#### DMCA

## Optimizing random walk search algorithms (2007)

Venue: | in p2p networks, Computer Networks |

Citations: | 10 - 1 self |

### Citations

3932 | Emergence of scaling in random networks
- Barabási, Albert
- 1999
(Show Context)
Citation Context ...d below. 6.1 Simulation scenario The network graph used for simulations consists of 10 4 nodes. The network is grown using the methodology specified in [13], which is an extension of Barabasi’s model =-=[4]-=-. This ensures that the node degree follows a power law distribution (defined in [16]) and the network has high clustering coefficient. The average node degree and the 17exponent of power law of the ... |

2209 | Probability inequalities for sums of bounded random variables
- Hoeffding
- 1963
(Show Context)
Citation Context ...he network is well bounded, by say K. Thus |E| ≤nK, which implies that dmin =Ω( |E| n ). Similarly an analogy may be established between uniform sampling and random walk by considering Chernoff bound =-=[7, 12]-=- on a sequence of Bernoulli trials. Consider k independent Bernoulli trials X1,X2,...Xn such that P [Xi =1]=p and P [Xi =0]=1− p. Here p is analogous of the popularity of the resource being searched f... |

2195 | Randomized Algorithms
- Motwani, Raghavan
- 1990
(Show Context)
Citation Context ...ple from the population and collecting coupons from them. Let Tn be the time it takes to collect a coupon of each kind and Tγn be the time it take to collect γn distinct coupons for 0 <γ<1. Then from =-=[26]-=- E[Tn] =O(n log n) (1) E[Tγn] = 1 O(n) 1 − γ (2) The time taken by the coupon collector to collect all the coupons by uniform sampling is analogous to the cover time 3 of the random walk. Consider ran... |

1096 |
The Art of Computer Systems Performance Analysis
- Jain
- 1991
(Show Context)
Citation Context ...dow is an estimate of the mean of the Bernoulli random variable (ps). We know that the standard deviation of the Bernoulli random variable, denoted by σ, equals √ ps(1 − ps). So from basic statistics =-=[14]-=- we may conclude that for an update window of size l searches, ps lies in the range [qi(j) − z0.99σ √ l ,qi(j)+ z0.99σ √ ] with l 99% confidence, where erf(z0.99) 4 = 0.99. Therefore, with 99% confide... |

976 |
A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
- Chernoff
- 1952
(Show Context)
Citation Context ...he network is well bounded, by say K. Thus |E| ≤nK, which implies that dmin =Ω( |E| n ). Similarly an analogy may be established between uniform sampling and random walk by considering Chernoff bound =-=[7, 12]-=- on a sequence of Bernoulli trials. Consider k independent Bernoulli trials X1,X2,...Xn such that P [Xi =1]=p and P [Xi =0]=1− p. Here p is analogous of the popularity of the resource being searched f... |

827 | Equation-Based Congestion Control for Unicast Applications
- Floyd, Handley, et al.
- 2000
(Show Context)
Citation Context ...h mechanisms. We now summarize the terminology used in this paper. A “search” is successful if it results in the discovery of 1 This concept is somewhat similar to “equation based congestion control” =-=[10]-=-. 2at least one node that has the resource being searched for. The success rate is defined as the fraction of successful searches given that the resource being searched for is present in the network.... |

692 | Search and Replication in Unstructured Peer-to-Peer Networks
- Lv, Cao, et al.
- 2002
(Show Context)
Citation Context ...rks. The objective of a search mechanism is to successfully locate resources while incurring low overhead and low delay. In order to fulfill this objective several random walk based search algorithms =-=[24, 15, 2, 29]-=- have been proposed for resource discovery in decentralized peer-to-peer networks. However, no analytical model has been proposed to quantify the effect of the parameters of random walk (such as the n... |

