We outline a class of graph similarity measures that uses the structural similarity of local neighborhoods to derive pairwise similarity scores for the nodes of two different graphs, and present a related similarity m...
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We outline a class of graph similarity measures that uses the structural similarity of local neighborhoods to derive pairwise similarity scores for the nodes of two different graphs, and present a related similarity measure that uses a linear update to generate both node and edge similarity scores. This measure is then applied to the task of graph matching. (c) 2007 Elsevier Ltd. All rights reserved.
Data co-clustering refers to the problem of simultaneous clustering of two data types. Typically, the data is stored in a contingency or co-occurrence matrix C where rows and columns of the matrix represent the data t...
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Data co-clustering refers to the problem of simultaneous clustering of two data types. Typically, the data is stored in a contingency or co-occurrence matrix C where rows and columns of the matrix represent the data types to be co-clustered. An entry C (ij) of the matrix signifies the relation between the data type represented by row i and column j. Co-clustering is the problem of deriving sub-matrices from the larger data matrix by simultaneously clustering rows and columns of the data matrix. In this paper, we present a novel graph theoretic approach to data co-clustering. The two data types are modeled as the two sets of vertices of a weighted bipartite graph. We then propose Isoperimetric Co-clustering Algorithm (ICA)-a new method for partitioning the bipartite graph. ICA requires a simple solution to a sparse system of linear equations instead of the eigenvalue or SVD problem in the popular spectral co-clustering approach. Our theoretical analysis and extensive experiments performed on publicly available datasets demonstrate the advantages of ICA over other approaches in terms of the quality, efficiency and stability in partitioning the bipartite graph.
In the first part of the paper we investigate a digraph Gamma(n) whose set of vertices is the set H = {0, 1,..., n - 1} and for which there is a directed edge from a is an element of H to b is an element of H if a(3) ...
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In the first part of the paper we investigate a digraph Gamma(n) whose set of vertices is the set H = {0, 1,..., n - 1} and for which there is a directed edge from a is an element of H to b is an element of H if a(3) equivalent to b (mod n). We specify two subdigraphs Gamma(1)(n) and Gamma(2)(n) of Gamma(n). Let Gamma(1)(n) be induced by the vertices which are coprime to n and Gamma(2)(n) be induced by the set of vertices which are not coprime with n. The conditions for regularity and semiregularity of these subdigraphs are presented. The digraph F(n) has an interesting structure for some special n. It is shown that every component of the digraph Gamma(n) is a cycle if and only if 3 does not divide the Euler totient function phi(n) and n is square-free. It is proved that Gamma(1)(2(k)) contains only cycles and Gamma(2)(2(k)) is a tree with the root in 0. Besides Gamma(1)(3(k)) contains two ternary trees with roots in 1 and 3(k) - 1 and Gamma(2)(3(k)) is a tree with the root in 0. All digraphs with 3 components are described. In the second part we consider the zero-divisor graph G(Z(n)) of the ring Z(n). Its maximum degree and the clique number are calculated. (C) 2008 Elsevier B.V. All rights reserved.
A hub set in a graph G is a set U C V(G) such that any two vertices outside U are connected by a path whose internal vertices lie in U. We prove that h(G) h(c)(G) >= 4 are obtained by substituting graphs into thre...
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A hub set in a graph G is a set U C V(G) such that any two vertices outside U are connected by a path whose internal vertices lie in U. We prove that h(G) <= h(c)(G) <= gamma(c)(G) <= h(G) + 1, where h(G), h(c)(G), and gamma(c)(G), respectively, are the minimum sizes of a hub set in G, a hub set inducing a connected subgraph, and a connected dominating set. Furthermore, all graphs with gamma(c)(G) > h(c)(G) >= 4 are obtained by substituting graphs into three consecutive vertices of a cycle;this yields a polynomial-time algorithm to check whether h(c) (G) = gamma(c) (G). C 2008 Elsevier B.V. All rights reserved.
Colouring a graph with its chromatic number of colours is known to be NP-hard. Identifying an algorithm in which decisions are made locally with no information about the graph's global structure is particularly ch...
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Colouring a graph with its chromatic number of colours is known to be NP-hard. Identifying an algorithm in which decisions are made locally with no information about the graph's global structure is particularly challenging. In this article we analyse the complexity of a decentralised colouring algorithm that has recently been proposed for channel selection in wireless computer networks. (C) 2008 Elsevier B.V. All rights reserved.
Two-dimensional phase unwrapping is the problem of deducing unambiguous "phase" from values known only modulo 2 pi. Many authors agree that the objective of phase unwrapping should be to find a weighted mini...
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Two-dimensional phase unwrapping is the problem of deducing unambiguous "phase" from values known only modulo 2 pi. Many authors agree that the objective of phase unwrapping should be to find a weighted minimum of the number of places where adjacent (discrete) phase values differ by more than pi (called discontinuities). This NP-hard problem is of considerable practical interest, largely due to its importance in interpreting data acquired with synthetic aperture radar (SAR) interferometry. Consequently, many heuristic algorithms have been proposed. We present an efficient multi-level graph algorithm for the approximate solution of an equivalent problem-minimal residue cut in the dual graph.
