A note on uniform power connectivity in the SINR model

In this paper we study the connectivity problem for wireless networks under the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio transmitters distributed in some area, we seek to build a directed strongly connected communication graph, and compute an edge coloring of this graph such that the transmitter-receiver pairs in each color class can communicate simultaneously. Depending on the interference model, more or less colors, corresponding to the number of frequencies or time slots, are necessary. We consider the SINR model that compares the received power of a signal at a receiver to the sum of the strength of other signals plus ambient noise . The strength of a signal is assumed to fade polynomially with the distance from the sender, depending on the so-called path-loss exponent $\alpha$. We show that, when all transmitters use the same power, the number of colors needed is constant in one-dimensional grids if $\alpha>1$ as well as in two-dimensional grids if $\alpha>2$. For smaller path-loss exponents and two-dimensional grids we prove upper and lower bounds in the order of $\mathcal{O}(\log n)$ and $\Omega(\log n/\log\log n)$ for $\alpha=2$ and $\Theta(n^{2/\alpha-1})$ for $\alpha<2$ respectively. If nodes are distributed uniformly at random on the interval $[0,1]$, a \emph{regular} coloring of $\mathcal{O}(\log n)$ colors guarantees connectivity, while $\Omega(\log \log n)$ colors are required for any coloring.Comment: 13 page

You Only Live Multiple Times: A Blackbox Solution for Reusing Crash-Stop Algorithms In Realistic Crash-Recovery Settings

Distributed agreement-based algorithms are often specified in a crash-stop asynchronous model augmented by Chandra and Toueg\u27s unreliable failure detectors. In such models, correct nodes stay up forever, incorrect nodes eventually crash and remain down forever, and failure detectors behave correctly forever eventually, However, in reality, nodes as well as communication links both crash and recover without deterministic guarantees to remain in some state forever. In this paper, we capture this realistic temporary and probabilitic behaviour in a simple new system model. Moreover, we identify a large algorithm class for which we devise a property-preserving transformation. Using this transformation, many algorithms written for the asynchronous crash-stop model run correctly and unchanged in real systems

CryptoConcurrency: (Almost) Consensusless Asset Transfer with Shared Accounts

A typical blockchain protocol uses consensus to make sure that mutually mistrusting users agree on the order in which their operations on shared data are executed. It is known, however, that asset transfer systems, by far the most popular application of blockchains, can be implemented without consensus. Assuming that no account can be accessed concurrently, i.e., that every account belongs to a single owner, one can efficiently implement an asset transfer system in a purely asynchronous, consensus-free manner. It has been also shown that asset transfer with shared accounts is impossible to implement without consensus. In this paper, we propose CryptoConcurrency, an asset transfer protocol that allows concurrent accesses to be processed in parallel, without involving consensus, whenever possible. More precisely, if concurrent transfer operations on a given account do not lead to overspending, i.e., can all be applied without the account balance going below zero, they proceed in parallel. Otherwise, the account's owners may have to access an external consensus object. We allow each account to use its own consensus implementation, which only the owners of this account trust

Permissionless and Asynchronous Asset Transfer

Most modern asset transfer systems use consensus to maintain a totally ordered chain of transactions. It was recently shown that consensus is not always necessary for implementing asset transfer. More efficient, asynchronous solutions can be built using reliable broadcast instead of consensus. This approach has been originally used in the closed (permissioned) setting. In this paper, we extend it to the open (permissionless) environment. We present {Pastro}, a permissionless and asynchronous asset-transfer implementation, in which quorum systems, traditionally used in reliable broadcast, are replaced with a weighted Proof-of-Stake mechanism. {Pastro} tolerates a dynamic adversary that is able to adaptively corrupt participants based on the assets owned by them

Core-Periphery in Networks: An Axiomatic Approach

Recent evidence shows that in many societies worldwide the relative sizes of the economic and social elites are continuously shrinking. Is this a natural social phenomenon? What are the forces that shape this process? We try to address these questions by studying a Core-Periphery social structure composed of a social elite, namely, a relatively small but well-connected and highly influential group of powerful individuals, and the rest of society, the periphery. Herein, we present a novel axiom-based model for the forces governing the mutual influences between the elite and the periphery. Assuming a simple set of axioms, capturing the elite's dominance, robustness, compactness and density, we are able to draw strong conclusions about the elite-periphery structure. In particular, we show that a balance of powers between elite and periphery and an elite size that is sub-linear in the network size are universal properties of elites in social networks that satisfy our axioms. We note that the latter is in controversy to the common belief that the elite size converges to a linear fraction of society (most recently claimed to be 1%). We accompany these findings with a large scale empirical study on about 100 real-world networks, which supports our results