Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

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Subject: search.filters.subject.Zero-one laws

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Now showing 1 - 8 of 8
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    A zero-one law for the existence of triangles in random key graphs
    (2011) Yagan, Osman; Makowski, Armand
    Random key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. For this class of random graphs we show the existence of a zero-one law for the appearance of triangles, and identify the corresponding critical scaling. This is done by applying the method of first and second moments to the number of triangles in the graph.
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    On random graphs associated with a pairwise key distribution scheme for wireless sensor networks (Extended version)
    (2010-07) Yagan, Osman; Makowski, Armand M.
    The pairwise key distribution scheme of Chan et al. was proposed as an alternative to the key distribution scheme of Eschenauer and Gligor (EG) to enable network security in wireless sensor networks. In this paper we consider the random graph induced by this pairwise scheme under the assumption of full visibility. We first establish a zero-one law for graph connectivity. Then, we discuss the number of keys needed in the memory of each sensor in order to achieve secure connectivity (with high probability). For a network of n sensors the required number of keys is shown to be on the order of log n, a key ring size comparable to that of the EG scheme (in realistic scenarios).
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    On random graphs associated with a pairwise key distribution scheme
    (2010-01-01) Yagan, Osman; Makowski, Armand M.
    The pairwise key distribution scheme of Chan et al. was proposed as an alternative to the key distribution scheme of Eschenauer and Gligor to enable network security in wireless sensor networks. We consider the random graph induced by this pairwise scheme under the assumption of full visibility, and show the existence of a zero-one law for graph connectivity.
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    On the existence of triangles in random key graphs
    (2009-07-04) Yagan, Osman; Makowski, Armand M.
    The random key graph, also known as the uniform random intersection graph, is a random graph induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. We show the existence of a zero-one law for the appearance of triangles in random key graphs by applying the method of first and second moments to the number of triangles in the graph.
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    Connectivity in random key graphs – Simple proofs for special cases
    (2009-01-14) Yagan, Osman; Makowski, Armand
    We consider the random graph induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. We report on recent results concerning a conjectured zero-one law for graph connectivity, and provide simple proofs for some special cases.
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    Zero-one laws for connectivity in random key graphs
    (2009-01-14) Yagan, Osman; Makowski, Armand;
    The random key graph is a random graph induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. We report on recent results concerning a conjectured zero-one law for graph connectivity.
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    Connectivity in one-dimensional geometric random graphs: Poisson approximations, zero-one laws and phase transitions
    (2008-10-24) Han, Guang; Makowski, Armand M.; Makowski, Armand M.
    Consider n points (or nodes) distributed uniformly and independently on the unit interval [0,1]. Two nodes are said to be adjacent if their distance is less than some given threshold value.For the underlying random graph we derive zero-one laws for the property of graph connectivity and give the asymptotics of the transition widths for the associated phase transition. These results all flow from a single convergence statement for the probability of graph connectivity under a particular class of scalings. Given the importance of this result, we give two separate proofs; one approach relies on results concerning maximal spacings, while the other one exploits a Poisson convergence result for the number of breakpoint users.
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    On the random graph induced by a randomized predistribution scheme under full visibility (Extended version)
    (2008) Yagan, Osman; Makowski, Armand M.
    We consider the random graph induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. We show the existence of a zero-one law for the absence of isolated nodes, and complement it by a Poisson convergence for the number of isolated nodes. Leveraging earlier resu lts and analogies with Erd\H{o}s-Renyi graphs, we explore similar results for the property of graph connectivity. Implications for secure connectivity are discussed.