Rendezvous in networks in spite of delay faults
Two mobile agents, starting from different nodes of an unknown network, have to meet at a node. Agents move in synchronous rounds using a deterministic algorithm. Each agent has a different label, which it can use in the execution of the algorithm, but it does not know the label of the other agent....
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| Veröffentlicht in: | Distributed computing Jg. 29; H. 3; S. 187 - 205 |
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| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2016
Springer Nature B.V Springer Verlag |
| Schlagworte: | |
| ISSN: | 0178-2770, 1432-0452 |
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| Abstract | Two mobile agents, starting from different nodes of an unknown network, have to meet at a node. Agents move in synchronous rounds using a deterministic algorithm. Each agent has a different label, which it can use in the execution of the algorithm, but it does not know the label of the other agent. Agents do not know any bound on the size of the network. In each round an agent decides if it remains idle or if it wants to move to one of the adjacent nodes. Agents are subject to
delay faults
: if an agent incurs a fault in a given round, it remains in the current node, regardless of its decision. If it planned to move and the fault happened, the agent is aware of it. We consider three scenarios of fault distribution: random (independently in each round and for each agent with constant probability
0
<
p
<
1
), unbounded adversarial (the adversary can delay an agent for an arbitrary finite number of consecutive rounds) and bounded adversarial (the adversary can delay an agent for at most
c
consecutive rounds, where
c
is unknown to the agents). The quality measure of a rendezvous algorithm is its cost, which is the total number of edge traversals. For random faults, we show an algorithm with cost polynomial in the size
n
of the network and
polylogarithmic
in the larger label
L
, which achieves rendezvous with very high probability in arbitrary networks. By contrast, for unbounded adversarial faults we show that rendezvous is not possible, even in the class of rings. Under this scenario we give a rendezvous algorithm with cost
O
(
n
ℓ
)
, where
ℓ
is the smaller label, working in arbitrary trees, and we show that
Ω
(
ℓ
)
is the lower bound on rendezvous cost, even for the two-node tree. For bounded adversarial faults, we give a rendezvous algorithm working for arbitrary networks, with cost polynomial in
n
, and
logarithmic
in the bound
c
and in the larger label
L
. |
|---|---|
| AbstractList | (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).Two mobile agents, starting from different nodes of an unknown network, have to meet at a node. Agents move in synchronous rounds using a deterministic algorithm. Each agent has a different label, which it can use in the execution of the algorithm, but it does not know the label of the other agent. Agents do not know any bound on the size of the network. In each round an agent decides if it remains idle or if it wants to move to one of the adjacent nodes. Agents are subject to delay faults: if an agent incurs a fault in a given round, it remains in the current node, regardless of its decision. If it planned to move and the fault happened, the agent is aware of it. We consider three scenarios of fault distribution: random (independently in each round and for each agent with constant probability ...), unbounded adversarial (the adversary can delay an agent for an arbitrary finite number of consecutive rounds) and bounded adversarial (the adversary can delay an agent for at most c consecutive rounds, where c is unknown to the agents). The quality measure of a rendezvous algorithm is its cost, which is the total number of edge traversals. For random faults, we show an algorithm with cost polynomial in the size n of the network and polylogarithmic in the larger label L, which achieves rendezvous with very high probability in arbitrary networks. By contrast, for unbounded adversarial faults we show that rendezvous is not possible, even in the class of rings. Under this scenario we give a rendezvous algorithm with cost ..., where ... is the smaller label, working in arbitrary trees, and we show that ... is the lower bound on rendezvous cost, even for the two-node tree. For bounded adversarial faults, we give a rendezvous algorithm working for arbitrary networks, with cost polynomial in n, and logarithmic in the bound c and in the larger label L. Two mobile agents, starting from different nodes of an unknown network, have to meet at a node. Agents move in synchronous rounds using a deterministic algorithm. Each agent has a different label, which it can use in the execution of the algorithm, but it does not know the label of the other agent. Agents do not know any bound on the size of the network. In each round an agent decides if it remains idle or if it wants to move to one of the adjacent nodes. Agents are subject to delay faults : if an agent incurs a fault in a given round, it remains in the current node, regardless of its decision. If it planned to move and the fault happened, the agent is aware of it. We consider three scenarios of fault distribution: random (independently in each round and for each agent with constant probability 0 < p < 1 ), unbounded adversarial (the adversary can delay an agent for an arbitrary finite number of consecutive rounds) and bounded adversarial (the adversary can delay an agent for at most c consecutive rounds, where c is unknown to the agents). The quality measure of a rendezvous algorithm is its cost, which is the total number of edge traversals. For random faults, we show an algorithm with cost polynomial in the size n of the network and polylogarithmic in the larger label L , which achieves rendezvous with very high probability in arbitrary networks. By contrast, for unbounded adversarial faults we show that rendezvous is not possible, even in the class of rings. Under this scenario we give a rendezvous algorithm with cost O ( n ℓ ) , where ℓ is the smaller label, working in arbitrary trees, and we show that Ω ( ℓ ) is the lower bound on rendezvous cost, even for the two-node tree. For bounded adversarial faults, we give a rendezvous algorithm working for arbitrary networks, with cost polynomial in n , and logarithmic in the bound c and in the larger label L . |
| Author | Pelc, Andrzej Chalopin, Jérémie Dieudonné, Yoann Labourel, Arnaud |
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| CitedBy_id | crossref_primary_10_1007_s00446_018_0338_2 crossref_primary_10_1016_j_tcs_2021_07_008 crossref_primary_10_1002_net_21810 crossref_primary_10_1007_s00446_017_0293_3 crossref_primary_10_1016_j_tcs_2018_05_002 |
| Cites_doi | 10.1007/s00453-006-0074-2 10.1137/S0363012996314130 10.1002/net.21453 10.1016/S0022-0000(02)00023-5 10.1016/j.ipl.2012.03.017 10.1137/S0363012993249195 10.2307/3214827 10.1016/j.tcs.2005.12.016 10.1002/nav.10011 10.1287/opre.49.1.107.11191 10.1057/jors.1992.89 10.1016/0304-4149(91)90090-Y 10.1007/s00446-011-0141-9 10.1137/130931990 10.1007/978-1-4614-6825-7_12 10.1137/100796534 10.1002/nav.1044 10.1016/j.tcs.2005.01.001 10.1007/978-3-540-27796-5_15 10.1145/93385.93409 10.1137/S036301299427816X 10.1145/1391289.1391291 10.1007/978-3-642-15763-9_28 10.1007/978-3-540-78773-0_52 10.1145/276884.276925 10.1145/2601068 10.1109/ICDCS.2003.1203510 10.1007/11780823_5 10.1007/978-3-540-77444-0_29 10.1145/2344422.2344427 10.1145/2438645.2438649 10.1145/2629656 10.1007/978-3-540-92221-6_29 |
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| Keywords | Mobile agent Rendezvous Deterministic algorithm Delay fault |
| Language | English |
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| SubjectTerms | Algorithms Computer Communication Networks Computer Hardware Computer Science Computer Systems Organization and Communication Networks Delay Faults Labels Multiagent Systems Networks Polynomials Rendezvous Software Engineering/Programming and Operating Systems Theory of Computation Trees |
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| Title | Rendezvous in networks in spite of delay faults |
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