## F-Chord: Improved uniform routing on Chord (2004)

Venue: | Proc. 11th Colloquium on Structural Information and Communication Complexity |

Citations: | 4 - 3 self |

### BibTeX

@INPROCEEDINGS{Cordasco04f-chord:improved,

author = {G. Cordasco and L. Gargano and M. Hammar and A. Negro and V. Scarano},

title = {F-Chord: Improved uniform routing on Chord},

booktitle = {Proc. 11th Colloquium on Structural Information and Communication Complexity},

year = {2004},

pages = {3104},

publisher = {SpringerVerlag}

}

### OpenURL

### Abstract

Abstract. We propose a family of novel schemes based on Chord retaining all positive aspects that made Chord a popular topology for routing in P2P networks. The schemes, based on the Fibonacci number system, allow to improve on the maximum/average number of hops for lookups and the routing table size per node. 1

### Citations

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Citation Context ...each node). Scalability has been recognized as the central challenge in designing such systems [14]. To obtain a scalable system, several P2P systems are based on distributed hash table (DHT) schemes =-=[3,15,16,18]-=-. In DHT schemes, data as well as nodes are associated with a key and each node in the system is responsible for storing a certain range of keys. Each Received November 2006; accepted February 2008 Co... |

1695 | Pastry: Scalable, distributed object location and routing for large-scale peerto-peer systems
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Citation Context ...i numbers We, briefly, recall here some basic facts on Fibonacci numbers which will be used in the sequel (see [6]). Let F ib(i) denote the i-th Fibonacci number. They are defined as F ib(0) = 0, F ib=-=(1)-=- = 1 and, for each i>1, For each index i, it holds F ib(i) = F ib(i − 1) + F ib(i − 2). F ib(i) = [φ i / √ 5], where φ = 1.618 . . . is the golden ratio and [ ] represents the nearest integer function... |

1037 | Tapestry: an infrastructure for fault-tolerant wide-area location and routing - Zhao, Kubiatowicz, et al. - 2001 |

556 | Chord: a scalable peer-to-peer lookup protocol for internet applications
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Citation Context ...each node). Scalability has been recognized as the central challenge in designing such systems [14]. To obtain a scalable system, several P2P systems are based on distributed hash table (DHT) schemes =-=[3,15,16,18]-=-. In DHT schemes, data as well as nodes are associated with a key and each node in the system is responsible for storing a certain range of keys. Each Received November 2006; accepted February 2008 Co... |

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Citation Context ... efficiency, namely diameter, degree, and average path length without giving up uniformity. First, we, briefly, recall here some basic facts on Fibonacci numbers which will be used in the sequel (see =-=[8]-=-). Let Fib(i) denote the i-th Fibonacci number. They are defined as Fib(0) = 0, Fib(1) = 1 and, for each i > 1, Fib(i) = Fib(i − 1) + Fib(i − 2). 326 NETWORKS—2008—DOI 10.1002/netFIG. 1. (a) Chord’s ... |

439 | Tapestry: A Resilient Global-Scale Overlay for Service Deployment
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Citation Context ...each node). Scalability has been recognized as the central challenge in designing such systems [14]. To obtain a scalable system, several P2P systems are based on distributed hash table (DHT) schemes =-=[3,15,16,18]-=-. In DHT schemes, data as well as nodes are associated with a key and each node in the system is responsible for storing a certain range of keys. Each Received November 2006; accepted February 2008 Co... |

295 | Viceroy: A scalable and dynamic emulation of the butterfly
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Citation Context ...n key. Adding or removing a node is accomplished at a cost of O(log 2 N) messages. A thorough study of uniform system is given in [16]. In general, Chord can be improved at the expenses of uniformity =-=[7, 9, 10]-=-. Recently, some non-greedy routing algorithms were proposed, that use De-Bruijn based DHT [4, 11], whose goal is to reach an optimal trade-off between degree and path length and, in particular, allow... |

