6 research outputs found
Algorithms for Computing Maximum Cliques in Hyperbolic Random Graphs
In this paper, we study the maximum clique problem on hyperbolic random graphs. A hyperbolic random graph is a mathematical model for analyzing scale-free networks since it effectively explains the power-law degree distribution of scale-free networks. We propose a simple algorithm for finding a maximum clique in hyperbolic random graph. We first analyze the running time of our algorithm theoretically. We can compute a maximum clique on a hyperbolic random graph G in O(m + n^{4.5(1-?)}) expected time if a geometric representation is given or in O(m + n^{6(1-?)}) expected time if a geometric representation is not given, where n and m denote the numbers of vertices and edges of G, respectively, and ? denotes a parameter controlling the power-law exponent of the degree distribution of G. Also, we implemented and evaluated our algorithm empirically. Our algorithm outperforms the previous algorithm [BFK18] practically and theoretically. Beyond the hyperbolic random graphs, we have experiment on real-world networks. For most of instances, we get large cliques close to the optimum solutions efficiently
Algorithms for Computing Maximum Cliques in Hyperbolic Random Graphs
In this paper, we study the maximum clique problem on hyperbolic random
graphs. A hyperbolic random graph is a mathematical model for analyzing
scale-free networks since it effectively explains the power-law degree
distribution of scale-free networks. We propose a simple algorithm for finding
a maximum clique in hyperbolic random graph. We first analyze the running time
of our algorithm theoretically. We can compute a maximum clique on a hyperbolic
random graph in expected time if a geometric
representation is given or in expected time if a
geometric representation is not given, where and denote the numbers of
vertices and edges of , respectively, and denotes a parameter
controlling the power-law exponent of the degree distribution of . Also, we
implemented and evaluated our algorithm empirically. Our algorithm outperforms
the previous algorithm [BFK18] practically and theoretically. Beyond the
hyperbolic random graphs, we have experiment on real-world networks. For most
of instances, we get large cliques close to the optimum solutions efficiently.Comment: Accepted in ESA 202
Parameterized Algorithm for the Disjoint Path Problem on Planar Graphs: Exponential in and Linear in
In this paper, we study the \textsf{Planar Disjoint Paths} problem: Given an
undirected planar graph with vertices and a set of pairs
of vertices, the goal is to find a set of
pairwise vertex-disjoint paths connecting and for all indices
. We present a -time algorithm for the
\textsf{Planar Disjoint Paths} problem. This improves the two previously
best-known algorithms: -time algorithm [Discrete Applied
Mathematics 1995] and -time algorithm [STOC 2020].Comment: SODA 202
Quantum Approximation for Wireless Scheduling
This paper proposes a quantum approximate optimization algorithm (QAOA)
method for wireless scheduling problems. The QAOA is one of the promising
hybrid quantum-classical algorithms for many applications and it provides
highly accurate optimization solutions in NP-hard problems. QAOA maps the given
problems into Hilbert spaces, and then it generates Hamiltonian for the given
objectives and constraints. Then, QAOA finds proper parameters from classical
optimization approaches in order to optimize the expectation value of generated
Hamiltonian. Based on the parameters, the optimal solution to the given problem
can be obtained from the optimum of the expectation value of Hamiltonian.
Inspired by QAOA, a quantum approximate optimization for scheduling (QAOS)
algorithm is proposed. First of all, this paper formulates a wireless
scheduling problem using maximum weight independent set (MWIS). Then, for the
given MWIS, the proposed QAOS designs the Hamiltonian of the problem. After
that, the iterative QAOS sequence solves the wireless scheduling problem. This
paper verifies the novelty of the proposed QAOS via simulations implemented by
Cirq and TensorFlow-Quantum
A Tutorial on Quantum Convolutional Neural Networks (QCNN)
Convolutional Neural Network (CNN) is a popular model in computer vision and
has the advantage of making good use of the correlation information of data.
However, CNN is challenging to learn efficiently if the given dimension of data
or model becomes too large. Quantum Convolutional Neural Network (QCNN)
provides a new solution to a problem to solve with CNN using a quantum
computing environment, or a direction to improve the performance of an existing
learning model. The first study to be introduced proposes a model to
effectively solve the classification problem in quantum physics and chemistry
by applying the structure of CNN to the quantum computing environment. The
research also proposes the model that can be calculated with O(log(n)) depth
using Multi-scale Entanglement Renormalization Ansatz (MERA). The second study
introduces a method to improve the model's performance by adding a layer using
quantum computing to the CNN learning model used in the existing computer
vision. This model can also be used in small quantum computers, and a hybrid
learning model can be designed by adding a quantum convolution layer to the CNN
model or replacing it with a convolution layer. This paper also verifies
whether the QCNN model is capable of efficient learning compared to CNN through
training using the MNIST dataset through the TensorFlow Quantum platform
Energy-Efficient Cluster Head Selection via Quantum Approximate Optimization
This paper proposes an energy-efficient cluster head selection method in the wireless ad hoc network by using a hybrid quantum-classical approach. The wireless ad hoc network is divided into several clusters via cluster head selection, and the performance of the network topology depends on the distribution of these clusters. For an energy-efficient network topology, none of the selected cluster heads should be neighbors. In addition, all the selected cluster heads should have high energy-consumption efficiency. Accordingly, an energy-efficient cluster head selection policy can be defined as a maximum weight independent set (MWIS) formulation. The cluster head selection policy formulated with MWIS is solved by using the quantum approximate optimization algorithm (QAOA), which is a hybrid quantum-classical algorithm. The accuracy of the proposed energy-efficient cluster head selection via QAOA is verified via simulations