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Recently, deep learning based methods have demonstrated promising results on the graph matching problem, by relying on the descriptive capability of deep features extracted on graph nodes. However, one main limitation with existing deep…
Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…
We prove new explicit inapproximability results for the Vertex Cover Problem on the Power Law Graphs and some functional generalizations of that class of graphs. Our results depend on special bounded degree amplifier constructions for those…
Computational complexity and approximation algorithms are reported for a problem of stabbing a set of straight line segments with the least cardinality set of disks of fixed radii $r>0$ where the set of segments forms a straight line…
Graph Neural Networks (GNNs) have already been widely applied in various graph mining tasks. However, they suffer from the shallow architecture issue, which is the key impediment that hinders the model performance improvement. Although…
We give polynomial-time approximation schemes for monotone maximization problems expressible in terms of distances (up to a fixed upper bound) and efficiently solvable in graphs of bounded treewidth. These schemes apply in all fractionally…
We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it…
Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open…
Jaberi [7] presented approximation algorithms for the problem of computing a minimum size 2-vertex strongly biconnected subgraph in directed graphs. We have implemented approximation algorithms presented in [7] and we have tested the…
We design a $1.49993$-approximation algorithm for the metric traveling salesperson problem (TSP) for instances in which an optimal solution to the subtour linear programming relaxation is half-integral. These instances received significant…
We define a reduction mechanism for LP and SDP formulations that degrades approximation factors in a controlled fashion. Our reduction mechanism is a minor restriction of classical reductions establishing inapproximability in the context of…
Correspondence is a ubiquitous problem in computer vision and graph matching has been a natural way to formalize correspondence as an optimization problem. Recently, graph matching solvers have included higher-order terms representing…
Betweenness centrality ranks the importance of nodes by their participation in all shortest paths of the network. Therefore computing exact betweenness values is impractical in large networks. For static networks, approximation based on…
In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…
We study the recently introduced problem of finding dense common subgraphs: Given a sequence of graphs that share the same vertex set, the goal is to find a subset of vertices $S$ that maximizes some aggregate measure of the density of the…
Structured sparse optimization is an important and challenging problem for analyzing high-dimensional data in a variety of applications such as bioinformatics, medical imaging, social networks, and astronomy. Although a number of structured…
Problems in differentiable rendering often involve optimizing scene parameters that cause motion in image space. The gradients for such parameters tend to be sparse, leading to poor convergence. While existing methods address this sparsity…
We prove new results for approximating the graphic TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees. For the graphic TSP itself, we improve the approximation ratio to 7/5. For a…
In a directed graph $G$ with non-correlated edge lengths and costs, the \emph{network design problem with bounded distances} asks for a cost-minimal spanning subgraph subject to a length bound for all node pairs. We give a bi-criteria…
Graph Neural Networks (GNNs) face two fundamental challenges when scaled to deep architectures: oversmoothing, where node representations converge to indistinguishable vectors, and oversquashing, where information from distant nodes fails…