71 research outputs found
On Fast and Robust Information Spreading in the Vertex-Congest Model
This paper initiates the study of the impact of failures on the fundamental
problem of \emph{information spreading} in the Vertex-Congest model, in which
in every round, each of the nodes sends the same -bit message
to all of its neighbors.
Our contribution to coping with failures is twofold. First, we prove that the
randomized algorithm which chooses uniformly at random the next message to
forward is slow, requiring rounds on some graphs, which we
denote by , where is the vertex-connectivity.
Second, we design a randomized algorithm that makes dynamic message choices,
with probabilities that change over the execution. We prove that for
it requires only a near-optimal number of rounds, despite a
rate of failures per round. Our technique of choosing
probabilities that change according to the execution is of independent
interest.Comment: Appears in SIROCCO 2015 conferenc
Pulse propagation, graph cover, and packet forwarding
We study distributed systems, with a particular focus on graph problems and fault tolerance. Fault-tolerance in a microprocessor or even System-on-Chip can be improved by using a fault-tolerant pulse propagation design. The existing design TRIX achieves this goal by being a distributed system consisting of very simple nodes. We show that even in the typical mode of operation without faults, TRIX performs significantly better than a regular wire or clock tree: Statistical evaluation of our simulated experiments show that we achieve a skew with standard deviation of O(log log H), where H is the height of the TRIX grid. The distance-r generalization of classic graph problems can give us insights on how distance affects hardness of a problem. For the distance-r dominating set problem, we present both an algorithmic upper and unconditional lower bound for any graph class with certain high-girth and sparseness criteria. In particular, our algorithm achieves a O(r·f(r))-approximation in time O(r), where f is the expansion function, which correlates with density. For constant r, this implies a constant approximation factor, in constant time. We also show that no algorithm can achieve a (2r + 1 − δ)-approximation for any δ > 0 in time O(r), not even on the class of cycles of girth at least 5r. Furthermore, we extend the algorithm to related graph cover problems and even to a different execution model. Furthermore, we investigate the problem of packet forwarding, which addresses the question of how and when best to forward packets in a distributed system. These packets are injected by an adversary. We build on the existing algorithm OED to handle more than a single destination. In particular, we show that buffers of size O(log n) are sufficient for this algorithm, in contrast to O(n) for the naive approach.Wir untersuchen verteilte Systeme, mit besonderem Augenmerk auf Graphenprobleme und Fehlertoleranz. Fehlertoleranz auf einem System-on-Chip (SoC) kann durch eine fehlertolerante Puls- Weiterleitung verbessert werden. Das bestehende Puls-Weiterleitungs-System TRIX toleriert Fehler indem es ein verteiltes System ist das nur aus sehr einfachen Knoten besteht. Wir zeigen dass selbst im typischen, fehlerfreien Fall TRIX sich weitaus besser verhält als man naiverweise erwarten würde: Statistische Analysen unserer simulierten Experimente zeigen, dass der Verzögerungs-Unterschied eine Standardabweichung von lediglich O(log logH) erreicht, wobei H die Höhe des TRIX-Netzes ist. Das Generalisieren einiger klassischer Graphen-Probleme auf Distanz r kann uns neue Erkenntnisse bescheren über den Zusammenhang zwischen Distanz und Komplexität eines Problems. Für das Problem der dominierenden Mengen auf Distanz r zeigen wir sowohl eine algorithmische obere Schranke als auch eine bedingungsfreie untere Schranke für jede Klasse von Graphen, die bestimmte Eigenschaften an Umfang und Dichte erfüllt. Konkret erreicht unser Algorithmus in Zeit O(r) eine Annäherungsgüte von O(r · f(r)). Für konstante r bedeutet das, dass der Algorithmus in konstanter Zeit eine Annäherung konstanter Güte erreicht. Weiterhin zeigen wir, dass kein Algorithmus in Zeit O(r) eine Annäherungsgüte besser als 2r + 1 erreichen kann, nicht einmal in der Klasse der Kreis-Graphen von Umfang mindestens 5r. Weiterhin haben wir das Paketweiterleitungs-Problem untersucht, welches sich mit der Frage beschäftigt, wann genau Pakete in einem verteilten System idealerweise weitergeleitetwerden sollten. Die Paketewerden dabei von einem Gegenspieler eingefügt. Wir bauen auf dem existierenden Algorithmus OED auf, um mehr als ein Paket-Ziel beliefern zu können. Dadurch zeigen wir, dass Paket-Speicher der Größe O(log n) für dieses Problem ausreichen, im Gegensatz zu den Paket-Speichern der Größe O(n) die für einen naiven Ansatz nötig wären
Broadcast CONGEST Algorithms against Adversarial Edges
We consider the corner-stone broadcast task with an adaptive adversary that
controls a fixed number of edges in the input communication graph. In this
model, the adversary sees the entire communication in the network and the
random coins of the nodes, while maliciously manipulating the messages sent
through a set of edges (unknown to the nodes). Since the influential work
of [Pease, Shostak and Lamport, JACM'80], broadcast algorithms against
plentiful adversarial models have been studied in both theory and practice for
over more than four decades. Despite this extensive research, there is no round
efficient broadcast algorithm for general graphs in the CONGEST model of
distributed computing. We provide the first round-efficient broadcast
algorithms against adaptive edge adversaries. Our two key results for -node
graphs of diameter are as follows:
1. For , there is a deterministic algorithm that solves the problem
within rounds, provided that the graph is 3
edge-connected. This round complexity beats the natural barrier of
rounds, the existential lower bound on the maximal length of edge-disjoint
paths between a given pair of nodes in . This algorithm can be extended to a
-round algorithm against adversarial edges in
edge-connected graphs.
2. For expander graphs with minimum degree of , there is
an improved broadcast algorithm with rounds against
adversarial edges. This algorithm exploits the connectivity and conductance
properties of G-subgraphs obtained by employing the Karger's edge sampling
technique.
Our algorithms mark a new connection between the areas of fault-tolerant
network design and reliable distributed communication.Comment: accepted to DISC2
Only Time Will Tell: Modelling Information Diffusion in Code Review with Time-Varying Hypergraphs
Background: Modern code review is expected to facilitate knowledge sharing:
All relevant information, the collective expertise, and meta-information around
the code change and its context become evident, transparent, and explicit in
the corresponding code review discussion. The discussion participants can
leverage this information in the following code reviews; the information
diffuses through the communication network that emerges from code review.
Traditional time-aggregated graphs fall short in rendering information
diffusion as those models ignore the temporal order of the information
exchange: Information can only be passed on if it is available in the first
place.
Aim: This manuscript presents a novel model based on time-varying hypergraphs
for rendering information diffusion that overcomes the inherent limitations of
traditional, time-aggregated graph-based models.
Method: In an in-silico experiment, we simulate an information diffusion
within the internal code review at Microsoft and show the empirical impact of
time on a key characteristic of information diffusion: the number of reachable
participants.
Results: Time-aggregation significantly overestimates the paths of
information diffusion available in communication networks and, thus, is neither
precise nor accurate for modelling and measuring the spread of information
within communication networks that emerge from code review.
Conclusion: Our model overcomes the inherent limitations of traditional,
static or time-aggregated, graph-based communication models and sheds the first
light on information diffusion through code review. We believe that our model
can serve as a foundation for understanding, measuring, managing, and improving
knowledge sharing in code review in particular and information diffusion in
software engineering in general.Comment: 10 pages, 6 figure
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