
A heavy path in a weighted graph represents a notion of connectivity and ordering that goes beyond two nodes. The heaviest path of length l in the graph, simply means a sequence of nodes with edges between them, such that the sum of edge…
In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in $P \cap Z^n$, assuming that $P$ is a polyhedron,…
Given a group $G$, let us connect two non-identity elements by an edge if and only if one is a power of another. This gives a graph structure on $G$ minus identity, called the reduced power graph. In this paper, we shall find the exact…
Smart grids are large and complex cyber physical infrastructures that require real-time monitoring for ensuring the security and reliability of the system. Monitoring the smart grid involves analyzing continuous data-stream from various…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
Interpolating between measures supported by polygonal or polyhedral domains is a problem that has been recently addressed by the semi-discrete optimal transport framework. Within this framework, one of the domains is discretized with a set…
In the dynamic Single-Source Shortest Paths (SSSP) problem, we are given a graph $G=(V,E)$ subject to edge insertions and deletions and a source vertex $s\in V$, and the goal is to maintain the distance $d(s,t)$ for all $t\in V$.…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
Formulations of the Image Decomposition Problem as a Multicut Problem (MP) w.r.t. a superpixel graph have received considerable attention. In contrast, instances of the MP w.r.t. a pixel grid graph have received little attention, firstly,…
Existing graph layout algorithms are usually not able to optimize all the aesthetic properties desired in a graph layout. To evaluate how well the desired visual features are reflected in a graph layout, many readability metrics have been…
We present a general graph-based modeling abstraction for optimization that we call an OptiGraph. Under this abstraction, any optimization problem is treated as a hierarchical hypergraph in which nodes represent optimization subproblems and…