Related papers: Quantum computing algorithms for inverse problems …
In the cut-query model, the algorithm can access the input graph $G=(V,E)$ only via cut queries that report, given a set $S\subseteq V$, the total weight of edges crossing the cut between $S$ and $V\setminus S$. This model was introduced by…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
Neutral atom technology has steadily demonstrated significant theoretical and experimental advancements, positioning itself as a front-runner platform for running quantum algorithms. One unique advantage of this technology lies in the…
In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of…
Various applications of graphs, in particular applications related to finding shortest paths, naturally get inputs with real weights on the edges. However, for algorithmic or visualization reasons, inputs with integer weights would often be…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
We study the inverse problem of recovering a tree graph together with the weights on its edges (equivalently a metric tree) from the knowledge of the Dirichlet-to-Neumann matrix associated with the Laplacian. We prove an explicit formula…
The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weight sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem.…
Given a set P of n points in the plane, the unit-disk graph G_{r}(P) with respect to a parameter r is an undirected graph whose vertex set is P such that an edge connects two points p, q \in P if the Euclidean distance between p and q is at…
The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…
Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric $n$-vertices colourable graph and a group of operations (colouring rules) on the graph: find the minimum sequence…
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…
We consider the quantum time complexity of the all pairs shortest paths (APSP) problem and some of its variants. The trivial classical algorithm for APSP and most all pairs path problems runs in $O(n^3)$ time, while the trivial algorithm in…
We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…
Graph routing problems have been investigated extensively in operations research, computer science and engineering due to their ubiquity and vast applications. In this paper, we study constant approximation algorithms for some variations of…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
Studies on Quantum Computing have been developed since the 1980s, motivating researches on quantum algorithms better than any classical algorithm possible. An example of such algorithms is Grover's algorithm, capable of finding $k$ (marked)…
We present an efficient quantum algorithm for some independent set problems in graph theory, based on non-abelian adiabatic mixing. We illustrate the performance of our algorithm with analysis and numerical calculations for two different…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…