Browsing by Subject "Graph Theory"

Now showing 1 - 7 of 7

Open Access
Automated construction of fuzzy event sets and its application to active databases
(IEEE, 2001) Saygin, Y.; Ulusoy, Özgür
Fuzzy sets and fuzzy logic research aims to bridge the gap between the crisp world of math and the real world. Fuzzy set theory was applied to many different areas, from control to databases. Sometimes the number of events in an event-driven system may become very high and unmanageable. Therefore, it is very useful to organize the events into fuzzy event sets also introducing the benefits of the fuzzy set theory. All the events that have occurred in a system can be stored in event histories which contain precious hidden information. In this paper, we propose a method for automated construction of fuzzy event sets out of event histories via data mining techniques. The useful information hidden in the event history is extracted into a matrix called sequential proximity matrix. This matrix shows the proximities of events and it is used for fuzzy rule execution via similarity based event detection and construction of fuzzy event sets. Our application platform is active databases. We describe how fuzzy event sets can be exploited for similarity based event detection and fuzzy rule execution in active database systems.
Open Access
Circuit partitioning using mean field annealing
(Elsevier, 1995) Bultan, T.; Aykanat, Cevdet
Mean field annealing (MFA) algorithm, proposed for solving combinatorial optimization problems, combines the characteristics of neural networks and simulated annealing. Previous works on MFA resulted with successful mapping of the algorithm to some classic optimization problems such as traveling salesperson problem, scheduling problem, knapsack problem and graph partitioning problem. In this paper, MFA is formulated for the circuit partitioning problem using the so called net-cut model. Hence, the deficiencies of using the graph representation for electrical circuits are avoided. An efficient implementation scheme, which decreases the complexity of the proposed algorithm by asymptotical factors is also developed. Comparative performance analysis of the proposed algorithm with two wellknown heuristics, simulated annealing and Kernighan-Lin, indicates that MFA is a successful alternative heuristic for the circuit partitioning problem. © 1995.
Open Access
Distributed k-Core view materialization and maintenance for large dynamic graphs
(Institute of Electrical and Electronics Engineers, 2014-10) Aksu, H.; Canim, M.; Chang, Yuan-Chi; Korpeoglu, I.; Ulusoy, O.
In graph theory, k-core is a key metric used to identify subgraphs of high cohesion, also known as the ‘dense’ regions of a graph. As the real world graphs such as social network graphs grow in size, the contents get richer and the topologies change dynamically, we are challenged not only to materialize k-core subgraphs for one time but also to maintain them in order to keep up with continuous updates. Adding to the challenge is that real world data sets are outgrowing the capacity of a single server and its main memory. These challenges inspired us to propose a new set of distributed algorithms for k-core view construction and maintenance on a horizontally scaling storage and computing platform. Our algorithms execute against the partitioned graph data in parallel and take advantage of k-core properties to aggressively prune unnecessary computation. Experimental evaluation results demonstrated orders of magnitude speedup and advantages of maintaining k-core incrementally and in batch windows over complete reconstruction. Our algorithms thus enable practitioners to create and maintain many k-core views on different topics in rich social network content simultaneously.
Open Access
Efficient analysis of large-scale social networks using big-data platforms
(2014) Aksu, Hidayet
In recent years, the rise of very large, rich content networks re-ignited interest to complex/social network analysis at the big data scale, which makes it possible to understand social interactions at large scale while it poses computation challenges to early works with algorithm complexity greater than O(n). This thesis analyzes social networks at very large-scales to derive important parameters and characteristics in an efficient and effective way using big-data platforms. With the popularization of mobile phone usage, telecommunication networks have turned into a socially binding medium and enables researches to analyze social interactions at very large scales. Degree distribution is one of the most important characteristics of social networks and to study degree characteristics and structural properties in large-scale social networks, in this thesis we first gathered a tera-scale dataset of telecommunication call detail records. Using this data we empirically evaluate some statistical models against the degree distribution of the country’s call graph and determine that a Pareto log-normal distribution provides the best fit, despite claims in the literature that power-law distribution is the best model. We also question and derive answers for how network operator, size, density and location affect degree distribution to understand the parameters governing it in social networks. Besides structural property analysis, community identification is of great interest in practice to learn high cohesive subnetworks about different subjects in a social network. In graph theory, k-core is a key metric used to identify subgraphs of high cohesion, also known as the ‘dense’ regions of a graph. As the real world graphs such as social network graphs grow in size, the contents get richer and the topologies change dynamically, we are challenged not only to materialize k-core subgraphs for one time but also to maintain them in order to keep up with continuous updates. These challenges inspired us to propose a new set of distributed algorithms for k-core view construction and maintenance on a horizontally scaling storage and computing platform. Experimental evaluation results demonstrated orders of magnitude speedup and advantages of maintaining k-core incrementally and in batch windows over complete reconstruction approaches. Moreover, the intensity of community engagement can be distinguished at multiple levels, resulting in a multiresolution community representation that has to be maintained over time. We also propose distributed algorithms to construct and maintain a multi-k-core graphs, implemented on the scalable big-data platform Apache HBase. Our experimental evaluation results demonstrate orders of magnitude speedup by maintaining multi-k-core incrementally over complete reconstruction. Furthermore, we propose a graph aware cache system designed for distributed graph processing. Experimental results demonstrate up to 15x speedup compared to traditional LRU based cache systems.