We consider scenarios in which two parties, each in possession of a graph, wish to compute some algorithm on their joint graph in a privacy-preserving manner, that is, without leaking any information about their input...
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ISBN:
(纸本)3540306846
We consider scenarios in which two parties, each in possession of a graph, wish to compute some algorithm on their joint graph in a privacy-preserving manner, that is, without leaking any information about their inputs except that revealed by the algorithm's output. Working in the standard secure multi-party computation paradigm, we present new algorithms for privacy-preserving computation of AND (all pairs shortest distance) and SSSD (single source shortest distance), as well as two new algorithms for privacy-preserving set union. Our algorithms are significantly more efficient than generic constructions. As in previous work on privacy-preserving data mining, we prove that our algorithms are secure provided the participants are "honest, but curious."
In this paper we consider the problem of computing an mRNA sequence of maximal similarity for a given mRNA of secondary structure constraints, introduced by Backofen et al. in [R. Backofen, N.S. Narayanaswamy, F. Swid...
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In this paper we consider the problem of computing an mRNA sequence of maximal similarity for a given mRNA of secondary structure constraints, introduced by Backofen et al. in [R. Backofen, N.S. Narayanaswamy, F. Swidan, On the complexity of protein similarity search under mRNA structure constraints, in: Proceedings of the Annual Symposium of Theoretical Aspects of Computer Science, in: LNCS, vol. 2285, Springer, 2002, pp. 274-286] denoted as the MRSO problem. The problem is known to be NP-complete for planar associated implied structure graphs of vertex degree at most 3. In [G. Blin, G. Fertin, D. Hermelin, S. Vialette, Fixed-parameter algorithms for protein similarity search under mRNA structure constraints, in: Proceedings of graph-Theoretical Concepts in Computer Science, in: LNCS, vol. 3787, Springer, 2005, pp. 271-282] a first polynomial dynamic programming algorithms for MRSO on implied structure graphs with maximum vertex degree 3 of bounded cut-width is shown. We give a simple but much more general polynomial dynamic programming solution for the MRSO problem for associated implied structure graphs of bounded clique-width. Our result implies that MRSO is polynomial for graphs of bounded tree-width, co-graphs, P-4-sparse graphs, and distance hereditary graphs. Further we conclude that the problem of comparing two solutions for MRSO is hard for the class p(parallel to)(NP), which is defined as the set of problems which can be solved in polynomial time with a number of parallel queries to an oracle in (c) 2007 Elsevier B.V. All rights reserved.
VERTEX COVERING BY PATHS ON TREES with applications in machine translation is the task to cover all vertices of a tree T = (V, E) by choosing a minimum-weight subset of given paths in the tree. The problem is NP-hard ...
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VERTEX COVERING BY PATHS ON TREES with applications in machine translation is the task to cover all vertices of a tree T = (V, E) by choosing a minimum-weight subset of given paths in the tree. The problem is NP-hard and has recently been solved by an exact algorithm running in O(4(C) center dot vertical bar V vertical bar(2)) time, where C denotes the maximum number of paths covering a tree vertex. We improve this running time to O(2(C) center dot C center dot vertical bar V vertical bar). On the route to this, we introduce the problem TREE-LIKE WEIGHTED HITTING SET which might be of independent interest. In addition, for the unweighted case Of VERTEX COVERING BY PATHS ON TREES, we present an exact algorithm using a search tree of size O(2(k) center dot k!), where k denotes the number of chosen covering paths. Finally, we briefly discuss the existence of a size-O(k(2)) problem kernel. (C) 2007 Elsevier B.V. All rights reserved.
Combinatorial problems such as those from graph theory pose serious challenges for parallel machines due to non-contiguous, concurrent accesses to global data structures with low degrees of locality. The hierarchical ...
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ISBN:
(纸本)0769523803
Combinatorial problems such as those from graph theory pose serious challenges for parallel machines due to non-contiguous, concurrent accesses to global data structures with low degrees of locality. The hierarchical memory systems of symmetric multiprocessor (SMP) clusters optimize for local, contiguous memory accesses, and so are inefficient platforms for such algorithms. Few parallel graph algorithms outperform their best sequential implementation on SMP clusters due to long memory latencies and high synchronization costs. In this paper, we consider the performance and scalability of two graph algorithms, list ranking and connected components, on two classes of shared-memory computers: symmetric multiprocessors such as the Sun Enterprise servers and multithreaded architectures (MTA) such as the Cray MTA-2. While previous studies have shown that parallel graph algorithms can speedup on SMPs, the systems' reliance on cache microprocessors limits performance. The MTA's latency tolerant processors and hardware support for fine-grain synchronization makes performance a function of parallelism. Since parallel graph algorithms have an abundance of parallelism, they perform and scale significantly better on the MTA. We describe and give a performance model for each architecture. We analyze the performance of the two algorithms and discuss how the features of each architecture affects algorithm development, ease of programming, performance, and scalability.
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