There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

物件導向軟體之架構(Object-Oriented Software Construction)探討

In 1974 an article appeared in Science magazine with the dry-sounding title “Judgment Under Uncertainty: Heuristics and Biases” by a pair of psychologists who were not well known outside their discipline of decision theory. In it Amos Tversky and Daniel Kahneman introduced the world to Prospect Theory, which mapped out how humans actually behave when faced with decisions about gains and losses, in contrast to how economists assumed that people behave. Prospect Theory turned Economics on its head by demonstrating through a series of ingenious experiments that people are much more concerned with losses than they are with gains, and that framing a choice from one perspective or the other will result in decisions that are exactly the opposite of each other, even if the outcomes are monetarily the same. Prospect Theory led cognitive psychology in a new direction that began to uncover other human biases in thinking that are probably not learned but are part of our brain’s wiring.

Thinking fast and slow.

This paper describes a new replication algorithm that is able to tolerate Byzantine faults. We believe that Byzantinefault-tolerant algorithms will be increasingly important in the future because malicious attacks and software errors are increasingly common and can cause faulty nodes to exhibit arbitrary behavior. Whereas previous algorithms assumed a synchronous system or were too slow to be used in practice, the algorithm described in this paper is practical: it works in asynchronous environments like the Internet and incorporates several important optimizations that improve the response time of previous algorithms by more than an order of magnitude. We implemented a Byzantine-fault-tolerant NFS service using our algorithm and measured its performance. The results show that our service is only 3% slower than a standard unreplicated NFS.

/pdf/practical-byzantine-fault-tolerance-58gb0de0hd.pdf

Practical Byzantine fault tolerance

Self-stabilization ensures that, after any transient fault, the system recovers in a finite time and eventually exhibits correct behavior. Speculation consists in guaranteeing that the system satisfies its requirements for any execution but exhibits significantly better performances for a subset of executions that are more probable. A speculative protocol is in this sense supposed to be both robust and efficient in practice.We introduce the notion of speculative stabilization which we illustrate through the mutual exclusion problem. We then present a novel speculatively stabilizing mutual exclusion protocol. Our protocol is self-stabilizing for any asynchronous execution. We prove that its stabilization time for synchronous executions is diam(g)/2 steps (where diam(g) denotes the diameter of the system).This complexity result is of independent interest. The celebrated mutual exclusion protocol of Dijkstra stabilizes in n steps (where n is the number of processes) in synchronous executions and the question whether the stabilization time could be strictly smaller than the diameter has been open since then (almost 40 years). We show that this is indeed possible for any underlying topology. We also provide a lower bound proof that shows that our new stabilization time of diam(g)/2 steps is optimal for synchronous executions, even if asynchronous stabilization is not required.

/pdf/introducing-speculation-in-self-stabilization-an-application-2olh79v283.pdf

Introducing speculation in self-stabilization: an application to mutual exclusion

The success of Bitcoin relies on the perception of a fair underlying peer-to-peer protocol: blockchain. Fairness here means that the reward (in bitcoins) given to any participant that helps maintain the consistency of the protocol by mining, is proportional to the computational power devoted by that participant to the mining task. Without such perception of fairness, honest miners might be disincentivized to maintain the protocol, leaving the space for dishonest miners to reach a majority and jeopardize the consistency of the entire system.

/pdf/on-the-unfairness-of-blockchain-1ux9mxb33d.pdf

On the Unfairness of Blockchain

We argued in previous columns that objectoriented distributed programming should not be confused with distributed OO programming and that it should not be confused with wrapping existing distributed systems with OO dressing. Taking OO distributed programming seriously entails identifying and classifying the basic abstractions underlying distributed computing. We attempted to keep our previous claims at an abstract and general level. In this column, we make those claims more concrete. More precisely, we describe OO distributed programming through an exercise consisting of abstracting and factoring out a fundamental component of a distributed system: failure detection. 1

Putting OO distributed programming to work

Peer-to-peer content dissemination applications suffer immensely from freeriders, i.e., nodes that do not provide their fair share. The Tit-for-Tat (TfT) incentives have received much attention as they help make such systems more robust against freeriding. However, these rely on an asymmetric component, namely opportunistic pushes, that let peers receive content without sending anything in return. Opportunistic push constitutes the Achilles' heel of TfT-based protocols as illustrated by the fact that all known attacks against them exploit it. This problem becomes even more serious when used by colluding freeriders. In this paper, we discuss the possibility of using accountability to secure gossip-based dissemination protocols based on asymmetric exchanges. The fact that gossip protocols are dynamic and randomized makes our approach robust against collusion and alleviates the need for cryptography. We present the challenges raised by an auditing approach and give insights into how to build a freerider-tracking protocol for gossip-based content dissemination.

/pdf/on-tracking-freeriders-in-gossip-protocols-42snczf5be.pdf

On tracking freeriders in gossip protocols

In the $k$-set agreement problem, each processor starts with a private input value and eventually decides on an output value. At most $k$ distinct output values may be chosen, and every processor's output value must be one of the proposed values. We consider a synchronous message passing system, and we prove a tight bound of $\lfloor f/k\rfloor+2$ rounds of communication for all processors to decide in every run in which at most $f$ processors fail. The lower bound proof proceeds through a simulation of a synchronous solution to $k$-set agreement in message passing, in an asynchronous shared memory system in which $k-1$ processors may fail, and which was proven to be impossible using topological approaches. In contrast to past complexity results on set agreement, our lower bound proof is purely algorithmic. It does not use any direct topological argument but uses instead the impossibility of asynchronous set agreement to encapsulate the needed topology. We thus derive an adaptive complexity lower bound for a message passing system from a static impossibility in a shared memory system.

/pdf/the-complexity-of-early-deciding-set-agreement-3opwmnvc5u.pdf

Rachid Guerraoui

Papers

Introducing speculation in self-stabilization: an application to mutual exclusion

On the Unfairness of Blockchain

Putting OO distributed programming to work

On tracking freeriders in gossip protocols

The Complexity of Early Deciding Set Agreement