Hybrid Graph Heuristics within a Hyper-heuristic Approach to Exam Timetabling Problems

This paper is concerned with the hybridization of two graph coloring heuristics (Saturation Degree and Largest Degree), and their application within a hyperheuristic for exam timetabling problems. Hyper-heuristics can be seen as algorithms which intelligently select appropriate algorithms/heuristics for solving a problem. We developed a Tabu Search based hyper-heuristic to search for heuristic lists (of graph heuristics) for solving problems and investigated the heuristic lists found by employing knowledge discovery techniques. Two hybrid approaches (involving Saturation Degree and Largest Degree) including one which employs Case Based Reasoning are presented and discussed. Both the Tabu Search based hyper-heuristic and the hybrid approaches are tested on random and real-world exam timetabling problems. Experimental results are comparable with the best state-of-the-art approaches (as measured against established benchmark problems). The results also demonstrate an increased level of generality in our approach.

Case-based reasoning in course timetabling: an attribute graph approach

An earlier Case-based Reasoning (CBR) approach developed by the authors for educational course timetabling problems employed structured cases to represent the complex relationships between courses. Previous solved cases represented by attribute graphs were organized hierarchically into a decision tree. The retrieval searches for graph isomorphism among these attribute graphs. In this paper, the approach is further developed to solve a wider range of problems. We also attempt to retrieve those graphs that have common similar structures but also have some differences. Costs that are assigned to these differences have an input upon the similarity measure. A large number of experiments are performed consisting of different randomly produced timetabling problems and the results presented here strongly indicate that a CBR approach could provide a significant step forward in the development of automated system to solve difficult timetabling problems. They show that using relatively little effort, we can retrieve these structurally similar cases to provide high quality timetables for new timetabling problems.

A graph-based hyper heuristic for timetabling problems

This paper presents an investigation of a simple generic hyper-heuristic approach upon a set of widely used constructive heuristics (graph coloring heuristics) in timetabling. Within the hyperheuristic framework, a Tabu Search approach is employed to search for permutations of graph heuristics which are used for constructing timetables in exam and course timetabling problems. This underpins a multi-stage hyper-heuristic where the Tabu Search employs permutations upon a different number of graph heuristics in two stages. We study this graph-based hyper-heuristic approach within the context of exploring fundamental issues concerning the search space of the hyper-heuristic (the heuristic space) and the solution space. Such issues have not been addressed in other hyper-heuristic research. These approaches are tested on both exam and course benchmark timetabling problems and are compared with the fine-tuned bespoke state-of-the-art approaches. The results are within the range of the best results reported in the literature. The approach described here represents a significantly more generally applicable approach than the current state of the art in the literature. Future work will extend this hyper-heuristic framework by employing methodologies which are applicable on a wider range of timetabling and scheduling problems.

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.

Packings and coverings of the complete graph with trees

In this thesis, we define the spectrum problem for packings (coverings) of G to be the problem of finding all graphs H such that a maximum G-packing (minimum G- covering) of the complete graph with the leave (excess) graph H exists. The set of achievable leave (excess) graphs in G-packings (G-coverings) of the complete graph is called the spectrum of leave (excess) graphs for G. Then, we consider this problem for trees with up to five edges. We will prove that for any tree T with up to five edges, if the leave graph in a maximum T-packing of the complete graph Kn has i edges, then the spectrum of leave graphs for T is the set of all simple graphs with i edges. In fact, for these T and i and H any simple graph with i edges, we will construct a maximum T-packing of Kn with the leave graph H. We will also show that for any tree T with k ≤ 5 edges, if the excess graph in a minimum T-covering of the complete graph Kn has i edges, then the spectrum of excess graphs for T is the set of all simple graphs and multigraphs with i edges, except for the case that T is a 5-star, for which the graph formed by four multiple edges is not achievable when n = 12.

Validation of AltiKa Matching Pursuit Rain Flag

The major drawback of Ka band, operating frequency of the AltiKa altimeter on board SARAL, is its sensitivity to atmospheric liquid water. Even light rain or heavy clouds can strongly attenuate the signal and distort the signal leading to erroneous geophysical parameters estimates. A good detection of the samples affected by atmospheric liquid water is crucial. As AltiKa operates at a single frequency, a new technique based on the detection by a Matching Pursuit algorithm of short scale variations of the slope of the echo waveform plateau has been developed and implemented prelaunch in the ground segment. As the parameterization of the detection algorithm was defined using Jason-1 data, the parameters were re-estimated during the cal-val phase, during which the algorithm was also updated. The measured sensor signal-to-noise ratio is significantly better than planned, the data loss due to attenuation by rain is significantly smaller than expected (<0.1%). For cycles 2 to 9, the flag detects about 9% of 1Hz data, 5.5% as rainy and 3.5 % as backscatter bloom (or sigma0 bloom). The results of the flagging process are compared to independent rain data from microwave radiometers to evaluate its performances in term of detection and false alarms.

Spectral Frame Analysis and Learning through Graph Structure

This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.

