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Complexity of counting subgraphs: Only the boundedness of the vertexcover number counts
"... Abstract—For a class C of graphs, #Sub(C) is the counting problem that, given a graph H from C and an arbitrary graph G, asks for the number of subgraphs of G isomorphic to H. It is known that if C has bounded vertexcover number (equivalently, the size of the maximum matching in C is bounded), the ..."
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Abstract—For a class C of graphs, #Sub(C) is the counting problem that, given a graph H from C and an arbitrary graph G, asks for the number of subgraphs of G isomorphic to H. It is known that if C has bounded vertexcover number (equivalently, the size of the maximum matching in C is bounded
Counting thin subgraphs via packings faster than meetinthemiddle time
 In SODA
, 2014
"... Abstract. Vassilevska and Williams (STOC 2009) showed how to count simple paths on k vertices and matchings on k/2 edges in an nvertex graph in time nk/2+O(1). In the same year, two different algorithms with the same runtime were given by Koutis and Williams (ICALP 2009), and Björklund et al. (ESA ..."
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Abstract. Vassilevska and Williams (STOC 2009) showed how to count simple paths on k vertices and matchings on k/2 edges in an nvertex graph in time nk/2+O(1). In the same year, two different algorithms with the same runtime were given by Koutis and Williams (ICALP 2009), and Björklund et al
Balanced Hashing, Color Coding and Approximate Counting (Extended Abstract)
"... Color Coding is an algorithmic technique for deciding efficiently if a given input graph contains a path of a given length (or another small subgraph of constant treewidth). Applications of the method in computational biology motivate the study of similar algorithms for counting the number of copie ..."
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Color Coding is an algorithmic technique for deciding efficiently if a given input graph contains a path of a given length (or another small subgraph of constant treewidth). Applications of the method in computational biology motivate the study of similar algorithms for counting the number
Network science Complex network Community detection
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
Query Evaluation with Constant Delay
"... I am grateful to Luc Segoufin who kindly accepted me to be his PhD student. He introduced me to the problem of query enumeration and encouraged me to look for the answers to all the questions that emerged during our collaboration. He was a truly great advisor, always supportive and available for dis ..."
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Parents, who directed me to follow the scientific path and where fully supportive at all times. Thanks to all the members of LSV – it was a pleasure working with You. I would like to thank the awesome people whom I have been working with in the same office on the 4th floor. Without all the nice riddles
Akademisk avhandling för teknisk doktorsexamen vid
, 1994
"... mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where the group ..."
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of the thesis can be summarized as follows. • We prove that for all Coxeter graphs constructed from an npath of unlabelled edges by adding a new labelled edge and a new vertex (sometimes two new edges and vertices), there is a permutational representation of the corresponding group. Group elements correspond
Adaptive Multiscale Detection of Filamentary Structures Embedded in a Background of Uniform Random Points
, 2003
"... We are given a set of n points that appears uniformly distributed in the unit square [0, 1] 2. We wish to test whether the set actually is generated from a nonuniform distribution having a small fraction of points concentrated on some (a priori unknown) curve with C αnorm bounded by β. An asymptot ..."
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Cited by 22 (6 self)
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and whose edges link such strips to their ‘good continuations’. The point cloud data are reduced to counts measuring membership in strips. Each anisotropy graph is reduced to a subgraph consisting of strips with ‘significant’ counts. The algorithm rejects H0 whenever some such subgraph contains a path
i i
"... , and we can say the Campbell bandwidth is the minimum average bandwidth for encoding the process across all possible distortion levels. IX. CONCLUSION We have presented two new derivations of the coefficient rate introduced by Campbell. One derivation solidifies its interpretation as a coefficien ..."
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, and we can say the Campbell bandwidth is the minimum average bandwidth for encoding the process across all possible distortion levels. IX. CONCLUSION We have presented two new derivations of the coefficient rate introduced by Campbell. One derivation solidifies its interpretation as a coefficient rate, and shows that the spectral entropy of a random process is proportional to the logarithm of the equivalent bandwidth of the smallest frequency band that contains most of the energy. The second derivation implies that the number of samples of a particular component should be proportional to the variance of that component. We discussed the implications of the latter result for realizationadaptive source coding and provided a connection with the familiar reverse waterfilling result from rate distortion theory. From the coefficient rate, we defined a quantity called the Campbell bandwidth of a random process, and we contrasted Fourier bandwidth, Shannon bandwidth, and Campbell bandwidth. ACKNOWLEDGMENT The authors are indebted to the referees for their constructive comments and insights.
POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR
"... 2010 to my wife, Joyce, and my family... Résumé ..."
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