Leader Election in Anonymous Rings: Franklin Goes Probabilistic

Bakhshi, Rena; Fokkink, Wan; Pang, Jun; Pol, Jaco van de

doi:10.1007/978-0-387-09680-3_4

Cited by 15 publications

(21 citation statements)

References 41 publications

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“…We also include a number of distributed algorithms. We ported the probabilistic leader election protocols [3], based on DolevKlawe-Rodeh and Franklin, from μCRL to mCRL2. We also included Hesselink's hardware register [27].…”

Section: Designmentioning

confidence: 99%

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Multi-core symbolic bisimulation minimisation

Dijk

Pol

2017

Int J Softw Tools Technol Transfer

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We introduce parallel symbolic algorithms for bisimulation minimisation, to combat the combinatorial state space explosion along three different paths. Bisimulation minimisation reduces a transition system to the smallest system with equivalent behaviour. We consider strong and branching bisimilarity for interactive Markov chains, which combine labelled transition systems and continuoustime Markov chains. Large state spaces can be represented concisely by symbolic techniques, based on binary decision diagrams. We present specialised BDD operations to compute the maximal bisimulation using signature-based partition refinement. We also study the symbolic representation of the quotient system and suggest an encoding based on representative states, rather than block numbers. Our implementation extends the parallel, shared memory, BDD library Sylvan, to obtain a significant speedup on multi-core machines. We propose the usage of partial signatures and of disjunctively partitioned transition relations, to increase the parallelisation opportunities. Also our new parallel data structure for block assignments increases scalability. We provide SigrefMC, a versatile tool that can be customised for bisimulation minimisation in various contexts. In particular, it supports models generated by the high-performance Work funded by the NWO Grant 612.001.101 (MaDriD) and by FWF, NFN Grant S11408-N23 (RiSE). model checker LTSmin, providing access to specifications in multiple formalisms, including process algebra. The extensive experimental evaluation is based on various benchmarks from the literature. We demonstrate a speedup up to 95× for computing the maximal bisimulation on one processor. In addition, we find parallel speedups on a 48-core machine of another 17× for partition refinement and 24× for quotient computation. Our new encoding of the reduced state space leads to smaller BDD representations, with up to a 5162-fold reduction.

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Section: Designmentioning

confidence: 99%

“…We recapitulate the notion of partition refinement with partial signatures in Sect. 3. Section 4 discusses how we extended Sylvan to parallelise signature-based partition refinement.…”

Section: Introductionmentioning

confidence: 99%

Multi-core symbolic bisimulation minimisation

Dijk

Pol

2017

Int J Softw Tools Technol Transfer

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“…swp6 A version of the sliding window protocol [1]. It has 2 data elements, the channels can contain at most one element and the window size is 6. fr53 A model of Franklin's leader election protocol for anonymous processes along a bidirectional ring of asynchronous channels, which terminates with probability one [2,11]. We chose an instance with 5 nodes and 3 identities.…”

Section: Experimental Evaluationmentioning

confidence: 99%

“…A τ-step is silent if the source and destination are equivalent (with respect to the previous partition) 2. http://fmt.cs.utwente.nl/tools/ltsmin/…”

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confidence: 99%

Distributed Branching Bisimulation Minimization by Inductive Signatures

Blom

Pol

2009

Electron. Proc. Theor. Comput. Sci.

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We present a new distributed algorithm for state space minimization modulo branching bisimulation. Like its predecessor it uses signatures for refinement, but the refinement process and the signatures have been optimized to exploit the fact that the input graph contains no tau-loops. The optimization in the refinement process is meant to reduce both the number of iterations needed and the memory requirements. In the former case we cannot prove that there is an improvement, but our experiments show that in many cases the number of iterations is smaller. In the latter case, we can prove that the worst case memory use of the new algorithm is linear in the size of the state space, whereas the old algorithm has a quadratic upper bound. The paper includes a proof of correctness of the new algorithm and the results of a number of experiments that compare the performance of the old and the new algorithms

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“…For such rings, the best known election algorithms are [15,10,13,5] with average message complexity Θ(n log n). Itai and Rodeh [16] have proposed an algorithm for synchronous unidirectional anonymous rings; its average message complexity is O(n).…”

Section: Introductionmentioning

confidence: 99%

Fast leader election in anonymous rings with bounded expected delay

Bakhshi

Endrullis

Fokkink

et al. 2011

Information Processing Letters

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We propose a probabilistic network model, called asynchronous bounded expected delay (ABE), which requires a known bound on the expected message delay. In ABE networks all asynchronous executions are possible, but executions with extremely long delays are less probable. Thus, the ABE model captures asynchrony that occurs in sensor networks and ad-hoc networks.At the example of an election algorithm, we show that the minimal assumptions of ABE networks are sufficient for the development of efficient algorithms. For anonymous, unidirectional ABE rings of known size n we devise a probabilistic election algorithm having average message and time complexity O(n).

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Leader Election in Anonymous Rings: Franklin Goes Probabilistic

Cited by 15 publications

References 41 publications

Multi-core symbolic bisimulation minimisation

Multi-core symbolic bisimulation minimisation

Distributed Branching Bisimulation Minimization by Inductive Signatures

Fast leader election in anonymous rings with bounded expected delay

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