Related papers: Graph comparison via nonlinear quantum search
In the Densest k-Subgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
Many studies have been conducted on seeking the efficient solution for subgraph similarity search over certain (deterministic) graphs due to its wide application in many fields, including bioinformatics, social network analysis, and…
Graph Isomorphism is such an important problem in computer science, that it has been widely studied over the last decades. It is well known that it belongs to NP class, but is not NP-complete. It is thought to be of comparable difficulty to…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
Finding the graphs that are most similar to a query graph in a large database is a common task with various applications. A widely-used similarity measure is the graph edit distance, which provides an intuitive notion of similarity and…
Any graph with maximum degree $\Delta$ admits a proper vertex coloring with $\Delta + 1$ colors that can be found via a simple sequential greedy algorithm in linear time and space. But can one find such a coloring via a sublinear algorithm?…
A graph $G=(V,E)$ is a {\it unipolar graph} if there exits a partition $V=V_1 \cup V_2$ such that, $V_1$ is a clique and $V_2$ induces the disjoint union of cliques. The complement-closed class of {\it generalized split graphs} are those…
The current noisy intermediate-scale quantum (NISQ) era is characterized by substantial errors and noise, which limit the practical feasibility of deep, many-qubit circuits. To address these constraints, quantum circuit cutting has emerged…
Graph partitioning schedules parallel calculations like sparse matrix-vector multiply (SpMV). We consider contiguous partitions, where the $m$ rows (or columns) of a sparse matrix with $N$ nonzeros are split into $K$ parts without…
Hypergraph clustering is a basic algorithmic primitive for analyzing complex datasets and systems characterized by multiway interactions, such as group email conversations, groups of co-purchased retail products, and co-authorship data.…
Edge-labeled graphs are widely used to describe relationships between entities in a database. Given a query subgraph that represents an example of what the user is searching for, we study the problem of efficiently searching for similar…
We show that in the quantum query model the complexity of detecting a triangle in an undirected graph on $n$ nodes can be done using $O(n^{1+{3\over 7}}\log^{2}n)$ quantum queries. The same complexity bound applies for outputting the…
Early but promising results in quantum computing have been enabled by the concurrent development of quantum algorithms, devices, and materials. Classical simulation of quantum programs has enabled the design and analysis of algorithms and…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
In the Graph Isomorphism problem two N-vertex graphs G and G' are given and the task is to determine whether there exists a permutation of the vertices of G that preserves adjacency and transforms G into G'. If yes, then G and G' are said…
In this paper we isolate the combinatorial property responsible (at least in part) for the computational speedups recently observed in some quantum walk algorithms. We find that continuous-time quantum walks can exploit the covering space…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…
The use of quantum computing in graph community detection and regularity checking related to Szemeredi's Regularity Lemma (SRL) are demonstrated with D-Wave Systems' quantum annealer and simulations. We demonstrate the capability of quantum…
Quantum walks are roughly analogous to classical random walks, and like classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs it is useful to find the…