Related papers: Optimal Scheduling of Graph States via Path Decomp…
We present an interactive framework that, given a membership test for a graph class $\mathcal{G}$ and a number $k$, finds and tests unavoidable sets for the class of graphs in $\mathcal{G}$ of path-width at most $k$. We put special emphasis…
Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…
Quantum tomography is an essential method of the photonic technology toolbox and is routinely used for evaluation of experimentally prepared states of light and characterization of devices transforming such states. The tomography procedure…
In this paper, we study the problem of optimal multi-robot path planning (MPP) on graphs. We propose two multiflow based integer linear programming (ILP) models that computes minimum last arrival time and minimum total distance solutions…
We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The…
The design and performance of computer vision algorithms are greatly influenced by the hardware on which they are implemented. CPUs, multi-core CPUs, FPGAs and GPUs have inspired new algorithms and enabled existing ideas to be realized.…
As the leading candidate of quantum error correction codes, surface code suffers from significant overhead, such as execution time. Reducing the circuit's execution time not only enhances its execution efficiency but also improves fidelity.…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
A periodic temporal graph, in its simplest form, is a graph in which every edge appears exactly once in the first $\Delta$ time steps, and then it reappears recurrently every $\Delta$ time steps, where $\Delta$ is a given period length.…
The Quantum Approximate Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…
Coverage path planning is a fundamental challenge in robotics, with diverse applications in aerial surveillance, manufacturing, cleaning, inspection, agriculture, and more. The main objective is to devise a trajectory for an agent that…
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…
A finite discrete graph is turned into a quantum (metric) graph once a finite length is assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We study the dependence of the spectral gap (the first positive…
We present linear time {\it in-place} algorithms for several basic and fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity…
Graph states are an important class of multipartite entangled quantum states. We propose a new approach for distributing graph states across a quantum network. We consider a quantum network consisting of nodes-quantum computers within which…
We propose an optimal algorithm for solving the longest path problem in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art…
Comparing two geometric graphs embedded in space is important in the field of transportation network analysis. Given street maps of the same city collected from different sources, researchers often need to know how and where they differ.…
In this paper, we investigate optimal control of network-coupled subsystems where the dynamics and the cost couplings depend on an underlying undirected weighted graph. The graph coupling matrix in the dynamics may be the adjacency matrix,…
To overcome the physical limitations of scaling monolithic quantum computers, distributed quantum computing (DQC) interconnects multiple smaller-scale quantum processing units (QPUs) to form a quantum network. However, this approach…
Graph states, and the entanglement they posses, are central to modern quantum computing and communications architectures. Local complementation---the graph operation that links all local-Clifford equivalent graph states---allows us to…