Clock synchronization in distributed multicomputer systems. Part II

The study substantiates the necessity of clock synchronization in distributed multicomputer systems. The basic definitions related to the concept of clock synchronization are given, and methods of clock synchronization are classified. Increasing the lifecycle of failure- and fault-tolerant distributed multicomputer systems for critical application is one of the most urgent problems at the current level of technology development. This is especially true for unattended distributed multicomputer systems for space applications. The second part deals with synchronization in systems with Byzantine faults, and this is a complex task due to the characteristic features of the fault model. The synchronization process in multi-cluster and multi-complex systems is associated with the multitasking of such systems, which makes the synchronization process even more relevant and multi-criteria. The paper considers the modern technologies providing the synchronization process in systems of critical use.

Clock synchronization in distributed multicomputer systems. Part I

The study substantiates the necessity of clock synchronization in distributed multicomputer systems. The basic definitions related to the concept of clock synchronization are given, and methods of clock synchronization are classified. Increasing the lifecycle of failure- and fault-tolerant distributed multicomputer systems for critical application is one of the most urgent problems at the current level of technology development. This is especially true for unattended distributed multicomputer systems for space applications. The development of such systems should begin with the construction of models of faults and self-controlled degradation, ensuring, firstly, their failure and fault tolerance and, secondly, maximum survivability, which is possible only if there are means of clock synchronization in such systems. All activities associated with ensuring the synchronization of any distributed multicomputer systems begin with the concept of synchronization of on-board functions, which is based on the generation of on-board time and includes the synchronization of on-board software and equipment that requires time synchronization or information about the course of time. The main elements of this concept are the processor clock module, the onboard software clock, the atomic navigation clock. The first part of the work gives basic definitions, and considers methods and algorithms related to the clock synchronization process. The second part is devoted to synchronization in systems with Byzantine faults and in multi-cluster and multi-complex, i.e. multitask, systems. The modern technologies providing the synchronization process in such systems are considered.

Search on a Line by Byzantine Robots

We consider the problem of fault-tolerant parallel search on an infinite line by [Formula: see text] robots. Starting from the origin, the robots are required to find a target at an unknown location. The robots can move with maximum speed [Formula: see text] and can communicate wirelessly among themselves. However, among the [Formula: see text] robots, there are [Formula: see text] robots that exhibit byzantine faults. A faulty robot can fail to report the target even after reaching it, or it can make malicious claims about having found the target when in fact it has not. Given the presence of such faulty robots, the search for the target can only be concluded when the non-faulty robots have sufficient evidence that the target has been found. We aim to design algorithms that minimize the value of [Formula: see text], the time to find a target at a (unknown) distance [Formula: see text] from the origin by [Formula: see text] robots among which [Formula: see text] are faulty. We give several different algorithms whose running time depends on the ratio [Formula: see text], the density of faulty robots, and also prove lower bounds. Our algorithms are optimal for some densities of faulty robots.

k-Root-n: An Efficient Algorithm for Avoiding Short Term Double-Spending Alongside Distributed Ledger Technologies such as Blockchain

Blockchains such as the bitcoin blockchain depend on reaching a global consensus on the distributed ledger; therefore, they suffer from well-known scalability problems. This paper proposes an algorithm that avoids double-spending in the short term with just O(√n) messages instead of O(n); each node receiving money off-chain performs the due diligence of consulting k√n random nodes to check if any of them is aware of double-spending. Two nodes receiving double-spent money will in this way consult at least one common node with very high probability, because of the ‘birthday paradox’, and any common honest node consulted will detect the fraud. Since the velocity of money in the real world has coins circulating through at most a few wallets per day, the size of the due diligence communication is small in the short term. This ‘k-root-n’ algorithm is suitable for an environment with synchronous or asynchronous (but with fairly low latency) communication and with Byzantine faults. The presented k-root-n algorithm should be practical to avoid double-spending with arbitrarily high probability, while feasibly coping with the throughput of all world commerce. It is resistant to Sybil attacks even beyond 50% of nodes. In the long term, the k-root-n algorithm is less efficient. Therefore, it should preferably be used as a complement, and not a replacement, to a global distributed ledger technology.

k-root-n: An Efficient Algorithm for Avoiding Short Term Double-Spending Alongside Distributed Ledger Technologies Such as Blockchain

Blockchains such as the bitcoin blockchain depend on reaching a global consensus on the distributed ledger; therefore, they suffer from well know scalability problems. This paper proposes an algorithm that avoids double-spending in the short term with just O(√n) messages; each node receiving money off-chain performs the due diligence of consulting k√n random nodes to check if any of them is aware of double-spending. Two nodes receiving double-spent money will in this way consult at least one common node with very high probability, due to the ‘birthday paradox’, and any common honest node consulted will detect the fraud. Since the velocity of money in the real world has coins circulating through at most a few wallets per day, the size of the due diligence communication is small in the short term. This `k-root-n’ algorithm is suitable for an environment with synchronous or asynchronous (but with fairly low latency) communication and with Byzantine faults. The presented k-root-n algorithm should be practical to avoid double-spending with arbitrarily high probability, while feasibly coping with the throughput of all world commerce. It is resistant to Sybil attacks even beyond 50% of nodes. In the long term, the k-root-n algorithm is less efficient. Therefore, it should preferably be used as a complement and not a replacement to a global distributed ledger technology.