Robustness of the Rotor-router Mechanism

Bampas, Evangelos; Gąsieniec, Leszek; Klasing, Ralf; Kosowski, Adrian; Radzik, Tomasz

doi:10.1007/978-3-642-10877-8_27

Cited by 9 publications

(10 citation statements)

References 13 publications

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“…Furthermore, local FRR that relies on randomization [6,10] or on state to remember packets [4]. However, both can be problematic in practice and are non-standard, requiring extra memory and randomization beyond hashing, while causing packet reordering.…”

Section: Related Workmentioning

confidence: 99%

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Shortcutting Fast Failover Routes in the Data Plane

Shukla

Foerster

2021

Proceedings of the Symposium on Architectures for Networking and Communications Systems

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In networks, availability is of paramount importance. As link failures are disruptive, modern networks in turn provide Fast ReRoute (FRR) mechanisms to rapidly restore connectivity. However, existing FRR approaches heavily impact performance until the slower convergence protocols kick in. The fast failover routes commonly involve unnecessary loops and detours, disturbing other traffic while causing costly packet loss. In this paper, we make a case for augmenting FRR mechanisms to avoid such inefficiencies. We introduce ShortCut that routes the packets in a loop free fashion, avoiding costly detours and decreasing link load. ShortCut achieves this by leveraging data plane programmability: when a loop is locally observed, it can be removed by short-cutting the respective route parts. As such, ShortCut is topology-independent and agnostic to the type of FRR currently deployed. Our first experimental simulations show that ShortCut can outperform control plane convergence mechanisms; moreover avoiding loops and keeping packet loss minimal opposed to existing FRR mechanisms. CCS CONCEPTS• Computer systems organization → Reliability.

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Section: Related Workmentioning

confidence: 99%

“…they visit both S2 and S3 from S1, one after another2 Our mechanism also works for destination-based routing via trees 3. ShortCut also works for routing and FRR without usage of the inport, as we can then simply assume the forwarding is identical for all node inports 4. An arborescence is a directed tree oriented towards its root.…”

mentioning

confidence: 99%

Shortcutting Fast Failover Routes in the Data Plane

Shukla

Foerster

2021

Proceedings of the Symposium on Architectures for Networking and Communications Systems

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“…It is a simple strategy, where upon successive visits to each node, the agent is traversing the outgoing edges in a round-robin fashion. Its exploration time is Θ(mD) for any graph with m edges and diameter D [2,30]. It is easy to see that this algorithm can be implemented in port-labelled graphs with zero bits of memory at the agent and only ⌈log d v ⌉ bits of memory at each node v with degree d v (note that this is the minimum possible amount of memory for any correct exploration algorithm using only memory at the nodes).…”

Section: Previous and Related Workmentioning

confidence: 99%

Tree exploration in dual-memory model

Bojko¹,

Gotfryd²,

Kowalski³

et al. 2021

Preprint

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We study the problem of online tree exploration by a deterministic mobile agent. Our main objective is to establish what features of the model of the mobile agent and the environment allow linear exploration time. We study agents that, upon entering to a node, do not receive as input the edge via which they entered. In such a model, deterministic memoryless exploration is infeasible, hence the agent needs to be allowed to use some memory. The memory can be located at the agent or at each node. The existing lower bounds show that if the memory is either only at the agent or only at the nodes, then the exploration needs superlinear time. We show that tree exploration in dual-memory model, with constant memory at the agent and logarithmic at each node is possible in linear time when one of two additional features is present: fixed initial state of the memory at each node (so called clean memory) or a single movable token. We present two algorithms working in linear time for arbitrary trees in these two models. On the other hand, in our lower bound we show that if the agent has a single bit of memory and one bit is present at each node, then exploration may require quadratic time on paths, if the initial memory at nodes could be set arbitrarily (so called dirty memory). This shows that having clean node memory or a token allows linear exploration of trees in the model with two types of memory, but having neither of those features may lead to quadratic exploration time even on a simple path.

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“…Subsequently, Yanovski et al [15] and Bampas et al [3] showed that the Eulerian cycle is in the worst case entered within Θ(D|E|) steps in a graph of diameter D. Considerations of specific graph classes were performed in [11]. Robustness properties of the rotor-router were further studied in [4], who considered the time required for the rotor-router to stabilize to a (new) Eulerian cycle after an edge is added or removed from the graph. Regarding the terminology, we note that the rotor-router model has also been referred to as the Propp machine [3] or Edge Ant Walk algorithm [14,15], and has also been described in [5] in terms of traversing a maze and marking edges with pebbles.…”

Section: Related Workmentioning

confidence: 99%

The multi-agent rotor-router on the ring

Klasing

Kosowski

Pająk

et al. 2013

Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing

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The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, an agent is initially placed at one of the nodes of the graph. Each node maintains a cyclic ordering of its outgoing arcs, and during successive visits of the agent, propagates it along arcs chosen according to this ordering in round-robin fashion. In this work we consider the setting in which multiple, indistinguishable agents are deployed in parallel in the nodes of the graph, and move around the graph in synchronous rounds, interacting with a single rotor-router system. We propose new techniques which allow us to perform a theoretical analysis of the multi-agent rotor-router model, and to compare it to the scenario of parallel independent random walks in a graph. Our main results concern the n-node ring, and suggest a strong similarity between the performance characteristics of this deterministic model and random walks.We show that on the ring the rotor-router with k agents admits a cover time of between Θ(n 2 /k 2 ) in the best case and Θ(n 2 / log k) in the worst case, depending on the initial locations of the agents, and that both these bounds are tight. The corresponding expected value of cover time for k random walks, depending on the initial locations of the walkers, is proven to belong to a similar range, namely between Θ(n 2 /(k 2 / log 2 k)) and Θ(n 2 / log k).Finally, we study the limit behavior of the rotor-router system. We show that, once the rotor-router system has stabilized, all the nodes of the ring are always visited by some agent every Θ(n/k) steps, regardless of how the system * Supported by ANR project DISPLEXITY and by NCN under contract DEC-2011/02/A/ST6/00201. The full version of this paper is available online at: http://hal.inria.fr/ hal-00735113.

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Robustness of the Rotor-router Mechanism

Cited by 9 publications

References 13 publications

Shortcutting Fast Failover Routes in the Data Plane

Shortcutting Fast Failover Routes in the Data Plane

Tree exploration in dual-memory model

The multi-agent rotor-router on the ring

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