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## 1An Upper Bound on the Convergence Time for Quantized Consensus of Arbitrary Static Graphs

Citations: | 3 - 0 self |

### Citations

889 | Algebraic Graph Theory,
- Godsil, Royle
- 2001
(Show Context)
Citation Context ...bound for certain network topologies by computing the effective resistance between a pair of nodes on the graph. This is attractive because we can then apply results from algebraic graph theory [15], =-=[16]-=- to compute the effective ar X iv :1 40 9. 68 28 v1s[ cs .SY ]s24sSe p 2 01 4 2resistance easily on the given graph structure. The remainder of this paper is organized as follows. Section 2 describes ... |

540 | Reversible Markov Chains and Random Walks on Graphs
- Aldous, Fill
(Show Context)
Citation Context ... |Ni| + 1 |Nj | ) for (i, j) ∈ E . (10) wii := 1− ∑ j∈Ni wij . (11) wi = ∑ j∈V wij = 1, w = ∑ i wi = N. (12) It is well-known that there is an analogy between a weighted graph and an electric network =-=[13]-=-. Let rij denote the resistance between to adjacent nodes, i.e. an edge (i, j) ∈ E , and let r′xy denote the effective resistance between any two nodes x, y. For example, in Fig. 1, rij = 2, rik = 1, ... |

132 | On distributed averaging algorithms and quantization effects,” 2007. [Online]. Available: http://arxiv.org/abs/0711.4179
- Nedic, Olshevsky, et al.
(Show Context)
Citation Context ...[10]. This work is motivated by a class of quantized consensus algorithms in [1]: nodes randomly and asynchronously update local estimate and exchange information. Unlike the distributed algorithm in =-=[11]-=-, where the sum of values in the network is not preserved, Kashyap et al. proposed an algorithm guaranteeing convergence with limited communication, more specifically, only involving quantization leve... |

121 |
Resistance distance,
- Klein, Randic
- 1993
(Show Context)
Citation Context ... x and y is less than or equal to the sum of the effective resistance r′qkqk+1 on the shortest path. This is due to the triangle inequality for effective resistance on undirected graphs (Theorem B in =-=[18]-=-). By (15) and (16), we have r′xy ≤ l−1∑ k=1 r′qkqk+1 ≤ l−1∑ k=1 N ×min(|Nqk |, |Nqk+1|) ≤ N × l∑ k=1 |Nqk | < 3N2 (17) By (13), we have HPB (x, y) < HPB (x, y) +HPB (y, x) = wr′xy < N × 3N2 = 3N3. (1... |

82 | Collisions among random walks on a graph,”
- Coppersmith, Tetali, et al.
- 1993
(Show Context)
Citation Context ... (Hidden Vertex). A vertex t in a graph is said to be hidden if for every other point in the graph, H(t, v) ≤ H(v, t). A hidden vertex is shown to exist for all reversible Markov chains in Lemma 3 in =-=[19]-=-. Lemma 4. The meeting time of any two random walders on the network G following the random processes X in Section III-B is less than 4HPB (G). Proof. In order to prove the lemma, we construct a coupl... |

33 | Gossip consensus algorithms via quantized communication - Carli, Fagnani, et al. - 2010 |

32 | On quantized consensus by means of gossip algorithm–Part II: convergence time,” - Lavaei, Murray - 2009 |

23 | Interval consensus: from quantized gossip to voting.
- Benezit, Thiran, et al.
- 2009
(Show Context)
Citation Context ...l upper bound of O(N3 logN) for the quantized consensus algorithm. It is, to the best knowledge of the authors, the tightest bound in literature for the quantized consensus algorithm proposed in [1], =-=[4]-=-. We use the degree of nodes on the shortest path on the graph to improve the bound on the hitting time of the biased random walk. • The analysis for arbitrary graphs is extended to a tighter bound fo... |

20 | Average consensus by gossip algorithms with quantized communication,” - Frasca, Carli, et al. - 2008 |

19 | Convergence speed of binary interval consensus.
- Draief, Vojnovic
- 2012
(Show Context)
Citation Context ...er bound for the expected convergence time of the quantized consensus algorithms is O(N2 logN). Note that this result agrees with the analysis of convergence time of complete graph in Section IV.A in =-=[2]-=-, where the authors derived an upper bound of O(N logN), regarding to local clock (See Section 2 for definition of local clock and global clock). Since every second, there are number of N clock ticks ... |

