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536,813
Maxmaxflow and Counting Subgraphs
, 2010
"... We introduce a new graph invariant Λ(G) that we call maxmaxflow, and put it in the context of some other wellknown graph invariants, notably maximum degree and its relatives. We prove the equivalence of two “dual ” definitions of maxmaxflow: one in terms of flows, the other in terms of cocycle base ..."
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Cited by 1 (1 self)
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bases. We then show how to bound the total number (or more generally, total weight) of various classes of subgraphs of G in terms of either maximum degree or maxmaxflow. Our results are motivated by a conjecture that the modulus of the roots of the chromatic polynomial of G can be bounded above by a
Parallel Subgraph Counting for Multicore Architectures
"... Abstract—Computing the frequency of small subgraphs on a large network is a computationally hard task. This is, however, an important graph mining primitive, with several applications, and here we present a novel multicore parallel algorithm for this task. At the core of our methodology lies a state ..."
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Abstract—Computing the frequency of small subgraphs on a large network is a computationally hard task. This is, however, an important graph mining primitive, with several applications, and here we present a novel multicore parallel algorithm for this task. At the core of our methodology lies a
Finding, Minimizing, and Counting Weighted Subgraphs (Extended Abstract)
, 2009
"... For a pattern graph H on k nodes, we consider the problems of finding and counting the number of (not necessarily induced) copies of H in a given large graph G on n nodes, as well as finding minimum weight copies in both nodeweighted and edgeweighted graphs. Our results include: â¢ The number of ..."
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For a pattern graph H on k nodes, we consider the problems of finding and counting the number of (not necessarily induced) copies of H in a given large graph G on n nodes, as well as finding minimum weight copies in both nodeweighted and edgeweighted graphs. Our results include: â¢ The number
Isomorphic Subgraphs
 Proc. Graph Drawing'99, LNCS 1731
, 1999
"... We are interested in finding symmetries in graphs and then use these symmetries for graph drawing algorithms. There are two general approaches to this problem, the first one is known as Geometric Symmetries on the basis of drawings, the other rests upon the graphtheoretical notion of graphs. For a ..."
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Cited by 2 (1 self)
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We are interested in finding symmetries in graphs and then use these symmetries for graph drawing algorithms. There are two general approaches to this problem, the first one is known as Geometric Symmetries on the basis of drawings, the other rests upon the graphtheoretical notion of graphs. For a
Tight Bounds for Graph Homomorphism and Subgraph Isomorphism∗
"... We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph G to graph H cannot be done in time V (H)o(V (G)). We also show an exponentialtime reduction from Graph Homomorphism to Subgraph Isomorphism. This rules out (subject to ETH) a possibili ..."
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We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph G to graph H cannot be done in time V (H)o(V (G)). We also show an exponentialtime reduction from Graph Homomorphism to Subgraph Isomorphism. This rules out (subject to ETH) a
Counting Stars and Other Small Subgraphs in Sublinear Time
"... Detecting and counting the number of copies of certain subgraphs (also known as network motifs or graphlets), is motivated by applications in a variety of areas ranging from Biology to the study of the WorldWideWeb. Several polynomialtime algorithms have been suggested for counting or detecting t ..."
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Cited by 10 (3 self)
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Detecting and counting the number of copies of certain subgraphs (also known as network motifs or graphlets), is motivated by applications in a variety of areas ranging from Biology to the study of the WorldWideWeb. Several polynomialtime algorithms have been suggested for counting or detecting
Parallel Subgraph Counting for Multicore Architectures
"... Abstract—Computing the frequency of small subgraphs on a large network is a computationally hard task. This is, however, an important graph mining primitive, with several applications, and here we present a novel multicore parallel algorithm for this task. At the core of our methodology lies a state ..."
Abstract
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Abstract—Computing the frequency of small subgraphs on a large network is a computationally hard task. This is, however, an important graph mining primitive, with several applications, and here we present a novel multicore parallel algorithm for this task. At the core of our methodology lies a
Results 1  10
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536,813