Journal of the ACM (JACM)
Approximation Algorithms for Some Parameterized Counting Problems
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Efficient Detection of Network Motifs
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Efficient semi-streaming algorithms for local triangle counting in massive graphs
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
QNet: a tool for querying protein interaction networks
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
Network motif discovery using subgraph enumeration and symmetry-breaking
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
Efficient algorithms for detecting signaling pathways in protein interaction networks
RECOMB'05 Proceedings of the 9th Annual international conference on Research in Computational Molecular Biology
Balanced families of perfect hash functions and their applications
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Counting stars and other small subgraphs in sublinear time
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
RAGE - A rapid graphlet enumerator for large networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
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World Wide Web, the Internet, coupled biological and chemical systems, neural networks, and social interacting species, are only a few examples of systems composed by a large number of highly interconnected dynamical units. These networks contain characteristic patterns, termed network motifs, which occur far more often than in randomized networks with the same degree sequence. Several algorithms have been suggested for counting or detecting the number of induced or non-induced occurrences of network motifs in the form of trees and bounded treewidth subgraphs of size O(logn), and of size at most 7 for some motifs. In addition, counting the number of motifs a node is part of was recently suggested as a method to classify nodes in the network. The promise is that the distribution of motifs a node participate in is an indication of its function in the network. Therefore, counting the number of network motifs a node is part of provides a major challenge. However, no such practical algorithm exists. We present several algorithms with time complexity $O\left(e^{2k}k\cdot n \cdot |E|\cdot \right.$ $\left.\log\frac{1}{\delta}/{\epsilon^2}\right)$ that, for the first time, approximate for every vertex the number of non-induced occurrences of the motif the vertex is part of, for k-length cycles, k-length cycles with a chord, and (k − 1)-length paths, where k = O(logn), and for all motifs of size of at most four. In addition, we show algorithms that approximate the total number of non-induced occurrences of these network motifs, when no efficient algorithm exists. Some of our algorithms use the color coding technique.