18 | Distributed anonymous discrete function computation.
- Hendrickx, Olshevsky, et al.
- 2011
(Show Context)
Citation Context ...he location of eigenvalues of some contact rate matrices, our result provides a universal upper bound on the convergence time of quantized consensus. Notably, a deterministic protocol was proposed in =-=[14]-=-, which achieves quantized consensus in O(N2). However, it cannot be extended beyond fixed graphs as the algorithms discussed in this paper, as analyzed in [12]. The contribution of this paper is as f... |

17 | Eds., Topics in Algebraic Graph Theory
- Beineke, Wilson, et al.
- 2004
(Show Context)
Citation Context ...ghter bound for certain network topologies by computing the effective resistance between a pair of nodes on the graph. This is attractive because we can then apply results from algebraic graph theory =-=[15]-=-, [16] to compute the effective ar X iv :1 40 9. 68 28 v1s[ cs .SY ]s24sSe p 2 01 4 2resistance easily on the given graph structure. The remainder of this paper is organized as follows. Section 2 desc... |

16 |
Randomized gossip algorithms,” Information Theory
- Boyd, Ghosh, et al.
- 2006
(Show Context)
Citation Context ...analysis in [2]. Index Terms—Distributed quantized consensus, gossip, convergence time I. INTRODUCTION Over the past decade, the problem of quantized consensus has received significant attention [1], =-=[3]-=-–[9]. It models averaging in a network with a limited capacity channel [1]. Distributed algorithms are attractive due to their flexibility, simple deployment and the lack of central control. This prob... |

15 | On the convergence time of asynchronous distributed quantized averaging algorithms.
- Zhu, Martınez
- 2011
(Show Context)
Citation Context ...hanged without revealing the initial observation from nodes. Analysis of convergence time on the complete graph and line graph is given in the original paper in [1], and an O(N5) bound was claimed in =-=[12]-=- by creating a random walk model. In this paper, unlike the natural random walk model claimed in [12], we construct a biased lazy random walk model for this random communication process to analyze the... |

12 | Average consensus on general strongly connected digraphs
- Cai, Ishii
- 2012
(Show Context)
Citation Context ...ysis in [2]. Index Terms—Distributed quantized consensus, gossip, convergence time I. INTRODUCTION Over the past decade, the problem of quantized consensus has received significant attention [1], [3]–=-=[9]-=-. It models averaging in a network with a limited capacity channel [1]. Distributed algorithms are attractive due to their flexibility, simple deployment and the lack of central control. This problem ... |

10 |
The hitting and cover times of random walks on finite graphs using local degree information
- Ikeda, Kubo, et al.
- 2009
(Show Context)
Citation Context ...i|, |Nj |). 4For all x, y ∈ V , let Q = (q1 = x, q2, q3, ..., ql−1, ql = y) be the shortest path on the graph connecting x and y . Now we claim that ∑l k=1 |Nqk | < 3N (from the proof of Theorem 2 in =-=[17]-=-). Since any node not lying on the shortest path can only be adjacent to at most three vertices on Q, we have l∑ k=1 |Nqk | ≤ 2l + 3(N − l) < 3N. (16) The first term 2l in Equation (16) is due to the ... |

6 | Convergence time analysis of quantized gossip algorithms on digraphs - Cai, Ishii - 2009 |

2 |
Ramakrishnan Srikant, “Quantized consensus
- Kashyap, Başar
- 2007
(Show Context)
Citation Context ...hronous clock setting. Eventually, all nodes reach consensus with quantized precision. We analyze the expected convergence time for the general quantized consensus algorithm proposed by Kashyap et al =-=[1]-=-. We use the theory of electric networks, random walks, and couplings of Markov chains to derive an O(N3 logN) upper bound for the expected convergence time on an arbitrary graph of size N , improving... |

1 |
Sghaier Guizani, “Self-healing sensor networks with distributed decision making
- Du, Zhang, et al.
- 2007
(Show Context)
Citation Context ...ks, peer-to-peer systems, etc. [2], [3]. It is especially relevant to remote and extreme environments where communication and computation are limited, for example, in a decision-making sensor network =-=[10]-=-. This work is motivated by a class of quantized consensus algorithms in [1]: nodes randomly and asynchronously update local estimate and exchange information. Unlike the distributed algorithm in [11]... |