Our goal is to develop the field of graph algorithms for networks. Based on algorithmic graph theory and graph modeling we want to understand what can be done in these large networks and what cannot. Furthermore, we want to derive practical distributed algorithms from known strong theoretical results. Finally, we want to extract possibly new graph problems by focusing on particular applications.

The main goal to achieve in networks are efficient searching of nodes or data, and efficient content transfers. We propose to implement strong theoretical results in that domain to make significant breakthrough in large network algorithms. These results concern small world routing, low stretch routing in doubling metrics and bounded width classes of graphs. They are detailed in the next section. This implies several challenges:

testing our target networks against general graph parameters known to bring theoretically tractability,

implementing strong theoretical results in the dynamic and distributed context of large networks.

A complementary approach consists in studying the combinatorial and graph structures that appear in our target networks. These structures may have inherent characteristics coming from the way the network is formed, or from the design goals of the target application.

Application domains include evaluating Internet performances, the design of new peer-to-peer applications, enabling large scale ad hoc networks and mapping the web.

The application of measuring and modeling Internet metrics such as latencies and bandwidth is to provide tools for optimizing Internet applications. This concerns especially large scale applications such as web site mirroring and peer-to-peer applications.

Peer-to-peer protocols are based on a all equal paradigm that allows to design highly reliable and scalable applications. Besides the file sharing application, peer-to-peer solutions could take over in web content dissemination resistant to high demand bursts or in mobility management. Envisioned peer-to-peer applications include video on demand, streaming, exchange of classified ads,...

Wifi networks have entered our every day life. However, enabling them at large scale is still a challenge. Algorithmic breakthrough in large ad hoc networks would allow to use them in fast and economic deployment of new radio communication systems.

The main application of the web graph structure consists in ranking pages. Enabling site level indexing and ranking is a possible application o f such studies.

In , we investigate the construction of sparse spanners preserving multiple paths.

A result from 2006 about page ranking versus site partition of the web is published this year .

In , we review algorithmic aspects of modular decomposition.

In , we prove an old conjecture about uniqueness of perfect phylogeny tree.

In , we analyze decentralized routing in small-world networks with an arbitrary underlying structure.

In we analyze the bit communication complexity of randomized rumor spreading.

On the one hand, in , we study the impact of degree balancing in de Bruijn-Based Overlay Networks; in the other hand, in we design Tree-Based Multicast Schemes in Peer-to-Peer Overlay Networks.

Consider a distributed network in which
*events*occur at arbitrary nodes and at unpredicted
times. An event occurring at node
uis sensed only by
uwhich in turn may invoke a communication protocol
that allows nodes to exchange messages with their
neighbors. We are interested in the following
*threshold detection (TD)*problem inherent to
distributed computing: Given some threshold
k, the goal of a TD protocol is to broadcast a
*termination*signal when at least
kevents have occurred (throughout the network).

In addition to its potential impact in terms of
improving the performances of XML search engines, our
ancestry scheme is also useful in the context of partially
ordered sets. Specifically, for any fixed integer
k, our scheme enables the construction of a
*universal*poset of size
O(
n^{k}log
^{4
k}n)for the family of
n-element posets with tree-dimension at most
k. This bound is almost tight thanks to a lower bound
of
n^{k-
o(1)}due to Alon and Scheinerman [Order '88].

An
*ancestry labeling scheme*labels the nodes of any tree
in such a way that ancestry queries between any two nodes
can be answered just by looking at their corresponding
labels. The common measure to evaluate the quality of an
ancestry scheme is by its
*label size*, that is the maximum number of bits
stored in a label, taken over all
n-node trees. The design of ancestry labeling schemes
finds applications in XML search engines. In these
contexts, even small improvements in the label size are
important. As a result, following the proposal of a simple
interval based ancestry scheme with label size
2log
nbits (Kannan et al., STOC 88), a
considerable amount of work was devoted to improve the
bound on the label size. The current state of the art upper
bound is
bits (Abiteboul et al., SICOMP 06) which is still
far from the known
log
n+
(loglog
n)lower bound (Alstrup et al.,
SODA 03). Motivated by the fact that typical XML trees have
extremely small depth,
parameterizes the quality
measure of an ancestry scheme not only by the number of
nodes in the given tree but also by its depth. Our main
result is the construction of an ancestry scheme that
labels
n-node trees of depth
dwith labels of size
log
n+ 2log
d+
O(1). In addition to our main
result, we prove a result that may be of independent
interest concerning the existence of a small
*universal graph*for the family of trees with bounded
depth.

