Réunion Aussois
du 25 au 27 mars 2015
Réunion Aussois
du 25 au 27 mars 2015
mars 2015
Mercredi 25 mars (Chairman : Achour Mostefaoui)
x 12:30 - 14:00 Déjeuner
x 14:00 - 14:45 Cyril Gavoille : Calculer les distances dans un graphe en
temps constant avec des étiquettes de 0.793n bits
x 14:45 - 15:30 Reut Levi : Constructing Near Spanning Trees with Few Local
x 15:30 - 16:00 Pause café
x 16:00 - 16:45 Alessia Milani : An introduction to Software Transactional
x 16:45 - 17:30 Matthieu Perrin : Update Consistency for Wait-free Concurrent
x 19:00 - 20:00 Apéritif
x 20:00 - 22:00 Diner
Jeudi 26 mars (Chairman : David Ilcinkas)
x 9:00 - 9:45 Yves Métivier : A Distributed Enumeration Algorithm and
Applications to All Pairs Shortest Paths, Diameter...
x 9:45 - 10:30 Moti Medina : Best of Two Local Models: Local Centralized
and Local Distributed Algorithms
x 10:30 - 11:15 Paolo Penna : Logit Dynamics with Concurrent Updates
x 11:15 - 17:00 Ski / réunion de travail
x 19:00 - 20:00 Apéritif
x 20:00 - 22:00 Diner
Vendredi 27 mars (Chairman : Pierre Fraigniaud)
x 9:00 - 9:45 George Giakkoupis : Randomized mutual exclusion with constant
x 9:45 - 10:30 Nicolas Hanusse: Peut-on router dans Internet avec des tables
de routage d'au plus 5 entrées ?
x 10:30 - 11:00 Pause Café
x 11:00 - 11:45 Adrian Kosowski : Discrete Lotka-Volterra Population Protocols:
Convergence, Majority Amplification, and
Equity for Under-Represented Minorities
x 11:45 - 13:15 Déjeuner
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Résumés:
Cyril Gavoille
Calculer les distances dans un graphe en temps constant avec des étiquettes de
0.793n bits.
Dans cet exposé je présenterai une structure de données compacte permettant de
calculer en temps constant la distance entre n'importe quelle paire de sommets
d'un graphe arbitraire à n sommets. Cette structure de données se présente sous
forme d'étiquette associée à chacun des sommets, la distance entre les u et v
étant décodée à partir d'un calcul impliquant seulement les étiquettes de u et
de v. La solution triviale, à l'aide d'un vecteur de distances de taille n,
produit des étiquettes de nlogn bits. En fait, aucune technique utilisant
o(nlogn) bits et décodant en temps constant n'est connue. Cependant, si on
relâche la contrainte du décodage en temps constant, des solutions avec O(n)
bits existent. Une des meilleures d'entres elles utilisent 11n bits pour un
décodage O(logn). Notre solution réduit la taille des étiquettes à 0.793n bits
avec un décodage constant et s'étend naturellement aux graphes valués.
Reut Levi
Constructing Near Spanning Trees with Few Local Inspections
Constructing a spanning tree of a graph is probably the most basic task in graph
theory. Motivated by several recent studies of local graph algorithms, we
consider the following problem: given a connected bounded-degree graph $G$, can
one construct a connected subgraph $G'$ consisting of $n+o(n)$ edges, where
given an edge $e$, the algorithm should decide whether $e \in G'$ by inspecting
only a {\em constant} number of edges of $G$? Our main results are:
- We show that if every $t$-vertex subgraph of $G$ has expansion $1/(\log
t)^{1+o(1)}$ then one can (deterministically) construct a sparse spanning
subgraph $G'$ of $G$ using few inspections. To this end we analyze a ``local''
version of a famous minimum-weight spanning tree algorithm.
- We show that the above expansion requirement is sharp even when allowing
randomization. To this end we construct a family of $3$-regular graphs of high
girth, in which every $t$-vertex subgraph has expansion $1/(\log t)^{1-o(1)}$.