A comprehensive study of multiplicative attribute graph model

Graphs are powerful tools to describe social, technological and biological networks, with nodes representing agents (people, websites, gene, etc.) and edges (or links) representing relations (or interactions) between agents. Examples of real-world networks include social networks, the World Wide Web, collaboration networks, protein networks, etc. Researchers often model these networks as random graphs. In this dissertation, we study a recently introduced social network model, named the Multiplicative Attribute Graph model (MAG), which takes into account the randomness of nodal attributes in the process of link formation (i.e., the probability of a link existing between two nodes depends on their attributes). Kim and Lesckovec, who defined the model, have claimed that this model exhibit some of the properties a real world social network is expected to have. Focusing on a homogeneous version of this model, we investigate the existence of zero-one laws for graph properties, e.g., the absence of isolated nodes, graph connectivity and the emergence of triangles. We obtain conditions on the parameters of the model, so that these properties occur with high or vanishingly probability as the number of nodes becomes unboundedly large. In that regime, we also investigate the property of triadic closure and the nodal degree distribution.

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''.

Graph analysis of verbal fluency test discriminate between patients with Alzheimer’s disease, Mild Cognitive Impairment and normal elderly controls

Verbal fluency is the ability to produce a satisfying sequence of spoken words during a given time interval. The core of verbal fluency lies in the capacity to manage the executive aspects of language. The standard scores of the semantic verbal fluency test are broadly used in the neuropsychological assessment of the elderly, and different analytical methods are likely to extract even more information from the data generated in this test. Graph theory, a mathematical approach to analyze relations between items, represents a promising tool to understand a variety of neuropsychological states. This study reports a graph analysis of data generated by the semantic verbal fluency test by cognitively healthy elderly (NC), patients with Mild Cognitive Impairment – subtypes amnestic(aMCI) and amnestic multiple domain (a+mdMCI) - and patients with Alzheimer’s disease (AD). Sequences of words were represented as a speech graph in which every word corresponded to a node and temporal links between words were represented by directed edges. To characterize the structure of the data we calculated 13 speech graph attributes (SGAs). The individuals were compared when divided in three (NC – MCI – AD) and four (NC – aMCI – a+mdMCI – AD) groups. When the three groups were compared, significant differences were found in the standard measure of correct words produced, and three SGA: diameter, average shortest path, and network density. SGA sorted the elderly groups with good specificity and sensitivity. When the four groups were compared, the groups differed significantly in network density, except between the two MCI subtypes and NC and aMCI. The diameter of the network and the average shortest path were significantly different between the NC and AD, and between aMCI and AD. SGA sorted the elderly in their groups with good specificity and sensitivity, performing better than the standard score of the task. These findings provide support for a new methodological frame to assess the strength of semantic memory through the verbal fluency task, with potential to amplify the predictive power of this test. Graph analysis is likely to become clinically relevant in neurology and psychiatry, and may be particularly useful for the differential diagnosis of the elderly.

Efficient domination through eigenvalues

The paper begins with a new characterization of (k,τ)(k,τ)-regular sets. Then, using this result as well as the theory of star complements, we derive a simplex-like algorithm for determining whether or not a graph contains a (0,τ)(0,τ)-regular set. When τ=1τ=1, this algorithm can be applied to solve the efficient dominating set problem which is known to be NP-complete. If −1−1 is not an eigenvalue of the adjacency matrix of the graph, this particular algorithm runs in polynomial time. However, although it does not work in polynomial time in general, we report on its successful application to a vast set of randomly generated graphs.

Bethe graphs attached to the vertices of a connected graph: a spectral approach

A weighted Bethe graph $B$ is obtained from a weighted generalized Bethe tree by identifying each set of children with the vertices of a graph belonging to a family $F$ of graphs. The operation of identifying the root vertex of each of $r$ weighted Bethe graphs to the vertices of a connected graph $\mathcal{R}$ of order $r$ is introduced as the $\mathcal{R}$-concatenation of a family of $r$ weighted Bethe graphs. It is shown that the Laplacian eigenvalues (when $F$ has arbitrary graphs) as well as the signless Laplacian and adjacency eigenvalues (when the graphs in $F$ are all regular) of the $\mathcal{R}$-concatenation of a family of weighted Bethe graphs can be computed (in a unified way) using the stable and low computational cost methods available for the determination of the eigenvalues of symmetric tridiagonal matrices. Unlike the previous results already obtained on this topic, the more general context of families of distinct weighted Bethe graphs is herein considered.

Motion compensation with minimal residue dispersion matching criteria

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnoloigia, 2016.

Graph-based structural analysis of planar mechanisms.

Kinematic structure of planar mechanisms addresses the study of attributes determined exclusively by the joining pattern among the links forming a mechanism. The system group classification is central to the kinematic structure and consists of determining a sequence of kinematically and statically independent-simple chains which represent a modular basis for the kinematics and force analysis of the mechanism. This article presents a novel graph-based algorithm for structural analysis of planar mechanisms with closed-loop kinematic structure which determines a sequence of modules (Assur groups) representing the topology of the mechanism. The computational complexity analysis and proof of correctness of the implemented algorithm are provided. A case study is presented to illustrate the results of the devised method.