Browsing by Subject "Graph theory"

Now showing 1 - 20 of 53

Open Access
Aberrant cerebral network topology and mild cognitive impairment in early Parkinson’s disease
(John Wiley & Sons, Inc., 2015-05-06) Pereira, J. B.; Aarsland, D.; Ginestet, C. E.; Lebedev, A. V.; Wahlund, L. O.; Simmons, A.; Volpe, G.; Westman, E.
The aim of this study was to assess whether mild cognitive impairment (MCI) is associatedwith disruption in large-scale structural networks in newly diagnosed, drug-na€ıve patients with Parkin-son’s disease (PD). Graph theoretical analyses were applied to 3T MRI data from 123 PD patients and 56controls from the Parkinson’s progression markers initiative (PPMI). Thirty-three patients were classifiedas having Parkinson’s disease with mild cognitive impairment (PD-MCI) using the Movement DisordersSociety Task Force criteria, while the remaining 90 PD patients were classified as cognitively normal (PD-CN). Global measures (clustering coefficient, characteristic path length, global efficiency, small-world-ness) and regional measures (regional clustering coefficient, regional efficiency, hubs) were assessed inthe structural networks that were constructed based on cortical thickness and subcortical volume data.PD-MCI patients showed a marked reduction in the average correlation strength between cortical andsubcortical regions compared with controls. These patients had a larger characteristic path length andreduced global efficiency in addition to a lower regional efficiency in frontal and parietal regions com-pared with PD-CN patients and controls. A reorganization of the highly connected regions in the networkwas observed in both groups of patients. This study shows that the earliest stages of cognitive decline inPD are associated with a disruption in the large-scale coordination of the brain network and with adecrease of the efficiency of parallel information processing.
Open Access
Algorithms for effective querying of compound graph-based pathway databases
(BioMed Central Ltd., 2009-11-16) Doğrusöz, Uğur; Çetintaş, Ahmet; Demir, Emek; Babur, Özgün
Background: Graph-based pathway ontologies and databases are widely used to represent data about cellular processes. This representation makes it possible to programmatically integrate cellular networks and to investigate them using the well-understood concepts of graph theory in order to predict their structural and dynamic properties. An extension of this graph representation, namely hierarchically structured or compound graphs, in which a member of a biological network may recursively contain a sub-network of a somehow logically similar group of biological objects, provides many additional benefits for analysis of biological pathways, including reduction of complexity by decomposition into distinct components or modules. In this regard, it is essential to effectively query such integrated large compound networks to extract the sub-networks of interest with the help of efficient algorithms and software tools. Results: Towards this goal, we developed a querying framework, along with a number of graph-theoretic algorithms from simple neighborhood queries to shortest paths to feedback loops, that is applicable to all sorts of graph-based pathway databases, from PPIs (protein-protein interactions) to metabolic and signaling pathways. The framework is unique in that it can account for compound or nested structures and ubiquitous entities present in the pathway data. In addition, the queries may be related to each other through "AND" and "OR" operators, and can be recursively organized into a tree, in which the result of one query might be a source and/or target for another, to form more complex queries. The algorithms were implemented within the querying component of a new version of the software tool PATIKAweb (Pathway Analysis Tool for Integration and Knowledge Acquisition) and have proven useful for answering a number of biologically significant questions for large graph-based pathway databases. Conclusion: The PATIKA Project Web site is http://www.patika.org. PATIKAweb version 2.1 is available at http://web.patika.org. © 2009 Dogrusoz et al; licensee BioMed Central Ltd.
Open Access
Algorithms for layout of disconnected graphs
(Elsevier, 2000) Doğrusöz, Uğur
We present efficient algorithms for the layout of disconnected objects in a graph (isolated nodes and components) for a specified aspect ratio. These linear and near-linear algorithms are based on alternate-bisection and two-dimensional packing methodologies. In addition, the parameters that affect the performance of these algorithms as well as the circumstances under which the two methodologies perform well are analyzed.
Open Access
Analysis of Lagrangian lower bounds for a graph partitioning problem
(Institute for Operations Research and the Management Sciences (INFORMS), 1999) Adil, G. K.; Ghosh, J. B.
