An architecture of a parallel computing system for matrix computations based on a systolic array of processors is considered and a version of incomplete block-factorizations of sparse matrices that arise in finite difference solution of... more
An architecture of a parallel computing system for matrix computations based on a systolic array of processors is considered and a version of incomplete block-factorizations of sparse matrices that arise in finite difference solution of three dimensional elliptic differential equations of second order is studied. The parallelization, both of factorization and solution processes, is investigated and the implementation of a stationary preconditioned iterative method on the considered computer architecture is described. Representative numerical tests for the efficiency of the consecutive version of the method for solving three-dimensional finite difference approximations to the Poisson equation are presented.
Research Interests:
ABSTRACT We study the design and implementation of algorithms...
... 2. Guiseppe Di Battista, Roberto Tamassia, and Luca Vismara, On-line convez planarzty testing, Proc. ... Math. Soc., vol. 2, pp. 464-466, 1951. 15. C. Thomassen, Planarity and duality of finite and infinite planar graphs, J.... more
... 2. Guiseppe Di Battista, Roberto Tamassia, and Luca Vismara, On-line convez planarzty testing, Proc. ... Math. Soc., vol. 2, pp. 464-466, 1951. 15. C. Thomassen, Planarity and duality of finite and infinite planar graphs, J. Combinatorial Theory, Series B 29, 1980, pp. 244-271. 16. ...
Research Interests:
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random... more
One of the most useful measures of cluster quality is the modularity of a partition, which measures the difference between the number of the edges joining vertices from the same cluster and the expected number of such edges in a random (unstructured) graph. In this paper we show that the problem of finding a partition maximizing the modularity of a given graph G can be reduced to a minimum weighted cut problem on a complete graph with the same vertices as G. We then show that the resulted minimum cut problem can be efficiently solved with existing software for graph partitioning and that our algorithm finds clusterings of a better quality and much faster than the existing clustering algorithms.
Research Interests:
ABSTRACT We prove separator theorems in which the size of the separator is minimized with respect to non-negative vertex costs. We show that for any planar graph G there exists a vertex separator of total sum of vertex costs at most cÖ{åv... more
ABSTRACT We prove separator theorems in which the size of the separator is minimized with respect to non-negative vertex costs. We show that for any planar graph G there exists a vertex separator of total sum of vertex costs at most cÖ{åv Î V(G)( cost (v))2}c\sqrt{\sum_{v\in V(G)}( cost (v))^2} and that this bound is optimal to within a constant factor. Moreover, such a separator can be found in linear time. This theorem implies a variety of other separation results. We describe applications of our separator theorems to graph embedding problems, to graph pebbling, and to multicommodity flow problems. Key words. Graph separators, Divide and conquer, Graph embeddings, Pebbling, Multicommodity flow.
Research Interests:
Research Interests:
ABSTRACT The crossing number of a graph G = (V,E), denoted by cr(G), is the smallest number of edge crossings in any drawing of G in the plane. Leighton [14] proved that for any n-vertex graph G of bounded degree, its crossing number... more
ABSTRACT The crossing number of a graph G = (V,E), denoted by cr(G), is the smallest number of edge crossings in any drawing of G in the plane. Leighton [14] proved that for any n-vertex graph G of bounded degree, its crossing number satisfies cr(G) + n = Ω(bw2(G)), where bw(G) is the bisection width of G. The lower bound method was extended for graphs of arbitrary vertex degrees to cr (G) + \tfrac116åu Î G du 2 = W(bw2 (G)) (G) + \tfrac{1} {{16}}\sum _{\upsilon \in G} d_\upsilon ^2 = \Omega (bw^2 (G)) in [15],[19], where d ν is the degree of any vertex ν. We improve this bound by showing that the bisection width can be replaced by a larger parameter — the cutwidth of the graph. Our result also yields an upper bound for the path-width of G in term of its crossing number.
Research Interests:
Research Interests:
... of that analysis is to discover patterns in the network traffic data that ... Keywords Networks, Protocol Graphs, Graph Decomposition, Patterns, Statistical Modeling, Anomaly Detection ... approaches for detecting malware and attacks... more
... of that analysis is to discover patterns in the network traffic data that ... Keywords Networks, Protocol Graphs, Graph Decomposition, Patterns, Statistical Modeling, Anomaly Detection ... approaches for detecting malware and attacks in computer systems: signature based, where a ...
This project focused on the development of methods for simulation of multi-phase and multicomponent fluid flows in porous media that combine recent advances in numerical methods with techniques for partitioning and load balancing based on... more
This project focused on the development of methods for simulation of multi-phase and multicomponent fluid flows in porous media that combine recent advances in numerical methods with techniques for partitioning and load balancing based on graph theory and graph algorithms. According to the research plan, we have concentrated our efforts and achieved our goals in the following interrelated groups of problems, which combine theoretical investigations with computational experimental work: