Simple Dynamics for Plurality Consensus

We study a \emph{Plurality-Consensus} process in which each of $n$ anonymous agents of a communication network initially supports an opinion (a color chosen from a finite set $[k]$). Then, in every (synchronous) round, each agent can revise his color according to the opinions currently held by a random sample of his neighbors. It is assumed that the initial color configuration exhibits a sufficiently large \emph{bias} $s$ towards a fixed plurality color, that is, the number of nodes supporting the plurality color exceeds the number of nodes supporting any other color by $s$ additional nodes. The goal is having the process to converge to the \emph{stable} configuration in which all nodes support the initial plurality. We consider a basic model in which the network is a clique and the update rule (called here the \emph{3-majority dynamics}) of the process is the following: each agent looks at the colors of three random neighbors and then applies the majority rule (breaking ties uniformly). We prove that the process converges in time $\mathcal{O}( \min\{ k, (n/\log n)^{1/3} \} \, \log n )$ with high probability, provided that $s \geqslant c \sqrt{ \min\{ 2k, (n/\log n)^{1/3} \}\, n \log n}$. We then prove that our upper bound above is tight as long as $k \leqslant (n/\log n)^{1/4}$. This fact implies an exponential time-gap between the plurality-consensus process and the \emph{median} process studied by Doerr et al. in [ACM SPAA'11]. A natural question is whether looking at more (than three) random neighbors can significantly speed up the process. We provide a negative answer to this question: In particular, we show that samples of polylogarithmic size can speed up the process by a polylogarithmic factor only.Comment: Preprint of journal versio

Entropy? Honest!

Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with a DESCRIPTION; this count (traditionally expressed in logarithmic form for a number of good reasons) is in essence the number of possibilities---specific instances or "scenarios," that MATCH that description. Very natural (and virtually inescapable) generalizations of the idea of description are the probability distribution and of its quantum mechanical counterpart, the density operator. We track the process of dynamically updating entropy as a system evolves. Three factors may cause entropy to change: (1) the system's INTERNAL DYNAMICS; (2) unsolicited EXTERNAL INFLUENCES on it; and (3) the approximations one has to make when one tries to predict the system's future state. The latter task is usually hampered by hard-to-quantify aspects of the original description, limited data storage and processing resource, and possibly algorithmic inadequacy. Factors 2 and 3 introduce randomness into one's predictions and accordingly degrade them. When forecasting, as long as the entropy bookkeping is conducted in an HONEST fashion, this degradation will ALWAYS lead to an entropy increase. To clarify the above point we introduce the notion of HONEST ENTROPY, which coalesces much of what is of course already done, often tacitly, in responsible entropy-bookkeping practice. This notion, we believe, will help to fill an expressivity gap in scientific discourse. With its help we shall prove that ANY dynamical system---not just our physical universe---strictly obeys Clausius's original formulation of the second law of thermodynamics IF AND ONLY IF it is invertible. Thus this law is a TAUTOLOGICAL PROPERTY of invertible systems!Comment: 27 pages, 11 figures. Published in the journal "Entropy" in June 2016. Abstracts from referee's reports quoted right after the abstrac

Change-centric improvement of team collaboration

In software development, teamwork is essential to the successful delivery of a final product. The software industry has historically built software utilizing development teams that share the workplace. Process models, tools, and methodologies have been enhanced to support the development of software in a collocated setting. However, since the dawn of the 21st century, this scenario has begun to change: an increasing number of software companies are adopting global software development to cut costs and speed up the development process. Global software development introduces several challenges for the creation of quality software, from the adaptation of current methods, tools, techniques, etc., to new challenges imposed by the distributed setting, including physical and cultural distance between teams, communication problems, and coordination breakdowns. A particular challenge for distributed teams is the maintenance of a level of collaboration naturally present in collocated teams. Collaboration in this situation naturally d r ops due to low awareness of the activity of the team. Awareness is intrinsic to a collocated team, being obtained through human interaction such as informal conversation or meetings. For a distributed team, however, geographical distance and a subsequent lack of human interaction negatively impact this awareness. This dissertation focuses on the improvement of collaboration, especially within geographically dispersed teams. Our thesis is that by modeling the evolution of a software system in terms of fine-grained changes, we can produce a detailed history that may be leveraged to help developers collaborate. To validate this claim, we first c r eate a model to accurately represent the evolution of a system as sequences of fine- grained changes. We proceed to build a tool infrastructure able to capture and store fine-grained changes for both immediate and later use. Upon this foundation, we devise and evaluate a number of applications for our work with two distinct goals: 1. To assist developers with real-time information about the activity of the team. These applications aim to improve developers’ awareness of team member activity that can impact their work. We propose visualizations to notify developers of ongoing change activity, as well as a new technique for detecting and informing developers about potential emerging conflicts. 2. To help developers satisfy their needs for information related to the evolution of the software system. These applications aim to exploit the detailed change history generated by our approach in order to help developers find answers to questions arising during their work. To this end, we present two new measurements of code expertise, and a novel approach to replaying past changes according to user-defined criteria. We evaluate the approach and applications by adopting appropriate empirical methods for each case. A total of two case studies – one controlled experiment, and one qualitative user study – are reported. The results provide evidence that applications leveraging a fine-grained change history of a software system can effectively help developers collaborate in a distributed setting

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..