540 | Reversible Markov Chains and Random Walks on Graphs. Book in preparation
- Aldous, Fill
- 1995
(Show Context)
Citation Context ... Let Cn be the cover time of a random walk on a graph of n nodes and let Cγn be the time taken by the random walk to visit γn distinct nodes. Then for dmin =Ω( |E| n ), E[Cn] and E[Cγn] are given by (=-=[6, 3]-=-) n log n E[Cn] ≤ O( ) 1 − λ2 (3) E[Cγn] ≤ 1 n O( ) 1 − γ 1 − λ2 (4) 3 Cover time of a random walk on a graph is the time the random walk takes to visit all the nodes of the graph. 8. Comparing (1),(... |

423 | Routing indices for peer-to-peer systems. In: - Crespo, Garcia-Molina - 2002 |

407 | Random Walks on Graphs: a Survey - Lovasz - 1993 |

298 |
Search in power law networks,
- Adamic, RM, et al.
- 2001
(Show Context)
Citation Context ...rks. The objective of a search mechanism is to successfully locate resources while incurring low overhead and low delay. In order to fulfill this objective several random walk based search algorithms =-=[24, 15, 2, 29]-=- have been proposed for resource discovery in decentralized peer-to-peer networks. However, no analytical model has been proposed to quantify the effect of the parameters of random walk (such as the n... |

226 | Random Walks in Peer-to-Peer Networks.
- Gkantsidis, Mihail, et al.
- 2004
(Show Context)
Citation Context ... popularity estimator is based on an exponentially weighted moving average that smoothes out the high frequency (noise) components. The work in this paper is based on an important observation made in =-=[11]-=- regarding the relationship between random walk and uniform sampling. It is shown in [11] that the set of nodes visited during m steps of random walk over the overlay graph of a P2P network has the sa... |

212 | H.: Improving search in peer-to-peer networks
- Yang, Garcia-Molina
(Show Context)
Citation Context ...le other algorithms maintain large amount of state information and use complex algorithms to update it. Flooding of search queries was used by initial versions of Gnutella [1]. In iterative deepening =-=[31]-=-, the querying node performs flooding with increasing depth until the search is successful. The search query is forwarded to randomly selected subset of neighbors in modified BFS [18]. In k-random wal... |

189 |
Mapping the gnutella network
- Ripeanu, Iamnitchi, et al.
- 2002
(Show Context)
Citation Context ...gh clustering coefficient. The average node degree and the 17exponent of power law of the network are 3.5 and 3, respectively, which are close to the actual values of Gnutella network as observed in =-=[28]-=- . In order to populate the network with a resource with popularity p, p × 104 nodes are randomly selected and marked to own the resource. In the simulations of EBAS, the update window size, l, is set... |

151 | A local search mechanism for peer-to-peer networks. In:
- Kalogeraki, Gunopulos, et al.
- 2002
(Show Context)
Citation Context ...rative deepening [31], the querying node performs flooding with increasing depth until the search is successful. The search query is forwarded to randomly selected subset of neighbors in modified BFS =-=[18]-=-. In k-random walk [24], the querying node employs k random walkers to search for the desired resource. A two level random walk is proposed in [15]. All the above mentioned algorithms require that the... |

110 | Adaptive probabilistic search for peer-to-peer networks. In:
- Tsoumakos, Roussopoulos
- 2003
(Show Context)
Citation Context ...rks. The objective of a search mechanism is to successfully locate resources while incurring low overhead and low delay. In order to fulfill this objective several random walk based search algorithms =-=[24, 15, 2, 29]-=- have been proposed for resource discovery in decentralized ∗ A part of this work was presented in the Second International Workshop on Hot Topics in Peer-to-Peer Systems, July 21 st , 2005, UCSD Camp... |

103 | Distributed construction of random expander networks.
- Law, Siu
- 2003
(Show Context)
Citation Context ...lay graphs, have been found to have a constant spectral gap [25]. Also, dynamic networks with large spectral gaps may be maintained by incurring a constant overhead for each node join/leave operation =-=[11, 21]-=-. Intuitively this means that on a graph with good connectivity, a random walk quickly looses its memory (i.e., knowledge of previous nodes visited), such that the sequence of nodes visited by it in k... |