168 | Koorde: A Simple Degree-Optimal Distributed Hash Table
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- 2003
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Citation Context ...f uniform system is given in [16]. In general, Chord can be improved at the expenses of uniformity [7, 9, 10]. Recently, some non-greedy routing algorithms were proposed, that use De-Bruijn based DHT =-=[4, 11]-=-, whose goal is to reach an optimal trade-off between degree and path length and, in particular, allow routing in Ω(log N/ log log N) with logarithmic degree. One can also improve the results by elimi... |

143 | Novel architectures for P2P applications: The continuous-discrete approach
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Citation Context ...f uniform system is given in [16]. In general, Chord can be improved at the expenses of uniformity [7, 9, 10]. Recently, some non-greedy routing algorithms were proposed, that use De-Bruijn based DHT =-=[4, 11]-=-, whose goal is to reach an optimal trade-off between degree and path length and, in particular, allow routing in Ω(log N/ log log N) with logarithmic degree. One can also improve the results by elimi... |

133 | Routing algorithms for dhts: Some open questions
- Ratnasamy, Shenker, et al.
- 2002
(Show Context)
Citation Context ...yway, sharing other resources is also common (like file storage systems and systems that use CPU time on each node). Scalability has been recognized as the central challenge in designing such systems =-=[14]-=-. To obtain a scalable system, several P2P systems are based on distributed hash table (DHT) schemes [3,15,16,18]. In DHT schemes, data as well as nodes are associated with a key and each node in the ... |

89 | Know thy neighbor’s neighbor: The power of lookahead in randomized p2p networks
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- 2004
(Show Context)
Citation Context ...th length and, in particular, allow routing in Ω(log N/ log log N) with logarithmic degree. One can also improve the results by eliminating the deterministic requirement. In fact, it is possible (see =-=[8, 12]-=-) to route greedily in Θ(log N/ log log N) with logarithmic degree by using randomization and the so called neighbor-ofneighbor (NoN) approach: a node uses, at each step, its neighbor’s neighborssto m... |

65 | On the fundamental tradeoffs between routing table size and network diameter in peer-to-peer networks
- Xu
- 2003
(Show Context)
Citation Context ...resent is at most 2δ(n), w.h.p. In the case of F-Chord(1) and F-Chord(1/2), with n ≤ N nodes in the network, results can be easily rewritten in terms of n with high probability, as already noticed in =-=[16, 17]-=-. When choosing a parameter α ∈ (1/2, 1), the presence of n < N nodes will automatically tune (due to the fact that the shortest jumps will point to the same node): to α(n) >α if one is using F-Chord(... |

47 |
Combinatorial group testing and its applications, World Scientific
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Citation Context ...a routing scheme that reaches equality for any choice of the parameters with |δ − d| ≤ 1. Proof. We proceed by induction on the sum δ +d. Trivially, N (0, 0) = N (1, 0) = N (0, 1) = 1 = F ib(1) = F ib=-=(2)-=-. Assume that (1) holds for any δ and d with δ + d < x. We will show that for any degree y and diameter z with y + z = x it holds that N (y, z) ≤ F ib(x + 1). We distinguish three cases on the number ... |

44 | A simple fault tolerant distributed hash table
- Naor, Wieder
(Show Context)
Citation Context ...ach edge bidirectionally, that is, using a double degree and, accordingly, augmenting the cost of maintaining the nodes’ routing table. In general, Chord can be improved at the expenses of uniformity =-=[9, 11, 12]-=-. Recently, some nongreedy routing algorithms were proposed, that use De-Bruijn based DHT [6, 13], whose goal is to reach an optimal trade-off between degree and average path length and, in particular... |

