This paper studies proof-of-work Nakamoto consensus protocols under bounded network delays, settling two long-standing questions in blockchain security: What is the most effective attack on block safety under a given block confirmation latency? And what is the resulting probability of safety violation? A Markov decision process (MDP) framework is introduced to precisely characterize the system state (including the blocktree and timings of all blocks mined), the adversary's potential actions, and the state transitions due to the adversarial action and the random block arrival processes. An optimal attack, called bait-and-switch, is proposed and proved to maximize the adversary's chance of violating block safety by ''beating Nakamoto in the race''. The exact probability of this violation is calculated for any given confirmation depth using Markov chain analysis, offering fresh insights into the interplay of network delay, confirmation rules, and blockchain security.

This paper investigates the fundamental trade-offs between block safety, confirmation latency, and transaction throughput of proof-of-work (PoW) longest-chain fork-choice protocols, also known as PoW Nakamoto consensus. New upper and lower bounds are derived for the probability of block safety violations as a function of honest and adversarial mining rates, a block propagation delay limit, and confirmation latency measured in both time and block depth. The results include the first non-trivial closed-form finite-latency bound applicable across all delays and mining rates up to the ultimate fault tolerance. Notably, the gap between these upper and lower bounds is narrower than previously established bounds for a wide range of parameters relevant to Bitcoin and its derivatives, including Litecoin and Dogecoin, as well as Ethereum Classic. Additionally, the study uncovers a fundamental trade-off between transaction throughput and confirmation latency, ultimately determined by the desired fault tolerance and the rate at which block propagation delay increases with block size.

A central issue of distributed computing systems is how to optimally allocate computing and storage resources and design data shuffling strategies such that the total execution time for computing and data shuffling is minimized. This is extremely critical when the computation, storage and communication resources are limited. In this paper, we study the resource allocation and coding scheme for the MapReduce-type framework with limited resources. In particular, we focus on the coded distributed computing (CDC) approach proposed by Li et al.. We first extend the asymmetric CDC (ACDC) scheme proposed by Yu et al. to the cascade case where each output function is computed by multiple servers. Then we demonstrate that whether CDC or ACDC is better depends on system parameters (e.g., number of computing servers) and task parameters (e.g., number of input files), implying that neither CDC nor ACDC is optimal. By merging the ideas of CDC and ACDC, we propose a hybrid scheme and show that it can strictly outperform CDC and ACDC. Furthermore, we derive an information-theoretic converse showing that for the MapReduce task using a type of weakly symmetric Reduce assignment, which includes the Reduce assignments of CDC and ACDC as special cases, the hybrid scheme with a corresponding resource allocation strategy is optimal, i.e., achieves the minimum execution time, for arbitrary amount of computing servers and storage memories.

Group testing can save testing resources in the context of the ongoing COVID-19 pandemic. In group testing, we are given n samples, one per individual, and arrange them into m < n pooled samples, where each pool is obtained by mixing a subset of the n individual samples. Infected individuals are then identified using a group testing algorithm. In this paper, we use side information (SI) collected from contact tracing (CT) within nonadaptive/single-stage group testing algorithms. We generate data by incorporating CT SI and characteristics of disease spread between individuals. These data are fed into two signal and measurement models for group testing, where numerical results show that our algorithms provide improved sensitivity and specificity. While Nikolopoulos et al. utilized family structure to improve nonadaptive group testing, ours is the first work to explore and demonstrate how CT SI can further improve group testing performance.

Relay is a traditional key technology to improve the communication reliability and enlarge the covering range of service. Recently, coded caching schemes that reduce traffic congestion through coding and injecting duplicate data among users have attracted wide interests. This paper studies a relay network where all nodes including the central server, relay nodes and users are equipped with cache memories. Each user demands a file from the server’s library, and is connected to the server through a specific relay node. We define the communication delay for this model and propose new coded caching schemes for the deterministic and random caching setups, respectively. The proposed schemes exploit the spared transmission time resource and can greatly reduce the transmission delay compared to the previously known caching schemes. Surprisingly, we show that even when relay nodes do not cooperate with each other, using a small amount of caching memories at each relay node is sufficient to achieve the same communication delay as if each relay had access to the full library. To our best knowledge, this is the first result showing that even the caching size is strictly smaller than the library’s size, increasing the caching size is wasteful in reducing the transmission latency.