Fast and Compact Distributed Verification and Self-stabilization of a DFS Tree

Kutten, Shay; Trehan, Chhaya

doi:10.1007/978-3-319-14472-6_22

Cited by 3 publications

(2 citation statements)

References 32 publications

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“…dynamic network topology and fault tolerance are core concerns of distributed computing [2,47] and various models (e.g. [41]) and topology maintenance [42] and self-* algorithms abound especially for self-stabilisation [15,16,28,39] and self-stabilising spanning trees and traversals [11,44,45].…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Fully Compact Routing in Low Memory Self-Healing Trees

Castañeda¹,

Lefèvre

Trehan

2020

Proceedings of the 21st International Conference on Distributed Computing and Networking

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The paper (Compact Routing Messages in Self-Healing Trees, TCS 2017) introduced CompactFTZ, the first self-healing compact routing algorithm that works in a distributed network with each node using only O(log n) words (i.e. O(log 2 n) bits) memory and thus O(log n) sized messages. The routing uses only O(1) and O(log n) words routing table and packet labels respectively on a self-healing tree that also works using only O(1) words repairing the network in face of a strong adversary deleting nodes. This deterministic algorithm sets up its data structures in a preprocessing phase and then updates the required data structures in only O(1) parallel time per healing round during execution of the algorithm.However, CompactFTZ has no constraints in its preprocessing phase which could be done in distributed large memory or even centrally. In this paper, we correct that by developing the algorithms for preprocessing of CompactFTZ in a fully distributed manner using only O(log n) words memory in optimal time. In fact, the preprocessing for the self-healing tree (ForgivingTree) component takes only O(1) memory. We develop a local function which each node invokes to instantly compute and then relay its repair instructions (known as its Will) in only O(1) time.We formalise the low memory CONGEST model setting used in previous low memory algorithms (e.g. [24]); nodes' working memory is restricted to be much smaller (in our case, O(log n)) than the numbers of their neighbours to whom they communicate through their I/O ports. We expand the model to allow for non-contiguous ports (e.g. empty ports or neighbours unmarked or lost in dynamic settings) and adversarial order of inputs from neighbours. Besides the Wills, we set up the tree structures and traversals for the routing scheme using only O(log n) memory and O(D) parallel time, where D is the diameter. Thus, we devise the first self-healing compact routing algorithm that can be fully set up and executed in low memory.

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Section: Related Work and Conclusionmentioning

confidence: 99%

Fully Compact Routing in Low Memory Self-Healing Trees

Castañeda¹,

Lefèvre

Trehan

2020

Proceedings of the 21st International Conference on Distributed Computing and Networking

View full text Add to dashboard Cite

show abstract

“…Finally, dynamic network topology and fault tolerance are core concerns of distributed computing [2,46] and various models (e.g. [39]) and topology maintenance and self-* algorithms abound [15,16,37,40,42,11,43,35,24].…”

Section: Related Workmentioning

confidence: 99%

Some Problems in Compact Message Passing

Castañeda¹,

Lefèvre²,

Trehan³

2018

Preprint

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This paper seeks to address the question of designing distributed algorithms for the setting of compact memory i.e. sublinear (in n -the number of nodes) bits working memory for connected networks of arbitrary topologies. The nodes in our networks may have much lower internal (working) memory (say, O(poly log n)) as compared to the number of their possible neighbours (O(n)) implying that a node may not be even able to store the IDs of all of its neighbours. These algorithms may be useful for large networks of small devices such as the Internet of Things, for wireless or ad-hoc networks, and, in general, as memory efficient algorithms.More formally, we introduce the Compact Message Passing (CM P ) model -an extension of the standard message passing model considered at a finer granularity where a node can interleave reads and writes with internal computations, using a port only once in a synchronous round. The interleaving is required for meaningful computations due to the low memory requirement and is akin to a distributed network with nodes executing streaming algorithms. Note that the internal memory size upper bounds the message sizes and hence e.g. for O(log n) memory, the model is weaker than the CONGEST model; for such models our algorithms will work directly too.We present some early results in the CMP model for nodes with O(log 2 n) bits working memory. We introduce the concepts of local compact functions and compact protocols and give solutions for some classic distributed problems (leader election, tree constructions and traversals). We build on these to solve the open problem of compact preprocessing for the compact self-healing routing algorithm CompactFTZ posed in Compact Routing Messages in Self-Healing Trees (Theoretical Computer Science 2017) by designing local compact functions for finding particular subtrees of labeled binary trees. Hence, we introduce the first fully compact self-healing routing algorithm. In the process, we also give independent fully compact versions of the Forgiving Tree [PODC 2008] and Thorup-Zwick's tree based compact routing [SPAA 2001].

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Randomized proof-labeling schemes

2018

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A proof-labeling scheme, introduced by Korman, Kutten and Peleg [PODC 2005], is a mechanism enabling to certify the legality of a network configuration with respect to a boolean predicate. Such a mechanism finds applications in many frameworks, including the design of fault-tolerant distributed algorithms. In a prooflabeling scheme, the verification phase consists of exchanging labels between neighbors. The size of these labels depends on the network predicate to be checked. There are predicates requiring large labels, of polylogarithmic size (e.g., MST), or even polynomial size (e.g., Symmetry). In this paper, we introduce the notion of randomized proof-labeling schemes. By reduction from deterministic schemes, we show that randomization enables the amount of communication to be exponentially reduced. As a consequence, we show that checking any network predicate can be done with probability of correctness as close to one as desired by exchanging just a logarithmic number of bits between neighbors. Moreover, we design a novel space lower bound technique that applies to both deterministic and randomized proof-labeling schemes. Using this technique, we establish several tight bounds on the verification complexity of classical distributed computing problems, such as MST construction, and of classical predicates such as acyclicity, connectivity, and cycle length.

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Fast and Compact Distributed Verification and Self-stabilization of a DFS Tree

Cited by 3 publications

References 32 publications

Fully Compact Routing in Low Memory Self-Healing Trees

Fully Compact Routing in Low Memory Self-Healing Trees

Some Problems in Compact Message Passing

Randomized proof-labeling schemes

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