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The "Subset Sum problem" is a very well-known NP-complete problem. In this work, a top-k variation of the "Subset Sum problem" is considered. This problem has wide application in recommendation systems, where instead of k best objects the k…
This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…
A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different…
We study the problem of optimal leader selection in consensus networks with noisy relative information. The objective is to identify the set of $k$ leaders that minimizes the formation's deviation from the desired trajectory established by…
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…
Distributed average consensus is the main mechanism in algorithms for decentralized computation. In distributed average consensus algorithm each node has an initial state, and the goal is to compute the average of these initial states in…
In this paper, we consider a subset selection problem in a spatial field where we seek to find a set of k locations whose observations provide the best estimate of the field value at a finite set of prediction locations. The measurements…
In temporal ordered clustering, given a single snapshot of a dynamic network in which nodes arrive at distinct time instants, we aim at partitioning its nodes into $K$ ordered clusters $\mathcal{C}_1 \prec \cdots \prec \mathcal{C}_K$ such…
Biclustering is the task of simultaneously clustering the rows and columns of the data matrix into different subgroups such that the rows and columns within a subgroup exhibit similar patterns. In this paper, we consider the case of…
We study the problem of optimal leader selection in consensus networks under two performance measures (1) formation coherence when subject to additive perturbations, as quantified by the steady-state variance of the deviation from the…
Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of $n$ agents located in an underlying metric space, our goal is to partition them into $k$ clusters,…
Focus accuracy affects the quality of the astronomical observations. Auto-focusing is necessary for imaging systems designed for astronomical observations. The automatic focus system searches for the best focus position by using a proposed…
In this paper, a reduced-rank scheme with joint iterative optimization is presented for direction of arrival estimation. A rank-reduction matrix and an auxiliary reduced-rank parameter vector are jointly optimized to calculate the output…
We study the problem of covering the maximum number of vertices in a graph by a collection of vertex-disjoint stars, each with a number of satellites in a given interval $[k, \ell]$, where $1 \le k < \ell$ and $\ell$ can be infinity. This…
A fundamental task underlying many important optimization problems, from influence maximization to sensor placement to content recommendation, is to select the optimal group of $k$ items from a larger set. Submodularity has been very…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…
Constrained $k$-submodular maximization is a general framework that captures many discrete optimization problems such as ad allocation, influence maximization, personalized recommendation, and many others. In many of these applications,…
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…
This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one…