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Combinatorial optimization (CO) is the fundamental problem at the intersection of computer science, applied mathematics, etc. The inherent hardness in CO problems brings up challenge for solving CO exactly, making deep-neural-network-based…
The maximum clique (MC) problem is a challenging graph mining problem which, due to its NP-hard nature, can take a substantial amount of execution time. The MC problem is dominated by set intersection operations similar to Maximal Clique…
We develop simple and general techniques to obtain faster (near-linear time) static approximation algorithms, as well as efficient dynamic data structures, for four fundamental geometric optimization problems: minimum piercing set (MPS),…
Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require…
Recently, studying fundamental graph problems in the \emph{Massively Parallel Computation (MPC) framework, inspired by the MapReduce paradigm, has gained a lot of attention. An assumption common to a vast majority of approaches is to allow…
Whether or not the problem of finding maximal independent sets (MIS) in hypergraphs is in (R)NC is one of the fundamental problems in the theory of parallel computing. Unlike the well-understood case of MIS in graphs, for the hypergraph…
The goal of multi-objective query optimization (MOQO) is to find query plans that realize a good compromise between conflicting objectives such as minimizing execution time and minimizing monetary fees in a Cloud scenario. A previously…
Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…
Mixed-Integer Programs (MIPs) are NP-hard optimization models that arise in a broad range of decision-making applications, including finance, logistics, energy systems, and network design. Although modern commercial solvers have achieved…
Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of…
Quantum optimization methods use a continuous degree-of-freedom of quantum states to heuristically solve combinatorial problems, such as the MAX-CUT problem, which can be attributed to various NP-hard combinatorial problems. This paper…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…
Understanding structural controllability of a complex network requires to identify a Minimum Input nodes Set (MIS) of the network. It has been suggested that finding an MIS is equivalent to computing a maximum matching of the network, where…
We revisit the recent polynomial-time algorithm for the MAX WEIGHT INDEPENDENT SET (MWIS) problem in bounded-degree graphs that do not contain a fixed graph whose every component is a subdivided claw as an induced subgraph [Abrishami,…
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…
This study explores distributed optimization problems with clique-wise coupling via operator splitting and how we can utilize this framework for performance analysis and enhancement. This framework extends beyond conventional pairwise…
Derandomization is one of the classic topics studied in the theory of parallel computations, dating back to the early 1980s. Despite much work, all known techniques lead to deterministic algorithms that are not work-efficient. For instance,…
Reconfigurable intelligent surface (RIS) has been anticipated to be a novel cost-effective technology to improve the performance of future wireless systems. In this paper, we investigate a practical RIS-aided multiple-input-multiple-output…
Quantum optimization as a field has largely been restricted by the constraints of current quantum computing hardware, as limitations on size, performance, and fidelity mean most non-trivial problem instances won't fit on quantum devices.…