Recently, Ahmadi and Tang (1991) demonstrated how various manufacturing problems can be modeled and solved as graph partitioning problems. They use Lagrangian relaxation of two different mixed integer programming formulations to obtain both heuristic solutions and lower bounds on optimal solution values. In this note, we point to certain inconsistencies in the reported results. Among other things, we show analytically that the first bound proposed is trivial (i.e., it can never have a value greater than zero) while the second is also trivial for certain sparse graphs. We also present limited empirical results on the behavior of this second bound as a function of graph density.
Open Access
Architectural requirements for energy efficient execution of graph analytics applications
(IEEE, 2015-11) Özdal, Muhammet Mustafa; Yeşil, Şerif; Kim, T.; Ayupov, A.; Burns, S.; Öztürk, Özcan
Intelligent data analysis has become more important in the last decade especially because of the significant increase in the size and availability of data. In this paper, we focus on the common execution models and characteristics of iterative graph analytics applications. We show that the features that improve work efficiency can lead to significant overheads on existing systems. We identify the opportunities for custom hardware implementation, and outline the desired architectural features for energy efficient computation of graph analytics applications. © 2015 IEEE.
Open Access
Automatic multimedia cross-modal correlation discovery
(ACM, 2004-08) Pan, J.-Y.; Yang, H.-J.; Faloutsos, C.; Duygulu, Pınar
Given an image (or video clip, or audio song), how do we automatically assign keywords to it? The general problem is to find correlations across the media in a collection of multimedia objects like video clips, with colors, and/or motion, and/or audio, and/or text scripts. We propose a novel, graph-based approach, "MMG", to discover such cross-modal correlations. Our "MMG" method requires no tuning, no clustering, no user-determined constants; it can be applied to any multi-media collection, as long as we have a similarity function for each medium; and it scales linearly with the database size. We report auto-captioning experiments on the "standard" Corel image database of 680 MB, where it outperforms domain specific, fine-tuned methods by up to 10 percentage points in captioning accuracy (50% relative improvement).
Open Access
A bound on the zero-error list coding capacity
(IEEE, 1993) Arıkan, Erdal
We present a new bound on the zero-error list coding capacity, and using which, show that the list-of-3 capacity of the 4/3 channel is at most 6/19 bits, improving the best previously known bound of 3/8. The relation of the bound to the graph-entropy bound of Koerner and Marton is also discussed.
Open Access
BRAPH: A graph theory software for the analysis of brain connectivity
(Public Library of Science, 2017) Mijalkov, M.; Kakaei, E.; Pereira, J. B.; Westman, E.; Volpe, G.
The brain is a large-scale complex network whose workings rely on the interaction between its various regions. In the past few years, the organization of the human brain network has been studied extensively using concepts from graph theory, where the brain is represented as a set of nodes connected by edges. This representation of the brain as a connectome can be used to assess important measures that reflect its topological architecture. We have developed a freeware MatLab-based software (BRAPH–BRain Analysis using graPH theory) for connectivity analysis of brain networks derived from structural magnetic resonance imaging (MRI), functional MRI (fMRI), positron emission tomography (PET) and electroencephalogram (EEG) data. BRAPH allows building connectivity matrices, calculating global and local network measures, performing non-parametric permutations for group comparisons, assessing the modules in the network, and comparing the results to random networks. By contrast to other toolboxes, it allows performing longitudinal comparisons of the same patients across different points in time. Furthermore, even though a user-friendly interface is provided, the architecture of the program is modular (object-oriented) so that it can be easily expanded and customized. To demonstrate the abilities of BRAPH, we performed structural and functional graph theory analyses in two separate studies. In the first study, using MRI data, we assessed the differences in global and nodal network topology in healthy controls, patients with amnestic mild cognitive impairment, and patients with Alzheimer’s disease. In the second study, using resting-state fMRI data, we compared healthy controls and Parkinson’s patients with mild cognitive impairment. © 2017 Mijalkov et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Open Access
Cell-graph mining for breast tissue modeling and classification
(IEEE, 2007-08) Bilgin, C.; Demir, Çiğdem; Nagi, C.; Yener, B.
