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The Maximum k-Defective Clique Problem (MDCP) aims to find a maximum k-defective clique in a given graph, where a k-defective clique is a relaxation clique missing at most k edges. MDCP is NP-hard and finds many real-world applications in…
Partially Observable Markov Decision Processes (POMDPs) provide an efficient way to model real-world sequential decision making processes. Motivated by the problem of maintenance and inspection of a group of infrastructure components with…
There is a rich literature on clustering functional data with applications to time-series modeling, trajectory data, and even spatio-temporal applications. However, existing methods routinely perform global clustering that enforces…
Non-convex sparse minimization (NSM), or $\ell_0$-constrained minimization of convex loss functions, is an important optimization problem that has many machine learning applications. NSM is generally NP-hard, and so to exactly solve NSM is…
This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector…
Given a bipartite graph, the maximum balanced biclique (\textsf{MBB}) problem, discovering a mutually connected while equal-sized disjoint sets with the maximum cardinality, plays a significant role for mining the bipartite graph and has…
Solving constrained multi-objective optimization problems (CMOPs) is a challenging task. While many practical algorithms have been developed to tackle CMOPs, real-world scenarios often present cases where the constraint functions are…
The Virtual Network Embedding Problem (VNEP) captures the essence of many resource allocation problems of today's infrastructure providers, which offer their physical computation and networking resources to customers. Customers request…
Virtual machine consolidation describes the process of reallocation of virtual machines (VMs) on a set of target servers. It can be formulated as a mixed integer linear programming problem which is proven to be an NP-hard problem. In this…
This paper presents two new approaches to decomposing and solving large Markov decision problems (MDPs), a partial decoupling method and a complete decoupling method. In these approaches, a large, stochastic decision problem is divided into…
Online solvers for partially observable Markov decision processes have difficulty scaling to problems with large action spaces. Monte Carlo tree search with progressive widening attempts to improve scaling by sampling from the action space…
In the Set Cover problem, we are given a set system with each set having a weight, and we want to find a collection of sets that cover the universe, whilst having low total weight. There are several approaches known (based on greedy…
Given a set $V$ of $n$ elements and a distance matrix $[d_{ij}]_{n\times n}$ among elements, the max-mean dispersion problem (MaxMeanDP) consists in selecting a subset $M$ from $V$ such that the mean dispersion (or distance) among the…
This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This…
Branch-and-bound (BnB) algorithms are widely used to solve combinatorial problems, and the performance crucially depends on its branching heuristic.In this work, we consider a typical problem of maximum common subgraph (MCS), and propose a…
Multi-robot Coverage Path Planning (MCPP) addresses the problem of computing paths for multiple robots to effectively cover a large area of interest. Conventional approaches to MCPP typically assume that robots move at fixed velocities,…
Object search is a fundamental task for robots deployed in indoor building environments, yet challenges arise due to observation instability, especially for open-vocabulary models. While foundation models (LLMs/VLMs) enable reasoning about…
In this work, we study two fundamental graph optimization problems, minimum vertex cover (MVC) and maximum-cardinality matching (MCM), for intersection graphs of geometric objects, e.g., disks, rectangles, hypercubes, etc., in…
The weighted set multi-cover problem is a fundamental generalization of set cover that arises in data-driven applications where one must select a small, low-cost subset from a large collection of candidates under coverage constraints. In…