Related papers: Quantum Speedup for Graph Sparsification, Cut Appr…

Let $G$ be an $n$-vertex graph with $m$ edges. When asked a subset $S$ of vertices, a cut query on $G$ returns the number of edges of $G$ that have exactly one endpoint in $S$. We show that there is a bounded-error quantum algorithm that…

We study differentially private algorithms for graph cut sparsification, a fundamental problem in algorithms, privacy, and machine learning. While significant progress has been made, the best-known private and efficient cut sparsifiers on…

We are presented with a graph, $G$, on $n$ vertices with $m$ edges whose edge set is unknown. Our goal is to learn the edges of $G$ with as few queries to an oracle as possible. When we submit a set $S$ of vertices to the oracle, it tells…

Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used in machine learning over homogeneous graphs. In heterogeneous graphs such as knowledge graphs, however, sparsification has not been systematically…

Designing dynamic graph algorithms against an adaptive adversary is a major goal in the field of dynamic graph algorithms. While a few such algorithms are known for spanning trees, matchings, and single-source shortest paths, very little…

In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…

We study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\,…

Whether or not the Sparsest Cut problem admits an efficient $O(1)$-approximation algorithm is a fundamental algorithmic question with connections to geometry and the Unique Games Conjecture. Revisiting spectral algorithms for Sparsest Cut,…

We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…

Spectral graph sparsification aims to find ultra-sparse subgraphs which can preserve spectral properties of original graphs. In this paper, a new spectral criticality metric based on trace reduction is first introduced for identifying…

We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…

We present several sparsification lower and upper bounds for classic problems in graph theory and logic. For the problems 4-Coloring, (Directed) Hamiltonian Cycle, and (Connected) Dominating Set, we prove that there is no polynomial-time…

In recent years, hypergraph generalizations of many graph cut problems have been introduced and analyzed as a way to better explore and understand complex systems and datasets characterized by multiway relationships. Recent work has made…

Motivated by the quantum speedup for dynamic programming on the Boolean hypercube by Ambainis et al. (2019), we investigate which graphs admit a similar quantum advantage. In this paper, we examine a generalization of the Boolean hypercube…

The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to…

In this paper, we study quantum algorithms for computing the exact value of the treewidth of a graph. Our algorithms are based on the classical algorithm by Fomin and Villanger (Combinatorica 32, 2012) that uses $O(2.616^n)$ time and…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…

Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…

We give quantum speedups of several general-purpose numerical optimisation methods for minimising a function $f:\mathbb{R}^n \to \mathbb{R}$. First, we show that many techniques for global optimisation under a Lipschitz constraint can be…