Online Multi-Coloring with Advice

We consider the problem of online graph multi-coloring with advice. Multi-coloring is often used to model frequency allocation in cellular networks. We give several nearly tight upper and lower bounds for the most standard topologies of cellular networks, paths and hexagonal graphs. For the path, negative results trivially carry over to bipartite graphs, and our positive results are also valid for bipartite graphs. The advice given represents information that is likely to be available, studying for instance the data from earlier similar periods of time.Comment: IMADA-preprint-c

A Review of Interference Reduction in Wireless Networks Using Graph Coloring Methods

The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being focused upon as a problem in today's world. In this paper we analyze the interference reduction problem from a graph theoretical viewpoint. A graph coloring methods are exploited to model the interference reduction problem. However, additional constraints to graph coloring scenarios that account for various networking conditions result in additional complexity to standard graph coloring. This paper reviews a variety of algorithmic solutions for specific network topologies.Comment: 10 pages, 5 figure

Tunneling behavior of Ising and Potts models in the low-temperature regime

We consider the ferromagnetic $q$-state Potts model with zero external field in a finite volume and assume that the stochastic evolution of this system is described by a Glauber-type dynamics parametrized by the inverse temperature $\beta$. Our analysis concerns the low-temperature regime $\beta \to \infty$, in which this multi-spin system has $q$ stable equilibria, corresponding to the configurations where all spins are equal. Focusing on grid graphs with various boundary conditions, we study the tunneling phenomena of the $q$-state Potts model. More specifically, we describe the asymptotic behavior of the first hitting times between stable equilibria as $\beta \to \infty$ in probability, in expectation, and in distribution and obtain tight bounds on the mixing time as side-result. In the special case $q=2$, our results characterize the tunneling behavior of the Ising model on grid graphs.Comment: 13 figure

Resource allocation in mobile cellular systems.

by Sung Chi Wan.Thesis (M.Phil.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 59-[63]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Design Issues in Mobile Communication Systems --- p.1Chapter 1.2 --- Radio Resource Management --- p.2Chapter 1.2.1 --- Constraint: Radio Interference --- p.2Chapter 1.2.2 --- Objective: High Capacity and Good Quality --- p.3Chapter 1.3 --- Channel Assignment --- p.3Chapter 1.3.1 --- Static Channel Assignment --- p.4Chapter 1.3.2 --- Dynamic Channel Assignment --- p.5Chapter 1.4 --- Review of Previous Results and Motivation --- p.6Chapter 1.5 --- Outline of the Thesis --- p.8Chapter 2 --- Static Channel Assignment --- p.9Chapter 2.1 --- Introduction --- p.9Chapter 2.2 --- Problem Formulation --- p.10Chapter 2.3 --- Pure Co channel Interference Case --- p.12Chapter 2.4 --- Systems of Special Structure --- p.16Chapter 2.5 --- Generalization of SP --- p.22Chapter 2.6 --- A Lower Bound for the General Case --- p.23Chapter 2.7 --- Numerical Examples --- p.25Chapter 2.8 --- Summary --- p.29Chapter 3 --- Dynamic Channel Assignment --- p.30Chapter 3.1 --- Introduction --- p.30Chapter 3.2 --- Distributed Packing Algorithm --- p.31Chapter 3.3 --- Performance Evaluation --- p.33Chapter 3.4 --- Summary --- p.38Chapter 4 --- Single-Channel User-Capacity Calculations --- p.39Chapter 4.1 --- Introduction --- p.39Chapter 4.2 --- Capacity as a Performance Measure --- p.40Chapter 4.3 --- Capacity of a Linear Celluar System --- p.41Chapter 4.4 --- Capacity of a 3-stripe Cellular System --- p.44Chapter 4.5 --- Summary --- p.46Chapter 5 --- Conclusion --- p.47Chapter 5.1 --- Summary of Results --- p.47Chapter 5.2 --- Suggestions for Further Research --- p.48Appendix --- p.49Chapter A --- On the Optimality of Sequential Packing --- p.49Chapter A.1 --- Graph Multi-coloring Problem --- p.49Chapter A.2 --- Sequential Packing Algorithm --- p.51Chapter A.3 --- Optimality of Sequential Packing --- p.52Chapter A.4 --- Concluding Remarks --- p.55Chapter B --- Derivation of the Capacity of 3-stripe system --- p.56Bibliography --- p.5

Machine learning approach to genome of two-dimensional materials with flat electronic bands

Many-body physics of electron-electron correlations plays a central role in condensed mater physics, it governs a wide range of phenomena, stretching from superconductivity to magnetism, and is behind numerous technological applications. To explore this rich interaction-driven physics, two-dimensional (2D) materials with flat electronic bands provide a natural playground thanks to their highly localised electrons. Currently, thousands of 2D materials with computed electronic bands are available in open science databases, awaiting such exploration. Here we used a new machine learning algorithm combining both supervised and unsupervised machine intelligence to automate the otherwise daunting task of materials search and classification, to build a genome of 2D materials hosting flat electronic bands. To this end, a feedforward artificial neural network was employed to identify 2D flat band materials, which were then classified by a bilayer unsupervised learning algorithm. Such a hybrid approach of exploring materials databases allowed us to reveal completely new material classes outside the known flat band paradigms, offering new systems for in-depth study on their electronic interactions