Distance-based accessibility indices

The paper attempts to develop a suitable accessibility index for networks where each link has a value such that a smaller number is preferred like distance, cost, or travel time. A measure called distance sum is characterized by three independent properties: anonymity, an appropriately chosen independence axiom, and dominance preservation, which requires that a node not far to any other is at least as accessible. We argue for the need of eliminating the independence property in certain applications. Therefore generalized distance sum, a family of accessibility indices, will be suggested. It is linear, considers the accessibility of vertices besides their distances and depends on a parameter in order to control its deviation from distance sum. Generalized distance sum is anonymous and satisfies dominance preservation if its parameter meets a sufficient condition. Two detailed examples demonstrate its ability to reflect the vulnerability of accessibility to link disruptions.

A tudásérték meghatározása minőségügyi szempontból, hálózatelemzési módszerekkel (The knowledge value in terms of quality with network analysis methods)

A minőségügy egyik kulcsfeladata, hogy azonosítsa az értékteremtés szempontjából kritikus tényezőket, meghatározza ezek értékét, valamint intézkedjen negatív hatásuk megelőzése és csökkentése érdekében. Az értékteremtés sok esetben folyamatokon keresztül történik, amelyek tevékenységekből, elvégzendő feladatokból állnak. Ezekhez megfelelő munkatársak kellenek, akiknek az egyik legfontosabb jellemzője az általuk birtokolt tudás. Mindezek alapján a feladat-tudás-erőforrás kapcsolatrendszer ismerete és kezelése minőségügyi feladat is. A komplex rendszerek elemzésével foglalkozó hálózatkutatás eszközt biztosíthat ehhez, ezért indokolt a minőségügyi területen történő alkalmazhatóságának vizsgálata. Az alkalmazási lehetőségek rendszerezése érdekében a szerzők kategorizálták a minőségügyi hálózatokat az élek (kapcsolatok) és a csúcsok (hálózati pontok) típusai alapján. Ezt követően definiálták a multimodális (több különböző csúcstípusból álló) tudáshálózatot, amely a feladatokból, az erőforrásokból, a tudáselemekből és a közöttük lévő kapcsolatokból épül fel. A hálózat segítségével kategóriákba sorolták a tudáselemeket, valamint a fokszámok alapján meghatározták értéküket. A multimodális hálózatból képzett tudáselem-hálózatban megadták az összefüggő csoportok jelentését, majd megfogalmaztak egy összefüggést a tudáselem-elvesztés kockázatának meghatározására. _______ The aims of quality management are to identify those factors that have significant influence on value production, qualify or quantify them, and make preventive and corrective actions in order to reduce their negative effects. The core elements of value production are processes and tasks, along with workforce having the necessary knowledge to work. For that reason the task-resource-knowledge structure is pertinent to quality management. Network science provides methods to analyze complex systems; therefore it seems reasonable to study the use of tools of network analysis in association with quality management issues. First of all the authors categorized quality networks according to the types of nodes (vertices) and links (edges or arcs). Focusing on knowledge management, they defined the multimodal knowledge network, consisting of tasks, resources, knowledge items and their interconnections. Based on their degree, network nodes can be categorized and their value can be quantified. Derived from the multimodal network knowledge-item network is to be created, where the meaning of cohesive subgroups is defined. Eventually they proposed a formula for determining the risk of knowledge loss.

3D TerraFly: Quality of service management for online interactive 3D geographic information system