We consider the problem of automated cancer diagnosis in the context of breast tissues. We present graph theoretical techniques that identify and compute quantitative metrics for tissue characterization and classification. We segment digital images of histopatological tissue samples using k-means algorithm. For each segmented image we generate different cell-graphs using positional coordinates of cells and surrounding matrix components. These cell-graphs have 500-2000 cells(nodes) with 1000-10000 links depending on the tissue and the type of cell-graph being used. We calculate a set of global metrics from cell-graphs and use them as the feature set for learning. We compare our technique, hierarchical cell graphs, with other techniques based on intensity values of images, Delaunay triangulation of the cells, the previous technique we proposed for brain tissue images and with the hybrid approach that we introduce in this paper. Among the compared techniques, hierarchical-graph approach gives 81.8% accuracy whereas we obtain 61.0%, 54.1% and 75.9% accuracy with intensity-based features, Delaunay triangulation and our previous technique, respectively. © 2007 IEEE.
Open Access
Color graph representation for structural analysis of tissue images
(2010) Altunbay, Doğan
Computer aided image analysis tools are becoming increasingly important in automated cancer diagnosis and grading. They have the potential of assisting pathologists in histopathological examination of tissues, which may lead to a considerable amount of subjectivity. These analysis tools help reduce the subjectivity, providing quantitative information about tissues. In literature, it has been proposed to implement such computational tools using different methods that represent a tissue with different set of image features. One of the most commonly used methods is the structural method that represents a tissue quantifying the spatial relationship of its components. Although previous structural methods lead to promising results for different tissue types, they only use the spatial relations of nuclear tissue components without considering the existence of different components in a tissue. However, additional information that could be obtained from other components of the tissue has an importance in better representing the tissue, and thus, in making more reliable decisions. This thesis introduces a novel structural method to quantify histopathological images for automated cancer diagnosis and grading. Unlike the previous structural methods, it proposes to represent a tissue considering the spatial distribution of different tissue components. To this end, it constructs a graph on multiple tissue components and colors its edges depending on the component types of their end points. Subsequently, a new set of structural features is extracted from these “color graphs” and used in the classification of tissues. Experiments conducted on 3236 photomicrographs of colon tissues that are taken from 258 different patients demonstrate that the color graph approach leads to 94.89 percent training accuracy and 88.63 percent test accuracy. Our experiments also show that the introduction of color edges to represent the spatial relationship of different tissue components and the use of graph features defined on these color edges significantly improve the classification accuracy of the previous structural methods.
Open Access
Color graphs for automated cancer diagnosis and grading
(Institute of Electrical and Electronics Engineers, 2010-03) Altunbay, D.; Cigir, C.; Sokmensuer, C.; Gunduz Demir, C.
This paper reports a new structural method to mathematically represent and quantify a tissue for the purpose of automated and objective cancer diagnosis and grading. Unlike the previous structural methods, which quantify a tissue considering the spatial distributions of its cell nuclei, the proposed method relies on the use of distributions of multiple tissue components for the representation. To this end, it constructs a graph on multiple tissue components and colors its edges depending on the component types of their endpoints. Subsequently, it extracts a new set of structural features from these color graphs and uses these features in the classification of tissues. Working with the images of colon tissues, our experiments demonstrate that the color-graph approach leads to 82.65% test accuracy and that it significantly improves the performance of its counterparts. © 2006 IEEE.
Open Access
A compound graph layout algorithm for biological pathways
(Springer, Berlin, Heidelberg, 2004-09-10) Doğrusöz, Uğur; Giral, Erhan; Çetintaş, Ahmet; Çivril, Ali; Demir, Emek
We present a new compound graph layout algorithm based on traditional force-directed layout scheme with extensions for nesting and other application-specific constraints. The algorithm has been successfully implemented within PATIKA, a pathway analysis tool for drawing complicated biological pathways with compartimental constraints and arbitrary nesting relations to represent molecular complexes and pathway abstractions. Experimental results show that execution times and quality of the produced drawings with respect to commonly accepted layout criteria and pathway drawing conventions are quite satisfactory. © Springer-Verlag Berlin Heidelberg 2004.
