Simple and Efficient Leader Election

We provide a simple and efficient population protocol for leader election that uses O(log n) states and elects exactly one leader in O(n (log n)^2) interactions with high probability and in expectation. Our analysis is simple and based on fundamental stochastic arguments. Our protocol combines the tournament based leader elimination by Alistarh and Gelashvili, ICALP\u2715, with the synthetic coin introduced by Alistarh et al., SODA\u2717

Communication Efficient Self-Stabilizing Leader Election

This paper presents a randomized self-stabilizing algorithm that elects a leader r in a general n-node undirected graph and constructs a spanning tree T rooted at r. The algorithm works under the synchronous message passing network model, assuming that the nodes know a linear upper bound on n and that each edge has a unique ID known to both its endpoints (or, alternatively, assuming the KT? model). The highlight of this algorithm is its superior communication efficiency: It is guaranteed to send a total of O? (n) messages, each of constant size, till stabilization, while stabilizing in O? (n) rounds, in expectation and with high probability. After stabilization, the algorithm sends at most one constant size message per round while communicating only over the (n - 1) edges of T. In all these aspects, the communication overhead of the new algorithm is far smaller than that of the existing (mostly deterministic) self-stabilizing leader election algorithms. The algorithm is relatively simple and relies mostly on known modules that are common in the fault free leader election literature; these modules are enhanced in various subtle ways in order to assemble them into a communication efficient self-stabilizing algorithm

Almost Logarithmic-Time Space Optimal Leader Election in Population Protocols

The model of population protocols refers to a large collection of simple indistinguishable entities, frequently called {\em agents}. The agents communicate and perform computation through pairwise interactions. We study fast and space efficient leader election in population of cardinality $n$ governed by a random scheduler, where during each time step the scheduler uniformly at random selects for interaction exactly one pair of agents. We propose the first $o(\log^2 n)$-time leader election protocol. Our solution operates in expected parallel time $O(\log n\log\log n)$ which is equivalent to $O(n \log n\log\log n)$ pairwise interactions. This is the fastest currently known leader election algorithm in which each agent utilises asymptotically optimal number of $O(\log\log n)$ states. The new protocol incorporates and amalgamates successfully the power of assorted {\em synthetic coins} with variable rate {\em phase clocks}

A New Look at Blockchain Leader Election: Simple, Efficient, Sustainable and Post-Quantum

In this work, we study the blockchain leader election problem. The purpose of such protocols is to elect a leader who decides on the next block to be appended to the blockchain, for each block proposal round. Solutions to this problem are vital for the security of blockchain systems. We introduce an efficient blockchain leader election method with security based solely on standard assumptions for cryptographic hash functions (rather than public-key cryptographic assumptions) and that does not involve a racing condition as in Proof-of-Work based approaches. Thanks to the former feature, our solution provides the highest confidence in security, even in the post-quantum era. A particularly scalable application of our solution is in the Proof-of-Stake setting, and we investigate our solution in the Algorand blockchain system. We believe our leader election approach can be easily adapted to a range of other blockchain settings. At the core of Algorand\u27s leader election is a verifiable random function (VRF). Our approach is based on introducing a simpler primitive which still suffices for the blockchain leader election problem. In particular, we analyze the concrete requirements in an Algorand-like blockchain setting to accomplish leader election, which leads to the introduction of indexed VRF (iVRF). An iVRF satisfies modified uniqueness and pseudorandomness properties (versus a full-fledged VRF) that enable an efficient instantiation based on a hash function without requiring any complicated zero-knowledge proofs of correct PRF evaluation. We further extend iVRF to an authenticated iVRF with forward-security, which meets all the requirements to establish an Algorand-like consensus. Our solution is simple, flexible and incurs only a 32-byte additional overhead when combined with the current best solution to constructing a forward-secure signature (in the post-quantum setting). We implemented our (authenticated) iVRF proposal in C language on a standard computer and show that it significantly outperforms other quantum-safe VRF proposals in almost all metrics. Particularly, iVRF evaluation and verification can be executed in 0.02 ms, which is even faster than ECVRF used in Algorand

Improved bully election algorithm for distributed systems

Electing a leader is a classical problem in distributed computing system. Synchronization between processes often requires one process acting as a coordinator. If an elected leader node fails, the other nodes of the system need to elect another leader without much wasting of time. The bully algorithm is a classical approach for electing a leader in a synchronous distributed computing system, which is used to determine the process with highest priority number as the coordinator. In this paper, we have discussed the limitations of Bully algorithm and proposed a simple and efficient method for the Bully algorithm which reduces the number of messages during the election. Our analytical simulation shows that, our proposed algorithm is more efficient than the Bully algorithm with fewer messages passing and fewer stages

Deterministic Symmetry Breaking in Ring Networks

We study a distributed coordination mechanism for uniform agents located on a circle. The agents perform their actions in synchronised rounds. At the beginning of each round an agent chooses the direction of its movement from clockwise, anticlockwise, or idle, and moves at unit speed during this round. Agents are not allowed to overpass, i.e., when an agent collides with another it instantly starts moving with the same speed in the opposite direction (without exchanging any information with the other agent). However, at the end of each round each agent has access to limited information regarding its trajectory of movement during this round. We assume that $n$ mobile agents are initially located on a circle unit circumference at arbitrary but distinct positions unknown to other agents. The agents are equipped with unique identifiers from a fixed range. The {\em location discovery} task to be performed by each agent is to determine the initial position of every other agent. Our main result states that, if the only available information about movement in a round is limited to %information about distance between the initial and the final position, then there is a superlinear lower bound on time needed to solve the location discovery problem. Interestingly, this result corresponds to a combinatorial symmetry breaking problem, which might be of independent interest. If, on the other hand, an agent has access to the distance to its first collision with another agent in a round, we design an asymptotically efficient and close to optimal solution for the location discovery problem.Comment: Conference version accepted to ICDCS 201