3D geographic information system (GIS) is data and computation intensive in nature. Internet users are usually equipped with low-end personal computers and network connections of limited bandwidth. Data reduction and performance optimization techniques are of critical importance in quality of service (QoS) management for online 3D GIS. In this research, QoS management issues regarding distributed 3D GIS presentation were studied to develop 3D TerraFly, an interactive 3D GIS that supports high quality online terrain visualization and navigation. ^ To tackle the QoS management challenges, multi-resolution rendering model, adaptive level of detail (LOD) control and mesh simplification algorithms were proposed to effectively reduce the terrain model complexity. The rendering model is adaptively decomposed into sub-regions of up-to-three detail levels according to viewing distance and other dynamic quality measurements. The mesh simplification algorithm was designed as a hybrid algorithm that combines edge straightening and quad-tree compression to reduce the mesh complexity by removing geometrically redundant vertices. The main advantage of this mesh simplification algorithm is that grid mesh can be directly processed in parallel without triangulation overhead. Algorithms facilitating remote accessing and distributed processing of volumetric GIS data, such as data replication, directory service, request scheduling, predictive data retrieving and caching were also proposed. ^ A prototype of the proposed 3D TerraFly implemented in this research demonstrates the effectiveness of our proposed QoS management framework in handling interactive online 3D GIS. The system implementation details and future directions of this research are also addressed in this thesis. ^

Ranked search on data graphs

Graph-structured databases are widely prevalent, and the problem of effective search and retrieval from such graphs has been receiving much attention recently. For example, the Web can be naturally viewed as a graph. Likewise, a relational database can be viewed as a graph where tuples are modeled as vertices connected via foreign-key relationships. Keyword search querying has emerged as one of the most effective paradigms for information discovery, especially over HTML documents in the World Wide Web. One of the key advantages of keyword search querying is its simplicity—users do not have to learn a complex query language, and can issue queries without any prior knowledge about the structure of the underlying data. The purpose of this dissertation was to develop techniques for user-friendly, high quality and efficient searching of graph structured databases. Several ranked search methods on data graphs have been studied in the recent years. Given a top-k keyword search query on a graph and some ranking criteria, a keyword proximity search finds the top-k answers where each answer is a substructure of the graph containing all query keywords, which illustrates the relationship between the keyword present in the graph. We applied keyword proximity search on the web and the page graph of web documents to find top-k answers that satisfy user’s information need and increase user satisfaction. Another effective ranking mechanism applied on data graphs is the authority flow based ranking mechanism. Given a top- k keyword search query on a graph, an authority-flow based search finds the top-k answers where each answer is a node in the graph ranked according to its relevance and importance to the query. We developed techniques that improved the authority flow based search on data graphs by creating a framework to explain and reformulate them taking in to consideration user preferences and feedback. We also applied the proposed graph search techniques for Information Discovery over biological databases. Our algorithms were experimentally evaluated for performance and quality. The quality of our method was compared to current approaches by using user surveys.

Notes on sufficient conditions for a graph to be Hamiltonian

The first part of this paper deals with an extension of Dirac's Theorem to directed graphs. It is related to a result often referred to as the Ghouila-Houri Theorem. Here we show that the requirement of being strongly connected in the hypothesis of the Ghouila-Houri Theorem is redundant. The Second part of the paper shows that a condition on the number of edges for a graph to be hamiltonian implies Ore's condition on the degrees of the vertices.

Magnetic ordering in Er₂Ti₂O₇ and elastic softening in Tb₂Ti₂O₇

Geometric frustration occurs in the rare earth pyrochlores due to magnetic rare earth ions occupying the vertices of the network of corner-sharing tetrahedra. In this research, we have two parts. In the first one we study the phase transition to the magnetically ordered state at low temperature in the pyrochlore Er₂Ti₂O₇. The molecular field method was used to solve this problem. In the second part, we analyse the crystal electric field Hamiltonian for the rare earth sites. The rather large degeneracy of the angular momentum J of the rare earth ion is lifted by the crystal electric field due to the neighboring ions in the crystal. By rewriting the Stevens operators in the crystal electric field Hamiltonian ᴴCEF in terms of charge quadruple operators, we can identify unstable order parameters in ᴴCEF . These may be related to lattice instabilities in Tb₂Ti₂O₇.

