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SublinearTime Algorithms for Tournament Graphs
"... Abstract. We show that a random walk on a tournament on n vertices finds either a sink or a 3cycle in expected time O n · log n · log ∗ n that is, sublinear both in the size of the description of the graph as well as in the number of vertices. This result is motivated by the search of a generic alg ..."
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Abstract. We show that a random walk on a tournament on n vertices finds either a sink or a 3cycle in expected time O n · log n · log ∗ n that is, sublinear both in the size of the description of the graph as well as in the number of vertices. This result is motivated by the search of a generic
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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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 sublineartime algorithms for approximating the number of copies of certain
A lineartime probabilistic counting algorithm for database applications
 ACM Transactions on Database Systems
, 1990
"... We present a probabilistic algorithm for counting the number of unique values in the presence of duplicates. This algorithm has O(q) time complexity, where q is the number of values including duplicates, and produces an estimation with an arbitrary accuracy prespecified by the user using only a smal ..."
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Cited by 102 (5 self)
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We present a probabilistic algorithm for counting the number of unique values in the presence of duplicates. This algorithm has O(q) time complexity, where q is the number of values including duplicates, and produces an estimation with an arbitrary accuracy prespecified by the user using only a
Dynamic Steiner Tree and Subgraph TSP
"... In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an nvertex graph G = (V,E,w) with positive real edge weights, and our goal is to maintain a tree inG which is a good approximation of the minimum Steiner tree spanning a termina ..."
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terminal set S ⊆ V, which changes over time. The changes applied to the terminal set are either terminal additions (incremental scenario), terminal removals (decremental scenario), or both (fully dynamic scenario). Our task here is twofold. We want to support updates in sublinear o(n) time, and keep
Criterions for locally dense subgraphs
"... Community detection is one of the most investigated problems in the field of complex networks. Although several methods were proposed, there is still no precise definition of communities. As a step towards a definition, I highlight two necessary properties of communities, separation and internal co ..."
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Community detection is one of the most investigated problems in the field of complex networks. Although several methods were proposed, there is still no precise definition of communities. As a step towards a definition, I highlight two necessary properties of communities, separation and internal cohesion, the latter being a new concept. I propose a local method of community detection based on twodimensional local optimization, which I tested on common benchmarks and on the word association database. 1
A MULTISCALE SUBLINEAR TIME FOURIER ALGORITHM FOR NOISY DATA
"... Abstract. We extend the recent sparse Fourier transform algorithm of [1] to the noisy setting, in which a signal of bandwidth N is given as a superposition of k N frequencies and additive noise. We present two such extensions, the second of which exhibits a novel form of errorcorrection in its fre ..."
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frequency estimation not unlike that of the βencoders in analogtodigital conversion [2]. The algorithm runs in time O(k log(k) log(N/k)) on average, provided the noise is not overwhelming. The errorcorrection property allows the algorithm to outperform FFTW [3], a highly optimized software package
Testing connectivity of faulty networks in sublinear timeI
"... Given a set F of vertices of a connected graph G, we study the problem of testing the connectivity of G−F in polynomial time with respect to F  and the maximum degree ∆ of G. We present two approaches. The first algorithm for this problem runs in O (F ∆2ε−1 log(F ∆ε−1)) time for every graph G ..."
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Given a set F of vertices of a connected graph G, we study the problem of testing the connectivity of G−F in polynomial time with respect to F  and the maximum degree ∆ of G. We present two approaches. The first algorithm for this problem runs in O (F ∆2ε−1 log(F ∆ε−1)) time for every graph G
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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Cited by 1 (0 self)
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with a considerably simpler proof and even shows that, assuming the Exponential Time Hypothesis (ETH), there is no f(k)no(k / log k) time algorithm for counting kmatchings in bipartite graphs for any computable function f. As a consequence, we obtain an independent and somewhat simpler proof
Results 1  10
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50,354