Coloring random graphs and maximizing local diversity

We study a variation of the graph coloring problem on random graphs of finite average connectivity. Given the number of colors, we aim to maximize the number of different colors at neighboring vertices (i.e. one edge distance) of any vertex. Two efficient algorithms, belief propagation and Walksat are adapted to carry out this task. We present experimental results based on two types of random graphs for different system sizes and identify the critical value of the connectivity for the algorithms to find a perfect solution. The problem and the suggested algorithms have practical relevance since various applications, such as distributed storage, can be mapped onto this problem.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Palette-colouring: a belief propagation approach

We consider a variation of the prototype combinatorial optimization problem known as graph colouring. Our optimization goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximize the number of different colours present in the set of nearest neighbours of each given vertex. This problem, which we pictorially call palette-colouring, has been recently addressed as a basic example of a problem arising in the context of distributed data storage. Even though it has not been proved to be NP-complete, random search algorithms find the problem hard to solve. Heuristics based on a naive belief propagation algorithm are observed to work quite well in certain conditions. In this paper, we build upon the mentioned result, working out the correct belief propagation algorithm, which needs to take into account the many-body nature of the constraints present in this problem. This method improves the naive belief propagation approach at the cost of increased computational effort. We also investigate the emergence of a satisfiable-to-unsatisfiable 'phase transition' as a function of the vertex mean degree, for different ensembles of sparse random graphs in the large size ('thermodynamic') limit.

A socio-economic approach to online vision graph generation and handover in distributed smart camera networks

In this paper we propose an approach based on self-interested autonomous cameras, which exchange responsibility for tracking objects in a market mechanism, in order to maximise their own utility. A novel ant-colony inspired mechanism is used to grow the vision graph during runtime, which may then be used to optimise communication between cameras. The key benefits of our completely decentralised approach are on the one hand generating the vision graph online which permits the addition and removal cameras to the network during runtime and on the other hand relying only on local information, increasing the robustness of the system. Since our market-based approach does not rely on a priori topology information, the need for any multi-camera calibration can be avoided. © 2011 IEEE.

Socio-economic vision graph generation and handover in distributed smart camera networks

In this article we present an approach to object tracking handover in a network of smart cameras, based on self-interested autonomous agents, which exchange responsibility for tracking objects in a market mechanism, in order to maximise their own utility. A novel ant-colony inspired mechanism is used to learn the vision graph, that is, the camera neighbourhood relations, during runtime, which may then be used to optimise communication between cameras. The key benefits of our completely decentralised approach are on the one hand generating the vision graph online, enabling efficient deployment in unknown scenarios and camera network topologies, and on the other hand relying only on local information, increasing the robustness of the system. Since our market-based approach does not rely on a priori topology information, the need for any multicamera calibration can be avoided. We have evaluated our approach both in a simulation study and in network of real distributed smart cameras.

Outlier-resisting graph embedding

Graph embedding is a general framework for subspace learning. However, because of the well-known outlier-sensitiveness disadvantage of the L2-norm, conventional graph embedding is not robust to outliers which occur in many practical applications. In this paper, an improved graph embedding algorithm (termed LPP-L1) is proposed by replacing L2-norm with L1-norm. In addition to its robustness property, LPP-L1 avoids small sample size problem. Experimental results on both synthetic and real-world data demonstrate these advantages. © 2009 Elsevier B.V. All rights reserved.

On Graph-Based Cryptography and Symbolic Computations

We have been investigating the cryptographical properties of in nite families of simple graphs of large girth with the special colouring of vertices during the last 10 years. Such families can be used for the development of cryptographical algorithms (on symmetric or public key modes) and turbocodes in error correction theory. Only few families of simple graphs of large unbounded girth and arbitrarily large degree are known. The paper is devoted to the more general theory of directed graphs of large girth and their cryptographical applications. It contains new explicit algebraic constructions of in finite families of such graphs. We show that they can be used for the implementation of secure and very fast symmetric encryption algorithms. The symbolic computations technique allow us to create a public key mode for the encryption scheme based on algebraic graphs.

An improved memory management scheme for large scale graph computing engine GraphChi

GraphChi is the first reported disk-based graph engine that can handle billion-scale graphs on a single PC efficiently. GraphChi is able to execute several advanced data mining, graph mining and machine learning algorithms on very large graphs. With the novel technique of parallel sliding windows (PSW) to load subgraph from disk to memory for vertices and edges updating, it can achieve data processing performance close to and even better than those of mainstream distributed graph engines. GraphChi mentioned that its memory is not effectively utilized with large dataset, which leads to suboptimal computation performances. In this paper we are motivated by the concepts of 'pin ' from TurboGraph and 'ghost' from GraphLab to propose a new memory utilization mode for GraphChi, which is called Part-in-memory mode, to improve the GraphChi algorithm performance. The main idea is to pin a fixed part of data inside the memory during the whole computing process. Part-in-memory mode is successfully implemented with only about 40 additional lines of code to the original GraphChi engine. Extensive experiments are performed with large real datasets (including Twitter graph with 1.4 billion edges). The preliminary results show that Part-in-memory mode memory management approach effectively reduces the GraphChi running time by up to 60% in PageRank algorithm. Interestingly it is found that a larger portion of data pinned in memory does not always lead to better performance in the case that the whole dataset cannot be fitted in memory. There exists an optimal portion of data which should be kept in the memory to achieve the best computational performance.

The Application of Graph Model for Automation of the User Interface Construction

The ability of automatic graphic user interface construction is described. It is based on the building of user interface as reflection of the data domain logical definition. The submitted approach to development of the information system user interface enables dynamic adaptation of the system during their operation. This approach is used for creation of information systems based on CASE-system METAS.