Open Access
Hypergraph models and algorithms for data-pattern-based clustering
(Springer, 2004) Ozdal, M. M.; Aykanat, Cevdet
In traditional approaches for clustering market basket type data, relations among transactions are modeled according to the items occurring in these transactions. However, an individual item might induce different relations in different contexts. Since such contexts might be captured by interesting patterns in the overall data, we represent each transaction as a set of patterns through modifying the conventional pattern semantics. By clustering the patterns in the dataset, we infer a clustering of the transactions represented this way. For this, we propose a novel hypergraph model to represent the relations among the patterns. Instead of a local measure that depends only on common items among patterns, we propose a global measure that is based on the cooccurences of these patterns in the overall data. The success of existing hypergraph partitioning based algorithms in other domains depends on sparsity of the hypergraph and explicit objective metrics. For this, we propose a two-phase clustering approach for the above hypergraph, which is expected to be dense. In the first phase, the vertices of the hypergraph are merged in a multilevel algorithm to obtain large number of high quality clusters. Here, we propose new quality metrics for merging decisions in hypergraph clustering specifically for this domain. In order to enable the use of existing metrics in the second phase, we introduce a vertex-to-cluster affinity concept to devise a method for constructing a sparse hypergraph based on the obtained clustering. The experiments we have performed show the effectiveness of the proposed framework.
Open Access
Image-space decomposition algorithms for sort-first parallel volume rendering of unstructured grids
(Springer, 2000) Kutluca, H.; Kurç, T. M.; Aykanat, Cevdet
Twelve adaptive image-space decomposition algorithms are presented for sort-first parallel direct volume rendering (DVR) of unstructured grids on distributed-memory architectures. The algorithms are presented under a novel taxonomy based on the dimension of the screen decomposition, the dimension of the workload arrays used in the decomposition, and the scheme used for workload-array creation and querying the workload of a region. For the 2D decomposition schemes using 2D workload arrays, a novel scheme is proposed to query the exact number of screen-space bounding boxes of the primitives in a screen region in constant time. A probe-based chains-on-chains partitioning algorithm is exploited for load balancing in optimal 1D decomposition and iterative 2D rectilinear decomposition (RD). A new probe-based optimal 2D jagged decomposition (OJD) is proposed which is much faster than the dynamic-programming based OJD scheme proposed in the literature. The summed-area table is successfully exploited to query the workload of a rectangular region in constant time in both OJD and RD schemes for the subdivision of general 2D workload arrays. Two orthogonal recursive bisection (ORB) variants are adapted to relax the straight-line division restriction in conventional ORB through using the medians-of-medians approach on regular mesh and quadtree superimposed on the screen. Two approaches based on the Hilbert space-filling curve and graph-partitioning are also proposed. An efficient primitive classification scheme is proposed for redistribution in 1D, and 2D rectilinear and jagged decompositions. The performance comparison of the decomposition algorithms is modeled by establishing appropriate quality measures for load-balancing, amount of primitive replication and parallel execution time. The experimental results on a Parsytec CC system using a set of benchmark volumetric datasets verify the validity of the proposed performance models. The performance evaluation of the decomposition algorithms is also carried out through the sort-first parallelization of an efficient DVR algorithm.
Open Access
Two-dimensional packing algorithms for layout of disconnected graphs
(Elsevier, 2002) Dogrusoz, U.
We present and contrast several efficient two-dimensional packing algorithms for specified aspect ratio. These near-linear algorithms are based on strip packing, tiling, and alternate-bisection methodologies and can be used in the layout of disconnected objects in graph visualization. The parameters that affect the performance of these algorithms as well as the circumstances under which they perform well are analyzed. © 2002 Elsevier Science Inc. All rights reserved.