Random Walk Step

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Rui Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Throughput and Delay Scaling in Supportive Two-Tier Networks
    IEEE Journal on Selected Areas in Communications, 2012
    Co-Authors: Rui Zhang
    Abstract:

    Consider a wireless network that has two tiers with different priorities: a primary tier vs. a secondary tier, which is an emerging network scenario with the advancement of cognitive radio technologies. The primary tier consists of Randomly distributed legacy nodes of density n, which have an absolute priority to access the spectrum. The secondary tier consists of Randomly distributed cognitive nodes of density m=nβ with β≥ 2, which can only access the spectrum opportunistically to limit the interference to the primary tier. Based on the assumption that the secondary tier is allowed to route the packets for the primary tier, we investigate the throughput and delay scaling laws of the two tiers in the following two scenarios: (i) the primary and secondary nodes are all static; (ii) the primary nodes are static while the secondary nodes are mobile. With the proposed protocols for the two tiers, we show that the primary tier can achieve a per-node throughput scaling of λp(n)=Θ(1/log n) in the above two scenarios. In the associated delay analysis for the first scenario, we show that the primary tier can achieve a delay scaling of Dp(n)=Θ(√(nβ log n λp(n))) with λp(n)=O(1/log n). In the second scenario, with two mobility models considered for the secondary nodes: an i.i.d. mobility model and a Random Walk model, we show that the primary tier can achieve delay scaling laws of Θ(1) and Θ(1/S), respectively, where S is the Random Walk Step size. The throughput and delay scaling laws for the secondary tier are also established, which are the same as those for a stand-alone network.

  • GLOBECOM - Delay-Throughput Tradeoff for Supportive Two-Tier Networks: A Static Primary Tier Vs. a Mobile Secondary Tier
    GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference, 2009
    Co-Authors: Rui Zhang
    Abstract:

    Consider a wireless network of two tiers with different priorities: a primary tier and a secondary tier, which is an emerging network scenario with the advancement of cognitive radio technologies. The primary tier is constructed over static nodes of density n, which are Randomly distributed and have an absolute priority to access the spectrum. The secondary tier contains mobile nodes of density m = nβ with β ≥ 2, which can only access the spectrum opportunistically to limit the interference to the primary tier. By allowing the secondary tier to relay the packets for the primary tier, we show that the achievable per-node throughput scaling for the primary tier can be improved to λp(n) = Θ(1/ log n). In the associated delay analysis, two mobility models are considered for the secondary nodes: an i.i.d. mobility model and a Random Walk model. We show that the primary tier can achieve delay scaling laws of Θ(1) and Θ(1/S) with the two mobility models, respectively, where S is the Random Walk Step size. Furthermore, we show that the primary tier can achieve a delay-throughput tradeoff of Dp(n) = O (nλp(n)) with λp(n) = O (1/ log n) for the Random Walk model. The throughput and delay scaling laws for the secondary tier are also established, which are the same as those for a stand-alone mobile network.

  • Throughput and Delay Scaling in Supportive Two-Tier Networks
    arXiv: Information Theory, 2009
    Co-Authors: Rui Zhang
    Abstract:

    Consider a wireless network that has two tiers with different priorities: a primary tier vs. a secondary tier, which is an emerging network scenario with the advancement of cognitive radio technologies. The primary tier consists of Randomly distributed legacy nodes of density $n$, which have an absolute priority to access the spectrum. The secondary tier consists of Randomly distributed cognitive nodes of density $m=n^\beta$ with $\beta\geq 2$, which can only access the spectrum opportunistically to limit the interference to the primary tier. Based on the assumption that the secondary tier is allowed to route the packets for the primary tier, we investigate the throughput and delay scaling laws of the two tiers in the following two scenarios: i) the primary and secondary nodes are all static; ii) the primary nodes are static while the secondary nodes are mobile. With the proposed protocols for the two tiers, we show that the primary tier can achieve a per-node throughput scaling of $\lambda_p(n)=\Theta(1/\log n)$ in the above two scenarios. In the associated delay analysis for the first scenario, we show that the primary tier can achieve a delay scaling of $D_p(n)=\Theta(\sqrt{n^\beta\log n}\lambda_p(n))$ with $\lambda_p(n)=O(1/\log n)$. In the second scenario, with two mobility models considered for the secondary nodes: an i.i.d. mobility model and a Random Walk model, we show that the primary tier can achieve delay scaling laws of $\Theta(1)$ and $\Theta(1/S)$, respectively, where $S$ is the Random Walk Step size. The throughput and delay scaling laws for the secondary tier are also established, which are the same as those for a stand-alone network.