Algorithms for Geometric Matching, Clustering, and Covering

With the popularization of GPS-enabled devices such as mobile phones, location data are becoming available at an unprecedented scale. The locations may be collected from many different sources such as vehicles moving around a city, user check-ins in social networks, and geo-tagged micro-blogging photos or messages. Besides the longitude and latitude, each location record may also have a timestamp and additional information such as the name of the location. Time-ordered sequences of these locations form trajectories, which together contain useful high-level information about people's movement patterns.

The first part of this thesis focuses on a few geometric problems motivated by the matching and clustering of trajectories. We first give a new algorithm for computing a matching between a pair of curves under existing models such as dynamic time warping (DTW). The algorithm is more efficient than standard dynamic programming algorithms both theoretically and practically. We then propose a new matching model for trajectories that avoids the drawbacks of existing models. For trajectory clustering, we present an algorithm that computes clusters of subtrajectories, which correspond to common movement patterns. We also consider trajectories of check-ins, and propose a statistical generative model, which identifies check-in clusters as well as the transition patterns between the clusters.

The second part of the thesis considers the problem of covering shortest paths in a road network, motivated by an EV charging station placement problem. More specifically, a subset of vertices in the road network are selected to place charging stations so that every shortest path contains enough charging stations and can be traveled by an EV without draining the battery. We first introduce a general technique for the geometric set cover problem. This technique leads to near-linear-time approximation algorithms, which are the state-of-the-art algorithms for this problem in either running time or approximation ratio. We then use this technique to develop a near-linear-time algorithm for this

shortest-path cover problem.

Irreducibility of Random Hilbert Schemes

We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.

Partition alignment in three dimensional unstructured mesh multi-physics modelling

Unstructured mesh codes for modelling continuum physics phenomena have evolved to provide the facility to model complex interacting systems. Parallelisation of such codes using single Program Multi Data (SPMD) domain decomposition techniques implemented with message passing has been demonstrated to provide high parallel efficiency, scalability to large numbers of processors P and portability across a wide range of parallel platforms. High efficiency, especially for large P requires that load balance is achieved in each parallel loop. For a code in which loops span a variety of mesh entity types, for example, elements, faces and vertices, some compromise is required between load balance for each entity type and the quantity of inter-processor communication required to satisfy data dependence between processors.

Integrability for Relativistic Spin Networks

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L^2 functions on three-dimensional hyperbolic space. To `evaluate' such a spin network we must do an integral; if this integral converges we say the spin network is `integrable'. Here we show that a large class of relativistic spin networks are integrable, including any whose underlying graph is the 4-simplex (the complete graph on 5 vertices). This proves a conjecture of Barrett and Crane, whose validity is required for the convergence of their state sum model.