32 | Optimal routing in chord
- Ganesan, Manku
- 2004
(Show Context)
Citation Context ... ib(m − 2i − 1) + F ib(m − 3) + 2F ib(m − 5)sthat: Hence, one can find the desired value of the average path length by observing Sα(m) 1 < F ib(m) 5 � � (m − 1) 1 + 1 φ2 � − 1 � + φ (1 − α)(m − 2)F ib=-=(5)-=-F ib(m − 7) + 1 F ib(m) The following are immediate corollaries of the above Theorems 2 and 3. Corollary 1 The F-Chord(1) scheme (=Fib-Chord) has degree 1.44042 log N − 2, diameter equal to 0.72021 lo... |

20 |
Optimum lopsided binary trees
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(Show Context)
Citation Context ...e best of our knowledge, while the problem is related to several search problems investigated in the literature, no useful results on problems totally fitting the above model and goals are known (see =-=[3]-=- and references therein quoted). A previous work in the P2P context in this direction is contained in [16]. Our starting point is Fibonacci search [2].s1.1 Our results: Let F ib(i) be the i-th Fibonac... |

20 | Know Thy Neighbor’s Neighbor: Better Routing for
- Naor, Wieder
- 2004
(Show Context)
Citation Context ...th length and, in particular, allow routing in Ω(log N/ log log N) with logarithmic degree. One can also improve the results by eliminating the deterministic requirement. In fact, it is possible (see =-=[8, 12]-=-) to route greedily in Θ(log N/ log log N) with logarithmic degree by using randomization and the so called neighbor-ofneighbor (NoN) approach: a node uses, at each step, its neighbor’s neighborssto m... |

18 | Ulysses: A robust, low-diameter, low-latency peer-to-peer network,” European transaction on telecommunications
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Citation Context ...n key. Adding or removing a node is accomplished at a cost of O(log 2 N) messages. A thorough study of uniform system is given in [16]. In general, Chord can be improved at the expenses of uniformity =-=[7, 9, 10]-=-. Recently, some non-greedy routing algorithms were proposed, that use De-Bruijn based DHT [4, 11], whose goal is to reach an optimal trade-off between degree and path length and, in particular, allow... |

6 |
A Simple Fault Tolerant
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Citation Context ...n key. Adding or removing a node is accomplished at a cost of O(log 2 N) messages. A thorough study of uniform system is given in [16]. In general, Chord can be improved at the expenses of uniformity =-=[7, 9, 10]-=-. Recently, some non-greedy routing algorithms were proposed, that use De-Bruijn based DHT [4, 11], whose goal is to reach an optimal trade-off between degree and path length and, in particular, allow... |

4 |
Chord: A Scalable Peer-to-Peer
- Stoica, Morris, et al.
- 2001
(Show Context)
Citation Context ...per node. 1 Introduction In this paper, we propose a family of new routing schemes that reduce the routing table size, and the maximum/average number of hops for lookup requests in Chord–like systems =-=[15]-=- without introducing any other protocol overhead. The improvement is obtained with no harm to the simplicity and ease of programming that are some of the many good characteristics that made Chord a po... |

3 | Non-uniform deterministic routing on F-Chord(α
- Cordasco, Gargano, et al.
(Show Context)
Citation Context ...o called neighborof-neighbor (NoN) approach: a node uses, at each step, its neighbor’s neighbors to make greedy decisions. These techniques can be adapted to our scheme thus obtaining similar results =-=[2]-=-. However, in this article we focus on deterministic and uniform routing schemes. Among other advantages, they offer an optimal greedy routing strategy that provides simplicity, fault tolerance (as lo... |

1 |
Degree-optimal routing for P2P systems, Theory of computing system
- Chiola, Cordasco, et al.
(Show Context)
Citation Context ...ength and, in particular, allow routing in �(log N/ log log N) with logarithmic degree. One can also improve Chord’s results by eliminating the deterministic requirement. In fact, it is possible (see =-=[1, 10]-=-) to route greedily in �(log N/ log log N) with logarithmic degree by using randomization and the so called neighborof-neighbor (NoN) approach: a node uses, at each step, its neighbor’s neighbors to m... |