  • Delay-Throughput Tradeoff for Supportive Two-Tier Networks: A Static Primary Tier Vs. a Mobile Secondary Tier
    GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference, 2009
    Co-Authors: Rui Zhang
    Abstract:

    Consider a wireless network of two tiers with different priorities: a primary tier and a secondary tier, which is an emerging network scenario with the advancement of cognitive radio technologies. The primary tier is constructed over static nodes of density n, which are Randomly distributed and have an absolute priority to access the spectrum. The secondary tier contains mobile nodes of density m = nß with ß ¿ 2, which can only access the spectrum opportunistically to limit the interference to the primary tier. By allowing the secondary tier to relay the packets for the primary tier, we show that the achievable per-node throughput scaling for the primary tier can be improved to ¿p(n) = ¿(1/log n). In the associated delay analysis, two mobility models are considered for the secondary nodes: an i.i.d. mobility model and a Random Walk model. We show that the primary tier can achieve delay scaling laws of ¿(1) and ¿(1/S) with the two mobility models, respectively, where S is the Random Walk Step size. Furthermore, we show that the primary tier can achieve a delay-throughput tradeoff of Dp(n) = O (n¿p(n)) with ¿p(n) = O(1/log n) for the Random Walk model. The throughput and delay scaling laws for the secondary tier are also established, which are the same as those for a stand-alone mobile network.

Aliakbar Tadaion - One of the best experts on this subject based on the ideXlab platform.

  • ISSPIT - A clustered caching placement in heterogeneous small cell networks with user mobility
    2015 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), 2015
    Co-Authors: Iman Keshavarzian, Zolfa Zeinalpour-yazdi, Aliakbar Tadaion
    Abstract:

    We consider the content caching problem in a set of the clustered small cells (SCs) in the heterogeneous network. Heterogeneous small cell networks is a promising solution to overcome the explosive growth of the mobile data traffic. A bottleneck of this solution is the capacity of backhaul links between small cells and the network core. However, an alternative solution is using SCs with low rate backhaul links which are equipped with storage devices to cache the popular files. We group SCs into some clusters based on the geographical situation. Each cluster has a cumulative cache storage which is the summation of the cache storage of SCs encountered at that cluster. During one time slot, users in a cluster can download the desired files from the cumulative cache storage of the cluster. Since users may move and change their positions, we model the problem of cluster cache placement as a discrete Markov chain. As the optimum caching placement problem is NP-hard, we provide an appropriate lower bound that guarantees k optimal solution where k is the Random Walk Step of the user's movement. Further, we derive a polynomial time approximation solution with performance for a situation which the information about the mobility pattern of mobile users in the wireless cell does not exist. Through some simulation examples, we compare the proposed algorithms with an existing solution using real wireless data.

  • A clustered caching placement in heterogeneous small cell networks with user mobility
    2015 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), 2015
    Co-Authors: Iman Keshavarzian, Zolfa Zeinalpour-yazdi, Aliakbar Tadaion
    Abstract:

    We consider the content caching problem in a set of the clustered small cells (SCs) in the heterogeneous network. Heterogeneous small cell networks is a promising solution to overcome the explosive growth of the mobile data traffic. A bottleneck of this solution is the capacity of backhaul links between small cells and the network core. However, an alternative solution is using SCs with low rate backhaul links which are equipped with storage devices to cache the popular files. We group SCs into some clusters based on the geographical situation. Each cluster has a cumulative cache storage which is the summation of the cache storage of SCs encountered at that cluster. During one time slot, users in a cluster can download the desired files from the cumulative cache storage of the cluster. Since users may move and change their positions, we model the problem of cluster cache placement as a discrete Markov chain. As the optimum caching placement problem is NP-hard, we provide an appropriate lower bound that guarantees k optimal solution where k is the Random Walk Step of the user's movement. Further, we derive a polynomial time approximation solution with performance for a situation which the information about the mobility pattern of mobile users in the wireless cell does not exist. Through some simulation examples, we compare the proposed algorithms with an existing solution using real wireless data.

