A Fast Approximation Algorithm for Computing theFrequencies of Subgraphs in a Given Graph
SIAM Journal on Computing
Journal of the ACM (JACM)
Approximation Algorithms for Some Parameterized Counting Problems
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Estimating the weight of metric minimum spanning trees in sublinear-time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Tight Bounds for Testing Bipartiteness in General Graphs
SIAM Journal on Computing
Approximating the Minimum Spanning Tree Weight in Sublinear Time
SIAM Journal on Computing
Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time
SIAM Journal on Computing
Modeling interactome: scale-free or geometric?
Bioinformatics
Efficient Detection of Network Motifs
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms
Theoretical Computer Science
Monte-Carlo algorithms for enumeration and reliability problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Approximating average parameters of graphs
Random Structures & Algorithms
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
Faster Algebraic Algorithms for Path and Packing Problems
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Constant-Time Approximation Algorithms via Local Improvements
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Finding paths of length k in O∗(2k) time
Information Processing Letters
Approximating the Number of Network Motifs
WAW '09 Proceedings of the 6th International Workshop on Algorithms and Models for the Web-Graph
Finding, minimizing, and counting weighted subgraphs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Counting Subgraphs via Homomorphisms
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Limits and Applications of Group Algebras for Parameterized Problems
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
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
A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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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 World-Wide-Web. Several polynomial-time algorithms have been suggested for counting or detecting the number of occurrences of certain network motifs. However, a need for more efficient algorithms arises when the input graph is very large, as is indeed the case in many applications of motif counting. In this paper we design sublinear-time algorithms for approximating the number of copies of certain constant-size subgraphs in a graph G. That is, our algorithms do not read the whole graph, but rather query parts of the graph. Specifically, we consider algorithms that may query the degree of any vertex of their choice and may ask for any neighbor of any vertex of their choice. The main focus of this work is on the basic problem of counting the number of length-2 paths and more generally on counting the number of stars of a certain size. Specifically, we design an algorithm that, given an approximation parameter 0 G, outputs an estimate vCs such that with high constant probability, (1-ε)vs(G) ≤ vs ≤ (1 + ε)vs(G), where vs(G) denotes the number of stars of size s + 1 in the graph. The expected query complexity and running time of the algorithm are [EQUATION] poly (log n, 1/ε). We also prove lower bounds showing that this algorithm is tight up to polylogarithmic factors in n and the dependence on ε. Our work extends the work of Feige (SIAM Journal on Computing, 2006) and Goldreich and Ron (Random Structures and Algorithms, 2008) on approximating the number of edges (or average degree) in a graph. Combined with these results, our result can be used to obtain an estimate on the variance of the degrees in the graph and corresponding higher moments. In addition, we give some (negative) results on approximating the number of triangles and on approximating the number of length-3-paths in sublinear time.