97 |
Growing scale-free networks with tunable clustering ,
- Holme, Kim
- 2002
(Show Context)
Citation Context ...stering coefficient, power-law distribution of node degree and small average path lengths. A method for growing a connected graph that has the properties of small world networks has been described in =-=[13]-=-. This method is used in our paper to generate overlay P2P topologies for validation of our analytical results and performance evaluation of our proposed algorithm. In [11] the authors show that rando... |

85 | On certain connectivity properties of the internet topology
- Mihail, Papadimitriou, et al.
(Show Context)
Citation Context ...snapshots [8]. This assumption implies that the difference between the 1 st and 2 nd eigenvalues of the probability transition matrix, known as spectral gap, of the P2P graph is bounded by a constant =-=[25]-=-. In order to keep the mathematical treatment simple enough for efficient real-time implementation, we assume that all query packets have the same size and we measure the overhead in terms of number o... |

64 |
Scalability issues in large peer-to-peer networks — a case study of Gnutella.
- Jovanovic, Annexstein, et al.
- 2001
(Show Context)
Citation Context ...the replication or deletion of the resource over time. 3 Related work Studies aimed at modeling P2P networks have revealed that the overlay network has characteristics similar to small world networks =-=[17, 16]-=-; high clustering coefficient, power-law distribution of node degree and small average path lengths. A method for growing a connected graph that has the properties of small world networks has been des... |

61 |
Modeling peer-to-peer network topologies through small-world models and power laws,” in Telecommunications Forum,
- Jovanovic, Annexstein, et al.
- 2001
(Show Context)
Citation Context ...dependent of the underlying topology. If the overlay network has an average degree d, then flooding the network with a query having TTL T will produce O((d − 1) T ) packets on the average. Studies in =-=[16]-=- have shown that the average node degree of Gnutella network is 3.5 and on the average 95% of all nodes are within 7 hops. If flooding is used for querying in this network, with TTL set to 7, the aver... |

50 | A comparison of peer-to-peer search methods”, - Tsoumakos, Roussopoulos - 2003 |

48 | Bounds on the cover time.
- Broder, Karlin
- 1989
(Show Context)
Citation Context ...d graph G(V,E), with |V | = n. Let dmin =minv∈V dv be the minimum vertex degree in the graph. Random walk over G has transition probability matrix A, where aij = 1 di (di is degree of vertex i). From =-=[6]-=-, A has n eigenvalues values λ1,λ2,...,λn such that 1=λ1 >λ2 ≥ λ3 ≥ ... ≥ λn > −1. For a graph with good global connectivity properties (no bad cuts/high graph conductance), λ2 << 1 which is a reasona... |

43 | Growing scale-free networks with small world behavior,” - Klemm, Eguíluz - 2002 |

20 | The Effectiveness of Realistic Replication Strategies on Quality of Availability for Peer-to-Peer Systems - On, Schmitt, et al. - 2003 |

8 | Search Performance Analysis in Peer-to-Peer Networks’, - Lin, Wang - 2003 |

6 |
Gnutella: To the Bandwidth Barrier and Beyond
- DSS
- 2000
(Show Context)
Citation Context ...ommunity grew to such enormous size that the entire bandwidth of Gnutella users connecting to the Internet using dial-up connection was “chocked” because of the large amount of queries they forwarded =-=[8]-=-. Although the unstructured P2P architecture is very appealing due to its properties of fault tolerance, self-organization and low overhead associated with node arrival and departure, efficient search... |

5 | A performance model for peer to peer file-sharing services. - Kant, Iyer, et al. - 2002 |

2 |
A two level random search protocol for peer-to peer networks
- Jawahar, Wu
- 2004
(Show Context)
Citation Context ...rks. The objective of a search mechanism is to successfully locate resources while incurring low overhead and low delay. In order to fulfill this objective several random walk based search algorithms =-=[24, 15, 2, 29]-=- have been proposed for resource discovery in decentralized peer-to-peer networks. However, no analytical model has been proposed to quantify the effect of the parameters of random walk (such as the n... |

1 | Modeling and analysis of random walk search in P2P networks - Bisnik, Abouzeid - 2005 |