Olivia Simpson - One of the best experts on this subject based on the ideXlab platform.

  • Computing heat kernel pagerank and a local clustering algorithm
    European Journal of Combinatorics, 2018
    Co-Authors: Fan Chung, Olivia Simpson
    Abstract:

    Abstract Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating Random Walks of bounded length and runs in time O ( log ( ϵ − 1 ) log n ϵ 3 log log ( ϵ − 1 ) ) , assuming performing a Random Walk Step and sampling from a distribution with bounded support take constant time. The quantitative ranking of vertices obtained with heat kernel pagerank can be used for local clustering algorithms. We present an efficient local clustering algorithm that finds cuts by performing a sweep over a heat kernel pagerank vector, using the heat kernel pagerank approximation algorithm as a subroutine. Specifically, we show that for a subset S of Cheeger ratio ϕ , many vertices in S may serve as seeds for a heat kernel pagerank vector which will find a cut of conductance O ( ϕ ) .

  • IWOCA - Computing Heat Kernel Pagerank and a Local Clustering Algorithm
    Lecture Notes in Computer Science, 2015
    Co-Authors: Fan Chung, Olivia Simpson
    Abstract:

    Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating Random Walks of bounded length and runs in time \(O\big (\frac{\log (\epsilon ^{-1})\log n}{\epsilon ^3\log \log (\epsilon ^{-1})}\big )\), assuming performing a Random Walk Step and sampling from a distribution with bounded support take constant time.

  • Computing Heat Kernel Pagerank and a Local Clustering Algorithm
    arXiv: Data Structures and Algorithms, 2015
    Co-Authors: Fan Chung, Olivia Simpson
    Abstract:

    Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating Random Walks of bounded length and runs in time $O\big(\frac{\log(\epsilon^{-1})\log n}{\epsilon^3\log\log(\epsilon^{-1})}\big)$, assuming performing a Random Walk Step and sampling from a distribution with bounded support take constant time. The quantitative ranking of vertices obtained with heat kernel pagerank can be used for local clustering algorithms. We present an efficient local clustering algorithm that finds cuts by performing a sweep over a heat kernel pagerank vector, using the heat kernel pagerank approximation algorithm as a subroutine. Specifically, we show that for a subset $S$ of Cheeger ratio $\phi$, many vertices in $S$ may serve as seeds for a heat kernel pagerank vector which will find a cut of conductance $O(\sqrt{\phi})$.

Iman Keshavarzian - One of the best experts on this subject based on the ideXlab platform.

  • ISSPIT - A clustered caching placement in heterogeneous small cell networks with user mobility
    2015 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), 2015
    Co-Authors: Iman Keshavarzian, Zolfa Zeinalpour-yazdi, Aliakbar Tadaion
    Abstract:

    We consider the content caching problem in a set of the clustered small cells (SCs) in the heterogeneous network. Heterogeneous small cell networks is a promising solution to overcome the explosive growth of the mobile data traffic. A bottleneck of this solution is the capacity of backhaul links between small cells and the network core. However, an alternative solution is using SCs with low rate backhaul links which are equipped with storage devices to cache the popular files. We group SCs into some clusters based on the geographical situation. Each cluster has a cumulative cache storage which is the summation of the cache storage of SCs encountered at that cluster. During one time slot, users in a cluster can download the desired files from the cumulative cache storage of the cluster. Since users may move and change their positions, we model the problem of cluster cache placement as a discrete Markov chain. As the optimum caching placement problem is NP-hard, we provide an appropriate lower bound that guarantees k optimal solution where k is the Random Walk Step of the user's movement. Further, we derive a polynomial time approximation solution with performance for a situation which the information about the mobility pattern of mobile users in the wireless cell does not exist. Through some simulation examples, we compare the proposed algorithms with an existing solution using real wireless data.

