Browsing by Subject "Graph theory."

Now showing 1 - 11 of 11

Open Access
Algorithms for effective querying of graph-based pathway databases
(2007) Çetintaş, Ahmet
As the scientific curiosity shifts toward system-level investigation of genomicscale information, data produced about cellular processes at molecular level has been accumulating with an accelerating rate. Graph-based pathway ontologies and databases have been in wide use for such data. This representation has made it possible to programmatically integrate cellular networks as well as investigating them using the well-understood concepts of graph theory to predict their structural and dynamic properties. In this regard, it is essential to effectively query such integrated large networks to extract the sub-networks of interest with the help of efficient algorithms and software tools. Towards this goal, we have developed a querying framework along with a number of graph-theoretic algorithms from simple neighborhood queries to shortest paths to feedback loops, applicable to all sorts of graph-based pathway databases from PPIs to metabolic pathways to signaling pathways. These algorithms can also account for compound or nested structures present in the pathway data, and have been implemented within the querying components of Patika (Pathway Analysis Tools for Integration and Knowledge Acquisition) tools and have proven to be useful for answering a number of biologically significant queries for a large graph-based pathway database.
Open Access
Balance preserving min-cut replication set for a K-way hypergraph partitioning
(2010) Yazıcı, Volkan
Replication is a widely used technique in information retrieval and database systems for providing fault-tolerance and reducing parallelization and processing costs. Combinatorial models based on hypergraph partitioning are proposed for various problems arising in information retrieval and database systems. We consider the possibility of using vertex replication to improve the quality of hypergraph partitioning. In this study, we focus on the Balance Preserving Min-Cut Replication Set (BPMCRS) problem, where we are initially given a maximum replication capacity and a K-way hypergraph partition with an initial imbalance ratio. The objective in the BPMCRS problem is finding optimal vertex replication sets for each part of the given partition such that the initial cutsize of the partition is improved as much as possible and the initial imbalance is either preserved or reduced under the given replication capacity constraint. In order to address the BPMCRS problem, we propose a model based on a unique blend of coarsening and integer linear programming (ILP) schemes. This coarsening algorithm is based on the Dulmage-Mendelsohn decomposition. Experiments show that the ILP formulation coupled with the Dulmage-Mendelsohn decomposition-based coarsening provides high quality results in feasible execution times for reducing the cost of a given K-way hypergraph partition.
Open Access
A bipartite graph model for placement, scheduling and replication in data grids
(2012) Dal, Burcu
Data grids provide geographically distributed resources for applications that generate and utilize large data sets. However, there are some issues that hinder to ensure fast access to data and low turnaround time for the jobs in data grids. To address these issues, several data replication and job scheduling strategies have been introduced to offer high data availability, low bandwidth consumption, and reduced turnaround time for grid systems. Multiple copies of existing data are maintained at different locations via data replication. Data replication strategies are broadly categorized as static and dynamic. In static replication strategies, replication is performed during the system design, and replica decisions are generally based on a cost model that includes data access costs, bandwidth characteristics and storage constraints of the grid system. In dynamic replication strategies, the replication operation is managed at runtime so that the system adapts to the changes in user request patterns dynamically. Job scheduling strategies fall under two main categories: online mode and batch mode. The online mode scheduler assigns tasks to sites as soon as they arrive. In the batch mode, the complete set of jobs are taken into account and scheduled at the same time by using all the grid information. In this thesis, we propose a bipartite graph model for tasks and files in the grid system, and then we partition this graph to obtain a data placement and job scheduling strategy. The obtained parts are further refined in order to be assigned to grid sites by using a KL-based heuristic that takes the bandwidth and hop information between sites into account. Replication is achieved by replicating a certain amount of most accessed files chosen prior to the partitioning process. Experimental results indicate that the increase in the partitioning quality reflects positively on the mapping quality. Morever, it is observed that the communication cost is notably decreased when the data replication is applied. Hence, our results show that by replicating a small amount of data files and placing files onto sites using bipartite graph model, we can obtain performance improvement for scheduling jobs compared to no replication.
Open Access
Critical probabilities of percolation on graphs and random trees
(2014) Kaya, Merve
We consider the model of independent percolation on various graphs and random trees. We investigate the critical probabilities of bond and site percolation on these graphs.
Open Access
Efficient algorithms for the minimum cost perfect matching problem on general graphs
(1993) Atamtürk, Alper
The minimum cost perfect matching problem is one of the rare combinatorial optimization problems for which polynomial time algorithms exist. Matching algorithms find applications in Postman Problem, Planar Multicommodity Flow Problem, in heuristics to the well known Traveling Salesman Problem, Vehicle Scheduling Problem, Graph Partitioning Problem, Set Partitioning Problem, in VLSI, et cetera. In this thesis, reviewing the existing primal-dual approaches in the literature, we present two efficient algorithms for the minimum cost perfect matching problem on general graphs. In both of the algorithms, we achieved drastic reductions in the total number of time consuming operations such as scanning, updating dual variables and reduced costs. Detailed computational analysis on randomly generated graphs has shown the proposed algorithms to be several times faster than other algorithms in the literature. Hence, we conjecture that employment of the new algorithms in the solution methods of above stated important problems would speed them up significantly.