BUILDING EFFICIENT AND COST-EFFECTIVE CLOUD-BASED BIG DATA MANAGEMENT SYSTEMS

In today’s big data world, data is being produced in massive volumes, at great velocity and from a variety of different sources such as mobile devices, sensors, a plethora of small devices hooked to the internet (Internet of Things), social networks, communication networks and many others. Interactive querying and large-scale analytics are being increasingly used to derive value out of this big data. A large portion of this data is being stored and processed in the Cloud due the several advantages provided by the Cloud such as scalability, elasticity, availability, low cost of ownership and the overall economies of scale. There is thus, a growing need for large-scale cloud-based data management systems that can support real-time ingest, storage and processing of large volumes of heterogeneous data. However, in the pay-as-you-go Cloud environment, the cost of analytics can grow linearly with the time and resources required. Reducing the cost of data analytics in the Cloud thus remains a primary challenge. In my dissertation research, I have focused on building efficient and cost-effective cloud-based data management systems for different application domains that are predominant in cloud computing environments. In the first part of my dissertation, I address the problem of reducing the cost of transactional workloads on relational databases to support database-as-a-service in the Cloud. The primary challenges in supporting such workloads include choosing how to partition the data across a large number of machines, minimizing the number of distributed transactions, providing high data availability, and tolerating failures gracefully. I have designed, built and evaluated SWORD, an end-to-end scalable online transaction processing system, that utilizes workload-aware data placement and replication to minimize the number of distributed transactions that incorporates a suite of novel techniques to significantly reduce the overheads incurred both during the initial placement of data, and during query execution at runtime. In the second part of my dissertation, I focus on sampling-based progressive analytics as a means to reduce the cost of data analytics in the relational domain. Sampling has been traditionally used by data scientists to get progressive answers to complex analytical tasks over large volumes of data. Typically, this involves manually extracting samples of increasing data size (progressive samples) for exploratory querying. This provides the data scientists with user control, repeatable semantics, and result provenance. However, such solutions result in tedious workflows that preclude the reuse of work across samples. On the other hand, existing approximate query processing systems report early results, but do not offer the above benefits for complex ad-hoc queries. I propose a new progressive data-parallel computation framework, NOW!, that provides support for progressive analytics over big data. In particular, NOW! enables progressive relational (SQL) query support in the Cloud using unique progress semantics that allow efficient and deterministic query processing over samples providing meaningful early results and provenance to data scientists. NOW! enables the provision of early results using significantly fewer resources thereby enabling a substantial reduction in the cost incurred during such analytics. Finally, I propose NSCALE, a system for efficient and cost-effective complex analytics on large-scale graph-structured data in the Cloud. The system is based on the key observation that a wide range of complex analysis tasks over graph data require processing and reasoning about a large number of multi-hop neighborhoods or subgraphs in the graph; examples include ego network analysis, motif counting in biological networks, finding social circles in social networks, personalized recommendations, link prediction, etc. These tasks are not well served by existing vertex-centric graph processing frameworks whose computation and execution models limit the user program to directly access the state of a single vertex, resulting in high execution overheads. Further, the lack of support for extracting the relevant portions of the graph that are of interest to an analysis task and loading it onto distributed memory leads to poor scalability. NSCALE allows users to write programs at the level of neighborhoods or subgraphs rather than at the level of vertices, and to declaratively specify the subgraphs of interest. It enables the efficient distributed execution of these neighborhood-centric complex analysis tasks over largescale graphs, while minimizing resource consumption and communication cost, thereby substantially reducing the overall cost of graph data analytics in the Cloud. The results of our extensive experimental evaluation of these prototypes with several real-world data sets and applications validate the effectiveness of our techniques which provide orders-of-magnitude reductions in the overheads of distributed data querying and analysis in the Cloud.

Leveraging Multiple Features for Image Retrieval and Matching

The goal of image retrieval and matching is to find and locate object instances in images from a large-scale image database. While visual features are abundant, how to combine them to improve performance by individual features remains a challenging task. In this work, we focus on leveraging multiple features for accurate and efficient image retrieval and matching. We first propose two graph-based approaches to rerank initially retrieved images for generic image retrieval. In the graph, vertices are images while edges are similarities between image pairs. Our first approach employs a mixture Markov model based on a random walk model on multiple graphs to fuse graphs. We introduce a probabilistic model to compute the importance of each feature for graph fusion under a naive Bayesian formulation, which requires statistics of similarities from a manually labeled dataset containing irrelevant images. To reduce human labeling, we further propose a fully unsupervised reranking algorithm based on a submodular objective function that can be efficiently optimized by greedy algorithm. By maximizing an information gain term over the graph, our submodular function favors a subset of database images that are similar to query images and resemble each other. The function also exploits the rank relationships of images from multiple ranked lists obtained by different features. We then study a more well-defined application, person re-identification, where the database contains labeled images of human bodies captured by multiple cameras. Re-identifications from multiple cameras are regarded as related tasks to exploit shared information. We apply a novel multi-task learning algorithm using both low level features and attributes. A low rank attribute embedding is joint learned within the multi-task learning formulation to embed original binary attributes to a continuous attribute space, where incorrect and incomplete attributes are rectified and recovered. To locate objects in images, we design an object detector based on object proposals and deep convolutional neural networks (CNN) in view of the emergence of deep networks. We improve a Fast RCNN framework and investigate two new strategies to detect objects accurately and efficiently: scale-dependent pooling (SDP) and cascaded rejection classifiers (CRC). The SDP improves detection accuracy by exploiting appropriate convolutional features depending on the scale of input object proposals. The CRC effectively utilizes convolutional features and greatly eliminates negative proposals in a cascaded manner, while maintaining a high recall for true objects. The two strategies together improve the detection accuracy and reduce the computational cost.

