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1,480
On the index of bicyclic graphs with perfect matchings
, 2004
"... Let B + (2k) be the set of all bicyclic graphs on 2k(k ¿ 2) vertices with perfect matchings. In this paper, we discuss some properties of the connected graphs with perfect matchings, and then determine graphs with maximal index in B + (2k). ..."
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Cited by 4 (0 self)
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Let B + (2k) be the set of all bicyclic graphs on 2k(k ¿ 2) vertices with perfect matchings. In this paper, we discuss some properties of the connected graphs with perfect matchings, and then determine graphs with maximal index in B + (2k).
ModelBased Analysis of Oligonucleotide Arrays: Model Validation, Design Issues and Standard Error Application
, 2001
"... Background: A modelbased analysis of oligonucleotide expression arrays we developed previously uses a probesensitivity index to capture the response characteristic of a specific probe pair and calculates modelbased expression indexes (MBEI). MBEI has standard error attached to it as a measure of ..."
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Cited by 775 (28 self)
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of accuracy. Here we investigate the stability of the probesensitivity index across different tissue types, the reproducibility of results in replicate experiments, and the use of MBEI in perfect match (PM)only arrays. Results: Probesensitivity indexes are stable across tissue types. The target gene
Exploration, normalization, and summaries of high density oligonucleotide array probe level data.
 Biostatistics,
, 2003
"... SUMMARY In this paper we report exploratory analyses of highdensity oligonucleotide array data from the Affymetrix GeneChip R system with the objective of improving upon currently used measures of gene expression. Our analyses make use of three data sets: a small experimental study consisting of f ..."
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Cited by 854 (33 self)
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familiar features of the perfect match and mismatch probe (P M and M M) values of these data, and examine the variancemean relationship with probelevel data from probes believed to be defective, and so delivering noise only. We explain why we need to normalize the arrays to one another using probe level
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 414 (21 self)
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of these problems. For instance, we obtain a 2approximation algorithm for the minimumweight perfect matching problem under the triangle inequality. Our running time of O(n log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n 3) time for dense graphs. A similar result
Approximating the permanent
 SIAM J. Computing
, 1989
"... Abstract. A randomised approximation scheme for the permanent of a 01 matrix is presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings in the ..."
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Cited by 345 (26 self)
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Abstract. A randomised approximation scheme for the permanent of a 01 matrix is presented. The task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph; the latter is accomplished by simulating a Markov chain whose states are the matchings
On the Signless Laplacian Spectral Radius of Bicyclic Graphs with Perfect Matchings
, 2014
"... The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined. ..."
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Cited by 8 (4 self)
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The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined.
On the perfect matching index of bridgeless cubic graphs
, 2009
"... If G is a bridgeless cubic graph, Fulkerson conjectured that we can find 6 perfect matchings M1,..., M6 of G with the property that every edge of G is contained in exactly two of them and Berge conjectured that its edge set can be covered by 5 perfect matchings. We define τ(G) as the least number ..."
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Cited by 9 (0 self)
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of perfect matchings allowing to cover the edge set of a bridgeless cubic graph and we study this parameter. The set of graphs with perfect matching index 4 seems interesting and we give some informations on this class.
On Sum–Connectivity Index of Bicyclic Graphs
, 909
"... We determine the minimum sum–connectivity index of bicyclic graphs with n vertices and matching number m, where 2 ≤ m ≤ ⌊ n 2 ⌋, the minimum and the second minimum, as well as the maximum and the second maximum sum–connectivity indices of bicyclic graphs with n ≥ 5 vertices. The extremal graphs are ..."
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Cited by 1 (0 self)
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We determine the minimum sum–connectivity index of bicyclic graphs with n vertices and matching number m, where 2 ≤ m ≤ ⌊ n 2 ⌋, the minimum and the second minimum, as well as the maximum and the second maximum sum–connectivity indices of bicyclic graphs with n ≥ 5 vertices. The extremal graphs
Improved lowdensity paritycheck codes using irregular graphs
 IEEE Trans. Inform. Theory
, 2001
"... Abstract—We construct new families of errorcorrecting codes based on Gallager’s lowdensity paritycheck codes. We improve on Gallager’s results by introducing irregular paritycheck matrices and a new rigorous analysis of harddecision decoding of these codes. We also provide efficient methods for ..."
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Cited by 223 (15 self)
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correct up to approximately 16 % errors, while our codes correct over 17%. In some cases our results come very close to reported results for turbo codes, suggesting that variations of irregular low density paritycheck codes may be able to match or beat turbo code performance. Index Terms
Faster ShortestPath Algorithms for Planar Graphs
 STOC 94
, 1994
"... We give a lineartime algorithm for singlesource shortest paths in planar graphs with nonnegative edgelengths. Our algorithm also yields a lineartime algorithm for maximum flow in a planar graph with the source and sink on the same face. The previous best algorithms for these problems required\O ..."
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Cited by 200 (15 self)
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lengths required \Omega\Gamma n 3=2 ) time. Our shortestpath algorithm yields an O(n 4=3 log n)time algorithm for finding a perfect matching in a planar bipartite graph. A similar improvement is obtained for maximum flow in a directed planar graph.
Results 1  10
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