Related papers: Greedy MAXCUT Algorithms and their Information Con…
Max-Cut is a classical graph-partitioning problem where given a graph $G = (V,E)$, the objective is to find a cut $(S,S^c)$ which maximizes the number of edges crossing the cut. In a seminal work, Goemans and Williamson gave an $\alpha_{GW}…
The task of maximizing coverage using multiple robots has several applications such as surveillance, exploration, and environmental monitoring. A major challenge of deploying such multi-robot systems in a practical scenario is to ensure…
Subset selection is a popular topic in recent years and a number of subset selection methods have been proposed. Among those methods, hypervolume subset selection is widely used. Greedy hypervolume subset selection algorithms can achieve…
Large-scale subset selection asks for a small useful set of examples, features, sensors, seed users, or context passages from an enormous ground set. Submodular maximization is a canonical model for such diminishing-returns problems, but…
We study the $k$-Submodular Cover ($kSC$) problem, a natural generalization of the classical Submodular Cover problem that arises in artificial intelligence and combinatorial optimization tasks such as influence maximization, resource…
We study the worst-case adaptive optimization problem with budget constraint that is useful for modeling various practical applications in artificial intelligence and machine learning. We investigate the near-optimality of greedy algorithms…
We provide a comprehensive reply to the comment written by Stefan Boettcher [arXiv:2210.00623] and argue that the comment singles out one particular non-representative example problem, entirely focusing on the maximum cut problem (MaxCut)…
In this paper, we study the \underline{R}obust \underline{o}ptimization for \underline{se}quence \underline{Net}worked \underline{s}ubmodular maximization (RoseNets) problem. We interweave the robust optimization with the sequence networked…
As the most typical graph clustering method, spectral clustering is popular and attractive due to the remarkable performance, easy implementation, and strong adaptability. Classical spectral clustering measures the edge weights of graph…
Greedy algorithms are a fundamental category of algorithms in mathematics and computer science, characterized by their iterative, locally optimal decision-making approach, which aims to find global optima. In this review, we will discuss…
We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent LP rounding algorithms and a hybrid algorithm…
We consider the Max-$3$-Section problem, where we are given an undirected graph $ G=(V,E)$ equipped with non-negative edge weights $w :E\rightarrow \mathbb{R}_+$ and the goal is to find a partition of $V$ into three equisized parts while…
A thesis submitted for the degree of Doctor of Philosophy of The Australian National University. In this work we introduce several new optimisation methods for problems in machine learning. Our algorithms broadly fall into two categories:…
We study the \textsc{$\alpha$-Fixed Cardinality Graph Partitioning ($\alpha$-FCGP)} problem, the generic local graph partitioning problem introduced by Bonnet et al. [Algorithmica 2015]. In this problem, we are given a graph $G$, two…
The maximum genus $\gamma_M(G)$ of a graph G is the largest genus of an orientable surface into which G has a cellular embedding. Combinatorially, it coincides with the maximum number of disjoint pairs of adjacent edges of G whose removal…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
Motivated by an application in kidney exchange, we study the following query-commit problem: we are given the set of vertices of a non-bipartite graph G. The set of edges in this graph are not known ahead of time. We can query any pair of…
We propose a new yet natural algorithm for learning the graph structure of general discrete graphical models (a.k.a. Markov random fields) from samples. Our algorithm finds the neighborhood of a node by sequentially adding nodes that…