Open Access
Compromising system and user interests in shelter location and evacuation planning
(Elsevier Ltd, 2015) Bayram V.; Tansel, B.T.; Yaman H.
Traffic management during an evacuation and the decision of where to locate the shelters are of critical importance to the performance of an evacuation plan. From the evacuation management authority's point of view, the desirable goal is to minimize the total evacuation time by computing a system optimum (SO). However, evacuees may not be willing to take long routes enforced on them by a SO solution; but they may consent to taking routes with lengths not longer than the shortest path to the nearest shelter site by more than a tolerable factor. We develop a model that optimally locates shelters and assigns evacuees to the nearest shelter sites by assigning them to shortest paths, shortest and nearest with a given degree of tolerance, so that the total evacuation time is minimized. As the travel time on a road segment is often modeled as a nonlinear function of the flow on the segment, the resulting model is a nonlinear mixed integer programming model. We develop a solution method that can handle practical size problems using second order cone programming techniques. Using our model, we investigate the importance of the number and locations of shelter sites and the trade-off between efficiency and fairness. © 2014 Elsevier Ltd.
Open Access
Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations
(IEEE, 1998-05) Kutay, Mehmet Alper; Erden, M. F.; Özaktaş, Haldun M.; Arıkan, Orhan; Candan, Ç.; Güleryüz, Ö.
It is possible to obtain either exact realizations or useful approximations of linear systems or matrix-vector products arising in many different applications, by synthesizing them in the form of repeated or multi-channel filtering operations in fractional Fourier domains, resulting in much more efficient implementations with acceptable decreases in accuracy. By varying the number and configuration of filter blocks, which may take the form of arbitrary flow graphs, it is possible to trade off between accuracy and efficiency in the desired manner. The proposed scheme constitutes a systematic way of exploiting the information inherent in the regularity or structure of a given linear system or matrix, even when that structure is not readily apparent.
Open Access
A decoupled local memory allocator
(Association for Computing Machinery, 2013) Diouf, B.; Hantaş, C.; Cohen, A.; Özturk, Ö.; Palsberg, J.
Compilers use software-controlled local memories to provide fast, predictable, and power-efficient access to critical data. We show that the local memory allocation for straight-line, or linearized programs is equivalent to a weighted interval-graph coloring problem. This problem is new when allowing a color interval to "wrap around," and we call it the submarine-building problem. This graph-theoretical decision problem differs slightly from the classical ship-building problem, and exhibits very interesting and unusual complexity properties. We demonstrate that the submarine-building problem is NP-complete, while it is solvable in linear time for not-so-proper interval graphs, an extension of the the class of proper interval graphs. We propose a clustering heuristic to approximate any interval graph into a not-so-proper interval graph, decoupling spill code generation from local memory assignment. We apply this heuristic to a large number of randomly generated interval graphs reproducing the statistical features of standard local memory allocation benchmarks, comparing with state-of-the-art heuristics. © 2013 ACM.
Open Access
Detection of compound structures using clustering of statistical and structural features
(IEEE, 2012) Akçay, H. Gökhan; Aksoy, Selim
We describe a new method for detecting compound structures in images by combining the statistical and structural characteristics of simple primitive objects. A graph is constructed by assigning the primitive objects to its vertices, and connecting potentially related objects using edges. Statistical information that is modeled using spectral, shape, and position data of individual objects as well as the structural information that is modeled in terms of spatial alignments of neighboring object groups are also encoded in this graph. Experiments using WorldView-2 data show that hierarchical clustering of the graph vertices can discover high-level compound structures that cannot be obtained using traditional techniques. © 2012 IEEE.