Open Access
Exploiting replicated data for communication load balancing in image-space parallel direct volume rendering of unstructured grids
(2009) Okuyan, Erkan
The focus of this work is on parallel volume rendering applications in which renderings with different parameters are successively repeated over the same dataset. The only reason for inter-task interaction is the existence of data primitives that are inputs to several tasks. Both computational structure and expected task execution times may change during successive rendering instances. Change in computational structure means change in the data primitive requirements of tasks. Since the individual processors of a parallel system have a limited storage capacity, we can reserve a limited amount of storage for holding replicas at each processor. For the parallelization of a particular rendering instance, the remapping model should utilize the replication pattern of the previous rendering instance(s) for reducing the communication overhead due to the data replication requirement of the current rendering instance. We propose a two-phase model for solving this problem. The hypergraphpartitioning-based model proposed for the first phase aims to minimize the total message volume that will be incurred due to the replication/migration of input data while maintaining balance on computational and receive-volume loads of processors. The network-flow-based model proposed for the second phase aims to minimize the maximum message volume handled by processors via utilizing the flexibility in assigning send-communication tasks to processors, which is introduced by data replication. The validity of our proposed model is verified on image-space parallelization of a direct volume rendering algorithm.
Open Access
Graphics on vehicles: a survey on application of graphics on three dimensional products
(1994) Meral, S. Nurtan
In this study, the reasons that led to the necessities of applications of graphics on three dimensional products and their application types are investigated. Vehicles are selected as an example group to analyze the three dimensional products. The criteria that must be considered while conveying the graphic design-which is often applied on two dimensional media- on to the three dimensional products, iire discussed on illustrated examples. It is concluded that the success of the application depends on considering design values of the product. Another conclusion is the importance of graphics as a variation tool in flexible mmiufacturing systems, which m^ike it possible to manufacture products according to personal needs and tastes.
Open Access
Parpatoh : A 2D-parallel hypergraph partitioning tool
(2006) Karaca, Evren
Hypergraph partitioning is a process that is being used to find solutions for optimization problems in various areas, including parallel volume rendering, parallel information retrieval and VLSI circuit design. While the current partitioning methods are adequate for hypergraphs up to certain size, these methods start to fail once the problem size exceeds this threshold. In this thesis we introduce ParPaToH, a parallel p-way hypergraph partitioning tool that makes use of a 2-D decomposition to reduce the communication overhead and implements a parallel-computing friendly version of the accepted multi-level partitioning paradigm to generate its partitioning. We present new concepts in hypergraph partitioning that lead to a coarse-grain parallel solution. Finally, we discuss the implementation of the tool in detail and present experimental results to demonstrate its effectiveness.
Open Access
Replicated hypergraph partitioning
(2010) Selvitopi, Reha Oğuz
Hypergraph partitioning is recently used in distributed information retrieval (IR) and spatial databases to correctly capture the communication and disk access costs. In the hypergraph models for these areas, the quality of the partitions obtained using hypergraph partitioning can be crucial for the objective of the targeted problem. Replication is a widely used terminology to address different performance issues in distributed IR and database systems. The main motivation behind replication is to improve the performance of the targeted issue at the cost of using more space. In this work, we focus on replicated hypergraph partitioning schemes that improve the quality of hypergraph partitioning by vertex replication. To this end, we propose a replicated partitioning scheme where replication and partitioning are performed in conjunction. Our approach utilizes successful multilevel and recursive bipartitioning methodologies for hypergraph partitioning. The replication is achieved in the uncoarsening phase of the multilevel methodology by extending the efficient Fiduccia-Mattheyses (FM) iterative improvement heuristic. We call this extended heuristic replicated FM (rFM). The proposed rFM heuristic supports move, replication and unreplication operations on the vertices by introducing new algorithms and vertex states. We show rFM has the same complexity as FM and integrate the proposed replication scheme into the multilevel hypergraph partitioning tool PaToH. We test the proposed replication scheme on realistic datasets and obtain promising results.
Open Access
Spatial subdivision for parallel ray casting/tracing
(1995) İşler, Veysi
Ray casting/tracing has been extensively studied for a long time, since it is an elegant way of producing realistic images. However, it is a computationally intensive algorithm. In this study, a taxonomy of parallel ray casting/tracing algorithms is presented cind the primary parallel ray casting/tracing systems are discussed and criticized. This work mainly focuses on the utilization of spatial subdivision technique for ray casting/tracing on a distributed-memory MIMD parallel computer. In this research, the reason for the use of parallel computers is not only the processing power but also the large memory space provided by them. The spatial subdivision technique has been adapted to parallel ray casting/tracing to decompose a three-dimensional complex scene that may not fit into the local memory of a single processor. The decomposition method achieves an even distribution of scene objects while allowing to exploit graphical coherence. Additionally, the decomposition method produces three-dimensional volumes which are mapped inexpensively to the processors so that the objects within adjacent volumes are stored in the local memories of close processors to decrease interprocessor communication cost. Then, the developed decomposition and mapping methods have been parallelized efficiently to reduce the preprocessing overhead. Finally, a splitting plane concept (called “jaggy splitting plane”) has been proposed to accomplish full utilization of the memory space of processors. Jaggy splitting plane avoids the shared objects which are the major sources of inefficient utilization of both memory and processing power. The proposed parallel algorithms have been implemented on the Intel iPSC/2 hypercube multicomputer (distributed-memory MIMD).
Open Access
A successive algorithm for the Chinese Postman Problem
(1991) Narin, Noyan
The Chinese Postman Problem being one of the well known problems in combinatorial optimization has many applications in real life problems such as mail delivery, road maintenance and bus scheduling. In this thesis work, we present a successive algorithm for the solution of Chinese Postman Problem. Additionally, we present efficient data structures for the existing algorithms in literature and for the implementation of our successive algorithm.