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In this study, we address the complex issue of graph clustering in signed graphs, which are characterized by positive and negative weighted edges representing attraction and repulsion among nodes, respectively. The primary objective is to…
One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very…
Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…
Spectral partitioning is a simple, nearly-linear time, algorithm to find sparse cuts, and the Cheeger inequalities provide a worst-case guarantee for the quality of the approximation found by the algorithm. Local graph partitioning…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
We show how one can phrase the cut improvement problem for graphs as a sparse recovery problem, whence one can use algorithms originally developed for use in compressive sensing (such as SubspacePursuit or CoSaMP) to solve it. We show that…
Given a simple connected graph $G = (V, E)$, we seek to partition the vertex set $V$ into $k$ non-empty parts such that the subgraph induced by each part is connected, and the partition is maximally balanced in the way that the maximum…
The growing complexity of modern Cyber-Physical Systems (CPS) and the frequent communication between their components make them vulnerable to malicious attacks. As a result, secure state estimation is a critical requirement for the control…
In a balanced graph decomposition, every vertex of the host graph appears in the same number of blocks. We propose the use of colored loops as a framework for unifying various other types of local balance conditions in graph decompositions.…
In this paper we propose a new parallel algorithm for solving global optimization (GO) multidimensional problems. The method unifies two powerful approaches for accelerating the search: parallel computations and local tuning on the behavior…
Image segmentation is a popular area of research in computer vision that has many applications in automated image processing. A recent technique called piecewise flat embeddings (PFE) has been proposed for use in image segmentation; PFE…
The graph matching optimization problem is an essential component for many tasks in computer vision, such as bringing two deformable objects in correspondence. Naturally, a wide range of applicable algorithms have been proposed in the last…
We introduce a new multi-dimensional nonlinear embedding -- Piecewise Flat Embedding (PFE) -- for image segmentation. Based on the theory of sparse signal recovery, piecewise flat embedding with diverse channels attempts to recover a…
Graph clustering, aiming to partition nodes of a graph into various groups via an unsupervised approach, is an attractive topic in recent years. To improve the representative ability, several graph auto-encoder (GAE) models, which are based…
This work studies distributed algorithms for locally optimal load-balancing: We are given a graph of maximum degree $\Delta$, and each node has up to $L$ units of load. The task is to distribute the load more evenly so that the loads of…
In this paper we tackle the problem of persistently covering a complex non-convex environment with a team of robots. We consider scenarios where the coverage quality of the environment deteriorates with time, requiring to constantly revisit…
The convergence performance of distributed optimization algorithms is of significant importance to solve optimal power flow (OPF) in a distributed fashion. In this paper, we aim to provide some insights on how to partition a power system to…
Local graph clustering methods aim to detect small clusters in very large graphs without the need to process the whole graph. They are fundamental and scalable tools for a wide range of tasks such as local community detection, node ranking…
An important objective for analyzing real-world graphs is to achieve scalable performance on large, streaming graphs. A challenging and relevant example is the graph partition problem. As a combinatorial problem, graph partition is NP-hard,…