arXiv subjects

Pankaj Khanchandani

Publications and source records attributed to Pankaj Khanchandani.

3 recordsLinked to original sources

arXiv2021

Byzantine Agreement with Unknown Participants and Failures

A set of mutually distrusting participants that want to agree on a common opinion must solve an instance of a Byzantine agreement problem. These problems have been extensively studied in the literature. However, most of the existing solutions assume that the participants are aware of $n$ -- the total number of participants in the system -- and $f$ -- an upper bound on the number of Byzantine participants. In this paper, we show that most of the fundamental agreement problems can be solved without affecting resiliency even if the participants do not know the values of (possibly changing) $n$ and $f$. Specifically, we consider a synchronous system where the participants have unique but not necessarily consecutive identifiers, and give Byzantine agreement algorithms for reliable broadcast, approximate agreement, rotor-coordinator, early terminating consensus and total ordering in static and dynamic systems, all with the optimal resiliency of $n> 3f$. Moreover, we show that synchrony is necessary as an agreement with probabilistic termination is impossible in a semi-synchronous or asynchronous system if the participants are unaware of $n$ and $f$.

cs.DC↗

arXiv2018

Reducing Compare-and-Swap to Consensus Number One Primitives

The consensus number of an object is the maximum number of processes among which binary consensus can be solved using any number of instances of the object and read-write registers. Herlihy [6] showed in his seminal work that if an object has a consensus number of n, then there is a universal construction for a wait-free and linearizable implementation of any non-trivial concurrent object or data structure that is shared among n processes. Thus, a synchronization object such as compare-and-swap with an infinite consensus number and the corresponding instruction can be viewed as "strong". On the other hand, a synchronization object such as fetch-and-add with consensus number two and the corresponding fetch-and-add instruction can be viewed as "weak". Ellen et al. [2] observed recently that an object supporting two weak instructions can also achieve infinite consensus number like an object that supports one strong instruction. Using Herlihy's universal construction, this implies that ignoring concerns about efficiency, one can design any concurrent data structure or algorithm using only weak instructions. However, is it possible that a combination of weak instructions is really powerful enough to efficiently replace a strong instruction, like compare-and-swap, without incurring a large overhead in time or space? In this paper, we answer this question by giving an O(1) time wait-free and linearizable implementation of a compare-and-swap register shared among n processes using read-write registers and O(1) registers that support two synchronization primitives half-max and max-write, each having consensus number one. Thus, any algorithm that solves some arbitrary synchronization problem using read-write and compare-and-swap registers can be transformed into an algorithm that has the same asymptotic time complexity and only uses consensus number one instructions.

cs.DS↗

arXiv2016

Self-stabilizing Byzantine Clock Synchronization with Optimal Precision

We revisit the approach to Byzantine fault-tolerant clock synchronization based on approximate agreement introduced by Lynch and Welch. Our contribution is threefold: (1) We provide a slightly refined variant of the algorithm yielding improved bounds on the skew that can be achieved and the sustainable frequency offsets. (2) We show how to extend the technique to also synchronize clock rates. This permits less frequent communication without significant loss of precision, provided that clock rates change sufficiently slowly. (3) We present a coupling scheme that allows to make these algorithms self-stabilizing while preserving their high precision. The scheme utilizes a low-precision, but self-stabilizing algorithm for the purpose of recovery.

cs.DC↗