Approximation Algorithms for Network Design and Orienteering

This thesis presents approximation algorithms for some NP-Hard combinatorial optimization problems on graphs and networks; in particular, we study problems related to Network Design. Under the widely-believed complexity-theoretic assumption that P is not equal to NP, there are no efficient (i.e., polynomial-time) algorithms that solve these problems exactly. Hence, if one desires efficient algorithms for such problems, it is necessary to consider approximate solutions: An approximation algorithm for an NP-Hard problem is a polynomial time algorithm which, for any instance of the problem, finds a solution whose value is guaranteed to be within a multiplicative factor of the value of an optimal solution to that instance. We attempt to design algorithms for which this factor, referred to as the approximation ratio of the algorithm, is as small as possible. The field of Network Design comprises a large class of problems that deal with constructing networks of low cost and/or high capacity, routing data through existing networks, and many related issues. In this thesis, we focus chiefly on designing fault-tolerant networks. Two vertices u,v in a network are said to be k-edge-connected if deleting any set of k − 1 edges leaves u and v connected; similarly, they are k-vertex connected if deleting any set of k − 1 other vertices or edges leaves u and v connected. We focus on building networks that are highly connected, meaning that even if a small number of edges and nodes fail, the remaining nodes will still be able to communicate. A brief description of some of our results is given below. We study the problem of building 2-vertex-connected networks that are large and have low cost. Given an n-node graph with costs on its edges and any integer k, we give an O(log n log k) approximation for the problem of finding a minimum-cost 2-vertex-connected subgraph containing at least k nodes. We also give an algorithm of similar approximation ratio for maximizing the number of nodes in a 2-vertex-connected subgraph subject to a budget constraint on the total cost of its edges. Our algorithms are based on a pruning process that, given a 2-vertex-connected graph, finds a 2-vertex-connected subgraph of any desired size and of density comparable to the input graph, where the density of a graph is the ratio of its cost to the number of vertices it contains. This pruning algorithm is simple and efficient, and is likely to find additional applications. Recent breakthroughs on vertex-connectivity have made use of algorithms for element-connectivity problems. We develop an algorithm that, given a graph with some vertices marked as terminals, significantly simplifies the graph while preserving the pairwise element-connectivity of all terminals; in fact, the resulting graph is bipartite. We believe that our simplification/reduction algorithm will be a useful tool in many settings. We illustrate its applicability by giving algorithms to find many trees that each span a given terminal set, while being disjoint on edges and non-terminal vertices; such problems have applications in VLSI design and other areas. We also use this reduction algorithm to analyze simple algorithms for single-sink network design problems with high vertex-connectivity requirements; we give an O(k log n)-approximation for the problem of k-connecting a given set of terminals to a common sink. We study similar problems in which different types of links, of varying capacities and costs, can be used to connect nodes; assuming there are economies of scale, we give algorithms to construct low-cost networks with sufficient capacity or bandwidth to simultaneously support flow from each terminal to the common sink along many vertex-disjoint paths. We further investigate capacitated network design, where edges may have arbitrary costs and capacities. Given a connectivity requirement R_uv for each pair of vertices u,v, the goal is to find a low-cost network which, for each uv, can support a flow of R_uv units of traffic between u and v. We study several special cases of this problem, giving both algorithmic and hardness results. In addition to Network Design, we consider certain Traveling Salesperson-like problems, where the goal is to find short walks that visit many distinct vertices. We give a (2 + epsilon)-approximation for Orienteering in undirected graphs, achieving the best known approximation ratio, and the first approximation algorithm for Orienteering in directed graphs. We also give improved algorithms for Orienteering with time windows, in which vertices must be visited between specified release times and deadlines, and other related problems. These problems are motivated by applications in the fields of vehicle routing, delivery and transportation of goods, and robot path planning.

