A New Search Algorithm for Finding the Simple Cycles of a Finite Directed Graph

Weinblatt, Herbert

doi:10.1145/321679.321684

Cited by 78 publications

(49 citation statements)

References 6 publications

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“…Tiernan 1970;Weinblatt 1972;Fosdick et al 1973;Johnson 1975 or, more specifically, of finding only cycles of given length (Alon et al 1994;Yuster 2011).…”

Section: Finding Boroughs and 2-clubsmentioning

confidence: 99%

Close communities in social networks: boroughs and 2-clubs

Laan

Marx

Mokken

2016

Soc. Netw. Anal. Min.

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The structure of close communication, contacts and association in social networks is studied in the form of maximal subgraphs of diameter 2 (2-clubs), corresponding to three types of close communities: hamlets, social circles and coteries. The concept of borough of a graph is defined and introduced. Each borough is a chained union of 2-clubs of the network and any 2-club of the network belongs to one borough. Thus the set of boroughs of a network, together with the 2-clubs held by them, are shown to contain the structure of close communication in a network. Applications are given with examples from real world network data.

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“…Tiernan 1970;Weinblatt 1972;Fosdick et al 1973;Johnson 1975 or, more specifically, of finding only cycles of given length (Alon et al 1994;Yuster 2011).…”

Section: Finding Boroughs and 2-clubsmentioning

confidence: 99%

Close communities in social networks: boroughs and 2-clubs

Laan

Marx

Mokken

2016

Soc. Netw. Anal. Min.

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“…Several algorithms were designed for the finding problem. In the algorithms of Tiernan [23] and Weinblatt [25] time exponential in the size of the graph may elapse between the output of a cycle and the next. However, one can obtain enumeration algorithms with a polynomial delay between the output of two consecutive cycles.…”

Section: Counting and Generating Lassos In Directed Graphsmentioning

confidence: 99%

Uniform Monte-Carlo Model Checking

Oudinet

Denise

Gaudel

et al. 2011

Lecture Notes in Computer Science

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Abstract. Grosu and Smolka have proposed a randomised Monte-Carlo algorithm for LTL model-checking. Their method is based on random exploration of the intersection of the model and of the Büchi automaton that represents the property to be checked. The targets of this exploration are so-called lassos, i.e. elementary paths followed by elementary circuits. During this exploration outgoing transitions are chosen uniformly at random.Grosu and Smolka note that, depending on the topology, the uniform choice of outgoing transitions may lead to very low probabilities of some lassos. In such cases, very big numbers of random walks are required to reach an acceptable coverage of lassos, and thus a good probability either of satisfaction of the property or of discovery of a counter-example. In this paper, we propose an alternative sampling strategy for lassos in the line of the uniform exploration of models presented in some previous work.The problem of finding all elementary cycles in a directed graph is known to be difficult: there is no hope for a polynomial time algorithm. Therefore, we consider a well-known sub-class of directed graphs, namely the reducible flow graphs, which correspond to well-structured programs and most control-command systems.We propose an efficient algorithm for counting and generating uniformly lassos in reducible flowgraphs. This algorithm has been implemented and experimented on a pathological example. We compare the lasso coverages obtained with our new uniform method and with uniform choice among the outgoing transitions.

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“…However, the problems they deal with are different from ours. Papers [4], [8] and in some sense [2] as well, are oriented on finding cycles, whereas [1] deals with the reduction of cyclic graphs and [5] is limited to "start-after-end" graphs and their transformation to acyclic ones.…”

Section: Cycles Of Activitiesmentioning

confidence: 99%