  • A clustered caching placement in heterogeneous small cell networks with user mobility
    2015 IEEE International Symposium on Signal Processing and Information Technology (ISSPIT), 2015
    Co-Authors: Iman Keshavarzian, Zolfa Zeinalpour-yazdi, Aliakbar Tadaion
    Abstract:

    We consider the content caching problem in a set of the clustered small cells (SCs) in the heterogeneous network. Heterogeneous small cell networks is a promising solution to overcome the explosive growth of the mobile data traffic. A bottleneck of this solution is the capacity of backhaul links between small cells and the network core. However, an alternative solution is using SCs with low rate backhaul links which are equipped with storage devices to cache the popular files. We group SCs into some clusters based on the geographical situation. Each cluster has a cumulative cache storage which is the summation of the cache storage of SCs encountered at that cluster. During one time slot, users in a cluster can download the desired files from the cumulative cache storage of the cluster. Since users may move and change their positions, we model the problem of cluster cache placement as a discrete Markov chain. As the optimum caching placement problem is NP-hard, we provide an appropriate lower bound that guarantees k optimal solution where k is the Random Walk Step of the user's movement. Further, we derive a polynomial time approximation solution with performance for a situation which the information about the mobility pattern of mobile users in the wireless cell does not exist. Through some simulation examples, we compare the proposed algorithms with an existing solution using real wireless data.

Fabrizio Sebastiani - One of the best experts on this subject based on the ideXlab platform.

  • LREC - SentiWordNet 3.0: An Enhanced Lexical Resource for Sentiment Analysis and Opinion Mining.
    2020
    Co-Authors: Stefano Baccianella, Andrea Esuli, Fabrizio Sebastiani
    Abstract:

    In this work we present SENTIWORDNET 3.0, a lexical resource explicitly devised for supporting sentiment classification and opinion mining applications. SENTIWORDNET 3.0 is an improved version of SENTIWORDNET 1.0, a lexical resource publicly available for research purposes, now currently licensed to more than 300 research groups and used in a variety of research projects worldwide. Both SENTIWORDNET 1.0 and 3.0 are the result of automatically annotating all WORDNET synsets according to their degrees of positivity, negativity, and neutrality. SENTIWORDNET 1.0 and 3.0 differ (a) in the versions of WORDNET which they annotate (WORDNET 2.0 and 3.0, respectively), (b) in the algorithm used for automatically annotating WORDNET, which now includes (additionally to the previous semi-supervised learning Step) a Random-Walk Step for refining the scores. We here discuss SENTIWORDNET 3.0, especially focussing on the improvements concerning aspect (b) that it embodies with respect to version 1.0. We also report the results of evaluating SENTIWORDNET 3.0 against a fragment of WORDNET 3.0 manually annotated for positivity, negativity, and neutrality; these results indicate accuracy improvements of about 20% with respect to SENTIWORDNET 1.0.

  • sentiwordnet 3 0 an enhanced lexical resource for sentiment analysis and opinion mining
    Language Resources and Evaluation, 2010
    Co-Authors: Stefano Baccianella, Andrea Esuli, Fabrizio Sebastiani
    Abstract:

    In this work we present SENTIWORDNET 3.0, a lexical resource explicitly devised for supporting sentiment classification and opinion mining applications. SENTIWORDNET 3.0 is an improved version of SENTIWORDNET 1.0, a lexical resource publicly available for research purposes, now currently licensed to more than 300 research groups and used in a variety of research projects worldwide. Both SENTIWORDNET 1.0 and 3.0 are the result of automatically annotating all WORDNET synsets according to their degrees of positivity, negativity, and neutrality. SENTIWORDNET 1.0 and 3.0 differ (a) in the versions of WORDNET which they annotate (WORDNET 2.0 and 3.0, respectively), (b) in the algorithm used for automatically annotating WORDNET, which now includes (additionally to the previous semi-supervised learning Step) a Random-Walk Step for refining the scores. We here discuss SENTIWORDNET 3.0, especially focussing on the improvements concerning aspect (b) that it embodies with respect to version 1.0. We also report the results of evaluating SENTIWORDNET 3.0 against a fragment of WORDNET 3.0 manually annotated for positivity, negativity, and neutrality; these results indicate accuracy improvements of about 20% with respect to SENTIWORDNET 1.0.