Open Access
An effective model to decompose linear programs for parallel solution
(Springer, 1996-08) Pınar, Ali; Aykanat, Cevdet
Although inherent parallelism in the solution of block angulax Linear Programming (LP) problems has been exploited in many research works, the literature that addresses decomposing constraint matrices into block angular form for parallel solution is very rare and recent. We have previously proposed hypergraph models, which reduced the problem to the hypergraph partitioning problem. However, the quality of the results reported were limited due to the hypergraph partitioning tools we have used. Very recently, multilevel graph partitioning heuristics have been proposed leading to very successful graph partitioning tools; Chaco and Metis. In this paper, we propose an effective graph model to decompose matrices into block angular form, which reduces the problem to the well-known graph partitioning by vertex separator problem. We have experimented the validity of our proposed model with various LP problems selected from NETLIB and other sources. The results are very attractive both in terms of solution quality and running times. © Springer-Verlag Berlin Heidelberg 1996.
Open Access
Encapsulating multiple communication-cost metrics in partitioning sparse rectangular matrices for parallel matrix-vector multiplies
(SIAM, 2004) Uçar, B.; Aykanat, Cevdet
This paper addresses the problem of one-dimensional partitioning of structurally unsymmetric square and rectangular sparse matrices for parallel matrix-vector and matrix-transpose-vector multiplies. The objective is to minimize the communication cost while maintaining the balance on computational loads of processors. Most of the existing partitioning models consider only the total message volume hoping that minimizing this communication-cost metric is likely to reduce other metrics. However, the total message latency (start-up time) may be more important than the total message volume. Furthermore, the maximum message volume and latency handled by a single processor are also important metrics. We propose a two-phase approach that encapsulates all these four communication-cost metrics. The objective in the first phase is to minimize the total message volume while maintaining the computational-load balance. The objective in the second phase is to encapsulate the remaining three communication-cost metrics. We propose communication-hypergraph and partitioning models for the second phase. We then present several methods for partitioning communication hypergraphs. Experiments on a wide range of test matrices show that the proposed approach yields very effective partitioning results. A parallel implementation on a PC cluster verifies that the theoretical improvements shown by partitioning results hold in practice.
Open Access
Exploiting locality in sparse matrix-matrix multiplication on many-core rchitectures
(IEEE Computer Society, 2017) Akbudak K.; Aykanat, Cevdet
Exploiting spatial and temporal localities is investigated for efficient row-by-row parallelization of general sparse matrix-matrix multiplication (SpGEMM) operation of the form C=A,B on many-core architectures. Hypergraph and bipartite graph models are proposed for 1D rowwise partitioning of matrix A to evenly partition the work across threads with the objective of reducing the number of B-matrix words to be transferred from the memory and between different caches. A hypergraph model is proposed for B-matrix column reordering to exploit spatial locality in accessing entries of thread-private temporary arrays, which are used to accumulate results for C-matrix rows. A similarity graph model is proposed for B-matrix row reordering to increase temporal reuse of these accumulation array entries. The proposed models and methods are tested on a wide range of sparse matrices from real applications and the experiments were carried on a 60-core Intel Xeon Phi processor, as well as a two-socket Xeon processor. Results show the validity of the models and methods proposed for enhancing the locality in parallel SpGEMM operations. © 1990-2012 IEEE.
Open Access
Fast optimal load balancing algorithms for 1D partitioning
(Academic Press, 2004) Pınar, A.; Aykanat, Cevdet
The one-dimensional decomposition of nonuniform workload arrays with optimal load balancing is investigated. The problem has been studied in the literature as the "chains-on-chains partitioning" problem. Despite the rich literature on exact algorithms, heuristics are still used in parallel computing community with the "hope" of good decompositions and the "myth" of exact algorithms being hard to implement and not runtime efficient. We show that exact algorithms yield significant improvements in load balance over heuristics with negligible overhead. Detailed pseudocodes of the proposed algorithms are provided for reproducibility. We start with a literature review and propose improvements and efficient implementation tips for these algorithms. We also introduce novel algorithms that are asymptotically and runtime efficient. Our experiments on sparse matrix and direct volume rendering datasets verify that balance can be significantly improved by using exact algorithms. The proposed exact algorithms are 100 times faster than a single sparse-matrix vector multiplication for 64-way decompositions on the average. We conclude that exact algorithms with proposed efficient implementations can effectively replace heuristics. © 2004 Elsevier Inc. All rights reserved.