Decomposition of graphs into trees /

"UILU-ENG 77 1715."

On the complexity of edge labelings for trees /

"UILU-ENG 78 1740."

On random 3-2 trees /

"UIUCDCS-R-74-679"

Enumerations of ordered trees /

Errata slip inserted.

Generating binary trees lexicographically /

Bibliography: p. 26.

Studies in graph algorithms : generation and labeling problems /

Thesis--Illinois.

Generating trees and other combinatorial objects lexicographically /

"UILU-ENG 77 1762."

Notes on AVL trees /

"Written as supplementary material for a course in data structures given by the Dept. of Computer Science of the University of Illinois at Urbana-Champaign, during the second semester of the 1970-71 academic year"--Leaf 1.

An O(/E/loglog/V/) algorithm for finding minimum spanning trees /

Includes bibliographical references.

Generating k-ary trees lexicographically /

"UILU-ENG 77 1758."

Semantic Mining based on graph theory and ontologies. Case Study: Cell Signaling Pathways

In this paper we use concepts from graph theory and cellular biology represented as ontologies, to carry out semantic mining tasks on signaling pathway networks. Specifically, the paper describes the semantic enrichment of signaling pathway networks. A cell signaling network describes the basic cellular activities and their interactions. The main contribution of this paper is in the signaling pathway research area, it proposes a new technique to analyze and understand how changes in these networks may affect the transmission and flow of information, which produce diseases such as cancer and diabetes. Our approach is based on three concepts from graph theory (modularity, clustering and centrality) frequently used on social networks analysis. Our approach consists into two phases: the first uses the graph theory concepts to determine the cellular groups in the network, which we will call them communities; the second uses ontologies for the semantic enrichment of the cellular communities. The measures used from the graph theory allow us to determine the set of cells that are close (for example, in a disease), and the main cells in each community. We analyze our approach in two cases: TGF-β and the Alzheimer Disease.

Spectral graph theory with applications to quantum adiabatic optimization

In this dissertation I draw a connection between quantum adiabatic optimization, spectral graph theory, heat-diffusion, and sub-stochastic processes through the operators that govern these processes and their associated spectra. In particular, we study Hamiltonians which have recently become known as ``stoquastic'' or, equivalently, the generators of sub-stochastic processes. The operators corresponding to these Hamiltonians are of interest in all of the settings mentioned above. I predominantly explore the connection between the spectral gap of an operator, or the difference between the two lowest energies of that operator, and certain equilibrium behavior. In the context of adiabatic optimization, this corresponds to the likelihood of solving the optimization problem of interest. I will provide an instance of an optimization problem that is easy to solve classically, but leaves open the possibility to being difficult adiabatically. Aside from this concrete example, the work in this dissertation is predominantly mathematical and we focus on bounding the spectral gap. Our primary tool for doing this is spectral graph theory, which provides the most natural approach to this task by simply considering Dirichlet eigenvalues of subgraphs of host graphs. I will derive tight bounds for the gap of one-dimensional, hypercube, and general convex subgraphs. The techniques used will also adapt methods recently used by Andrews and Clutterbuck to prove the long-standing ``Fundamental Gap Conjecture''.

Optimization of Energy Distribution in Solar Panel Array Configurations by Graph Theory and Minkowski’s Paths

Nowadays, the development of the photovoltaic (PV) technology is consolidated as a source of renewable energy. The research in the topic of maximum improvement on the energy efficiency of the PV plants is today a major challenge. The main requirement for this purpose is to know the performance of each of the PV modules that integrate the PV field in real time. In this respect, a PLC communications based Smart Monitoring and Communications Module, which is able to monitor at PV level their operating parameters, has been developed at the University of Malaga. With this device you can check if any of the panels is suffering any type of overriding performance, due to a malfunction or partial shadowing of its surface. Since these fluctuations in electricity production from a single panel affect the overall sum of all panels that conform a string, it is necessary to isolate the problem and modify the routes of energy through alternative paths in case of PV panels array configuration.

Graph theory based QoE-driven cooperation stimulation for content dissemination in device-To-device communication

With multimedia dominating the digital contents, Device-To-Device (D2D) communication has been proposed as a promising data offloading solution in the big data area. As the quality of experience (QoE) is a major determining factor in the success of new multimedia applications, we propose a QoEdriven cooperative content dissemination (QeCS) scheme in this work. Specifically, all users predict the QoE of the potential connections characterized by the mean opinion score (MOS), and send the results to the content provider (CP). Then CP formulates a weighted directed graph according to the network topology and MOS of each potential connection. In order to stimulate cooperation among the users, the content dissemination mechanism is designed through seeking 1-factor of the weighted directed graph with the maximum weight thus achieving maximum total user MOS. Additionally, a debt mechanism is adopted to combat the cheat attacks. Furthermore, we extend the proposed QeCS scheme by considering a constrained condition to the optimization problem for fairness improvement. Extensive simulation results demonstrate that the proposed QeCS scheme achieves both efficiency and fairness especially in large scale and density networks.

On optimal computation of MPLS label binding for multipoint-to-point connections

Most network operators have considered reducing Label Switched Routers (LSR) label spaces (i.e. the number of labels that can be used) as a means of simplifying management of underlaying Virtual Private Networks (VPNs) and, hence, reducing operational expenditure (OPEX). This letter discusses the problem of reducing the label spaces in Multiprotocol Label Switched (MPLS) networks using label merging - better known as MultiPoint-to-Point (MP2P) connections. Because of its origins in IP, MP2P connections have been considered to have tree- shapes with Label Switched Paths (LSP) as branches. Due to this fact, previous works by many authors affirm that the problem of minimizing the label space using MP2P in MPLS - the Merging Problem - cannot be solved optimally with a polynomial algorithm (NP-complete), since it involves a hard- decision problem. However, in this letter, the Merging Problem is analyzed, from the perspective of MPLS, and it is deduced that tree-shapes in MP2P connections are irrelevant. By overriding this tree-shape consideration, it is possible to perform label merging in polynomial time. Based on how MPLS signaling works, this letter proposes an algorithm to compute the minimum number of labels using label merging: the Full Label Merging algorithm. As conclusion, we reclassify the Merging Problem as Polynomial-solvable, instead of NP-complete. In addition, simulation experiments confirm that without the tree-branch selection problem, more labels can be reduced