Alessia Milani
An introduction to Software Transactional Memory
Software Transactional memory (or STM for short) is a promising programming
paradigm that aims at simplifying concurrent programming by using the notion of
a transaction. A transaction executes a piece of code containing accesses to
data items which are shared by several processes in a concurrent setting. By
using transactions, the programmer needs only enhance its sequential code with
invocations of special operations to read or write data items. It is guaranteed
that if any operation of a transaction takes place, they all do, and that if
they do, they appear to other threads to do so atomically, as one indivisible
operation.
In this talk, I will present the STM paradigm and the main algorithmic
techniques to implement it.
Matthieu Perrin
Update Consistency for Wait-free Concurrent Objects
In large scale systems such as the Internet, replicating data is an essential
feature in order to provide availability and fault-tolerance. Attiya and Welch
proved that using strong consistency criteria such as atomicity is costly as
each operation may need an execution time linear with the latency of the
communication network. Weaker consistency criteria like causal consistency and
PRAM consistency do not ensure convergence. The different replicas are not
guaranteed to converge towards a unique state. Eventual consistency guarantees
that all replicas eventually converge when the participants stop
updating. However, it fails to fully specify the semantics of the operations on
shared objects and requires additional non-intuitive and error-prone distributed
specification techniques.
This talk will introduce and formalize a new consistency criterion, called
"update consistency", that requires the state of a replicated object to be
consistent with a linearization of all the updates. In other words, whereas
atomicity imposes a linearization of all of the operations, this criterion
imposes this only on updates. Consequently some read operations may return
out-dated values. Update consistency is stronger than eventual consistency, so
we can replace eventually consistent objects with update consistent ones in any
program. Finally, update consistency is universal, in the sense that any object
can be implemented under this criterion in a distributed system where any number
of nodes may crash.
Yves Métivier
A Distributed Enumeration Algorithm and Applications to All Pairs
Shortest Paths, Diameter...
We consider the standard message passing model; we assume the system is fully
synchronous: all processes start at the same time and time proceeds in
synchronised rounds. In each round each vertex can transmit a different message
of size $O(1)$ to each of its neighbours. This paper proposes and analyses a
distributed enumeration algorithm of vertices of a graph having a distinguished
vertex which satisfies that two vertices with consecutive numbers are at
distance at most $3$. We prove that its time complexity is $O(n)$ where $n$ is
the number of vertices of the graph. Furthermore, the size of each message is
$O(1)$ thus its bit complexity is also $O(n).$ We provide some links between
this enumeration and Hamiltonian graphs from which we deduce that this
enumeration is optimal in the sense that there does not exist an enumeration
which satisfies that two vertices with consecutive numbers are at distance at
most $2$.
We deduce from this enumeration, algorithms which compute all pairs shortest
paths and the diameter with a time complexity and a bit complexity equal to
$O(n)$. This improves the best known distributed algorithms (under the same
hypotheses) for computing all pairs shortest paths or the diameter presented by
Peleg, Roditty and Tal and and by Holzer and Wattenhofer having a time
complexity equal to $O(n)$ and which use messages of size $O(\log n)$ bits.
Moti Medina
Best of Two Local Models: Local Centralized and Local Distributed Algorithms
We consider two models of computation: centralized local algorithms and local
distributed algorithms. Algorithms in one model are adapted to the other model
to obtain improved algorithms. Distributed vertex coloring is employed to
design improved centralized local algorithms for: maximal independent set,
maximal matching, and an approximation scheme for maximum (weighted) matching
over bounded degree graphs. The improvement is threefold: the algorithms are
deterministic, stateless, and the number of probes grows polynomially in log^∗n,
where n is the number of vertices of the input graph. The recursive centralized
local improvement technique by Nguyen and Onak~\cite{onak2008} is employed to
obtain an improved distributed approximation scheme for maximum (weighted)
matching. The improvement is twofold: we reduce the number of rounds from O(log
n) to O(log^∗n) for a wide range of instances and, our algorithms are
deterministic rather than randomized.