Top-K Query Processing in Edge-Labeled Graph Data

Edge-labeled graphs have proliferated rapidly over the last decade due to the increased popularity of social networks and the Semantic Web. In social networks, relationships between people are represented by edges and each edge is labeled with a semantic annotation. Hence, a huge single graph can express many different relationships between entities. The Semantic Web represents each single fragment of knowledge as a triple (subject, predicate, object), which is conceptually identical to an edge from subject to object labeled with predicates. A set of triples constitutes an edge-labeled graph on which knowledge inference is performed. Subgraph matching has been extensively used as a query language for patterns in the context of edge-labeled graphs. For example, in social networks, users can specify a subgraph matching query to find all people that have certain neighborhood relationships. Heavily used fragments of the SPARQL query language for the Semantic Web and graph queries of other graph DBMS can also be viewed as subgraph matching over large graphs. Though subgraph matching has been extensively studied as a query paradigm in the Semantic Web and in social networks, a user can get a large number of answers in response to a query. These answers can be shown to the user in accordance with an importance ranking. In this thesis proposal, we present four different scoring models along with scalable algorithms to find the top-k answers via a suite of intelligent pruning techniques. The suggested models consist of a practically important subset of the SPARQL query language augmented with some additional useful features. The first model called Substitution Importance Query (SIQ) identifies the top-k answers whose scores are calculated from matched vertices' properties in each answer in accordance with a user-specified notion of importance. The second model called Vertex Importance Query (VIQ) identifies important vertices in accordance with a user-defined scoring method that builds on top of various subgraphs articulated by the user. Approximate Importance Query (AIQ), our third model, allows partial and inexact matchings and returns top-k of them with a user-specified approximation terms and scoring functions. In the fourth model called Probabilistic Importance Query (PIQ), a query consists of several sub-blocks: one mandatory block that must be mapped and other blocks that can be opportunistically mapped. The probability is calculated from various aspects of answers such as the number of mapped blocks, vertices' properties in each block and so on and the most top-k probable answers are returned. An important distinguishing feature of our work is that we allow the user a huge amount of freedom in specifying: (i) what pattern and approximation he considers important, (ii) how to score answers - irrespective of whether they are vertices or substitution, and (iii) how to combine and aggregate scores generated by multiple patterns and/or multiple substitutions. Because so much power is given to the user, indexing is more challenging than in situations where additional restrictions are imposed on the queries the user can ask. The proposed algorithms for the first model can also be used for answering SPARQL queries with ORDER BY and LIMIT, and the method for the second model also works for SPARQL queries with GROUP BY, ORDER BY and LIMIT. We test our algorithms on multiple real-world graph databases, showing that our algorithms are far more efficient than popular triple stores.

Spectra and Laplacian spectra of arbitrary powers of lexicographic products of graphs

Consider two graphs G and H. Let H^k[G] be the lexicographic product of H^k and G, where H^k is the lexicographic product of the graph H by itself k times. In this paper, we determine the spectrum of H^k[G]H and H^k when G and H are regular and the Laplacian spectrum of H^k[G] and H^k for G and H arbitrary. Particular emphasis is given to the least eigenvalue of the adjacency matrix in the case of lexicographic powers of regular graphs, and to the algebraic connectivity and the largest Laplacian eigenvalues in the case of lexicographic powers of arbitrary graphs. This approach allows the determination of the spectrum (in case of regular graphs) and Laplacian spectrum (for arbitrary graphs) of huge graphs. As an example, the spectrum of the lexicographic power of the Petersen graph with the googol number (that is, 10^100 ) of vertices is determined. The paper finishes with the extension of some well known spectral and combinatorial invariant properties of graphs to its lexicographic powers.