Paolo Penna
Logit Dynamics with Concurrent Updates
In this talk I will discuss results on a family of noisy best-response dynamics
used to model players bounded rationality. In these dynamics, the higher the
payoff derived from a strategy the higher the probability that the player will
actually choose that strategy. For the class of potential games, the stationary
distribution has a simple closed formula (Blume '93,'97), which describes the
long term behavior of the system. This type of results is based on a particular
"schedule" of the player, that is, the process consists of selecting *one*
player uniformly at random for updating his/her strategy.
It is therefore natural to ask if the system behavior changes significantly when
a different "schedule" is adopted (still selected players update their
strategies according to the same noisy best response). In particular, in this
talk I will present an extreme case in which *all* players update their
strategies simultaneously (i.e. in parallel).
We shall see two results that relate this dynamics to the one introduced by
Blume:
(1) A certain reversibility condition of the process is equivalent to a class of
local interaction games, in which players are nodes of a "social" graph and they
play some potential game with each of the neighbors.
(2) Though the stationary distribution changes when considering parallel
updates, what we "observe" in the two dynamics is essentially the same if the
social graph is "close" to bipartite.
This is a joint work with Vincenzo Auletta, Diodato Ferraioli, Francesco
Pasquale, and Giuseppe Persiano.
George Giakkoupis
Randomized mutual exclusion with constant amortized RMR complexity
In this paper we settle an open question by determining the remote memory
reference (RMR) complexity of randomized mutual exclusion, on the distributed
shared memory model (DSM) with atomic registers, in a weak but natural (and
stronger than oblivious) adversary model. In particular, we present a mutual
exclusion algorithm that has constant expected amortized RMR complexity and is
deterministically deadlock free. Prior to this work, no randomized algorithm
with o(log n/ log log n) RMR complexity was known for the DSM model. Our
algorithm is fairly simple, and compares favorably with one by Bender and
Gilbert (FOCS 2011) for the CC model, which has expected amortized RMR
complexity O(log^2 log n) and provides only probabilistic deadlock freedom.
Nicolas Hanusse
Peut-on router dans Internet avec des tables de routage d'au plus 5 entrées ?
Les schémas de routage compact ont pour objectif de proposer des solutions de
routage avec des tables de routage de taille sous-linéaire par rapport au nombre
de routeurs N et garantissant des chemins de longueurs proches des plus courts
chemins. Le meilleur schéma de routage compact générique existant utilisent des
tables N^1/2 et garanti 3 fois les plus courts chemins. Nous proposons un schéma
de routage spécialisé pour les graphes sans-échelle qui sont représentatifs des
réseaux réels ainsi que sa construction distribuée. Pour une famille de graphes
aléatoires en loi de puissance, nous pouvons garantir des tables beaucoup plus
petites que le schéma générique sans détériorer significativement l'étirement
des routage. L'exposé indiquera la pertinence de notre schéma sur plusieurs
topologies.
Adrian Kosowski
Discrete Lotka-Volterra Population Protocols: Convergence, Majority Amplification, and Equity for Under-Represented Minorities
In this talk we consider a natural class of population protocols whose dynamics
are modelled by the discrete version of Lotka-Volterra equations. In such
protocols, when an agent $a$ of type (species) $i$ interacts with an agent $b$
of type (species) $j$ with $a$ as the initiator, then $b$'s type becomes $i$
with probability $P_{ij}$. In such an interaction, we think of $a$ as the
predator, $b$ as the prey, and the type of the prey is either converted to that
of the predator or stays as is. Such protocols capture the dynamics of some
opinion spreading models and generalize the well-known Rock-Paper-Scissors
discrete dynamics.
We start by considering the convergence time and show that any
Lotka-Volterra-type protocol on an $n$-agent population converges to some
absorbing state in time polynomial in $n$, w.h.p., when any pair of agents is
allowed to interact. By contrast, when the interaction graph is a star, even the
Rock-Paper-Scissors protocol requires exponential time to converge. We then
study threshold effects exhibited by Lotka-Volterra-type protocols with 3 and
more species under interactions between any pair of agents, giving examples of
protocols which achieve ``majority amplification'' and ``coin-flip consensus''
effects in a distributed system. Some of our techniques may be of independent
value.
Programme