Let
fbe a function on pairs of vertices. An
* f-labeling scheme*for a family of graphs
labels the vertices of all graphs in
such that for every graph
and every two vertices

Let
be a family of connected graphs of size at most
nand let
denote the collection of graphs of size at most
n, such that each graph in
is composed of a disjoint union of some graphs in
. We first investigate methods for translating
f-labeling schemes for
to
f-labeling schemes for
. In particular, we show that in many cases, given
an
f-labeling scheme of size
g(
n)for a graph family
, one can construct an
f-labeling scheme of size
g(
n) + loglog
n+
O(1)for
. We also show that in several cases, the above
mentioned extra additive term of
loglog
n+
O(1)is necessary. In addition, we
show that the family of
n-node graphs which are unions of disjoint circles
enjoys an adjacency labeling scheme of size
log
n+
O(1). This illustrates a
non-trivial example showing that the above mentioned extra
additive term is sometimes not necessary.

We then turn to investigate distance labeling schemes on
the class of circles of at most
nvertices and show an upper bound of
1.5log
n+
O(1)and a lower bound of
4/3log
n-
O(1)for the size of any such
labeling scheme.

Previous studies on related questions deal with distributed algorithms that simultaneously compute a configuration and verify that this configuration has a certain desired property. It turns out that this combined approach enables the verification to be less costly sometimes, since the configuration is typically generated so as to be easily verifiable. In contrast, our approach separates the configuration design from the verification. That is, it first generates the desired configuration without bothering with the need to verify it, and then handles the task of constructing a suitable verification scheme. Our approach thus allows for a more modular design of algorithms, and has the potential to aid in verifying properties even when the original design of the structures for maintaining them was done without verification in mind.

We consider asynchronous message-passing systems in
which some links are timely and processes may crash. Each
run defines a timeliness graph among correct processes:
(
p,
q)is an edge of the timeliness
graph if the link from
pto
qis timely (that is, there is a bound on
communication delays from
pto
q). The main goal in
is to approximate this
timeliness graph by graphs having some properties (such as
being trees, rings, ...). Given a family
Sof graphs, for runs such that the timeliness graph
contains at least one graph in
Sthen using an extraction algorithm, each correct
process has to converge to the same graph in
Sthat is, in a precise sense, an approximation of the
timeliness graph of the run. For example, if the timeliness
graph contains a ring, then using an extraction algorithm,
all correct processes eventually converge to the same ring
and in this ring all nodes will be correct processes and
all links will be timely. We first present a general
extraction algorithm and then a more specific extraction
algorithm that is communication efficient (i.e., eventually
all the messages of the extraction algorithm use only links
of the extracted graph).

agreement is possible if (and only
if)
l>3
tin a synchronous model;

agreement is impossible, independently of the number of failures, in an eventually synchronous model;

eventual agreement is possible, if
(and only if)
l>3
t, in an asynchronous
model.

The problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through two different ways: ordering and weighting. Ordering consists in putting a total order on the domain, which induces an orientation between neighboring solutions in a way that prevents circuits from appearing, and then counting only minimal elements. Weighting consists in putting onto each solution a non-negative real value based on its neighborhood in a way that the total weight is at least 1 for each satisfiable instance. In , we investigate the combinatorial properties of these two systems of estimation. First we give some sufficient conditions for a weighting system to be correct, and then we compare it to ordering under different conditions.

For Toeplitz matrices following a higher order three
term recurrence between the main diagonal and 2 other
diagonals
land
rapart, and possibly circulant perturbations, we
extend the kernel method for computing analytically
eigenvectors along their eigenvalues. Unlike, the
tridiagonal case with corner perturbations which involves
sine functions, it is related to the
(
p+ 1,
p)Pascal triangle for the special
cases where the diagonals are respectively at distance
land
r=
plfrom the main diagonal

EnseignantUnivFr[CNRS PRISM, University of Versailles Saint Quentin en Yvelines, France]

Managed by University Paris Diderot, H. Fauconnier is leading this project granting J. Clément from Région Ile de France.

Pierre Fraigniaud is leading an ANR project “blanc” (i.e. fundamental research) about the fundamental aspects of large interaction networks enabling massive distributed storage, efficient decentralized information retrieval, quick inter-user exchanges, and/or rapid information dissemination. The project is mostly oriented towards the design and analysis of algorithms for these (logical) networks, by taking into account proper ties inherent to the underlying infrastructures upon which they are built. The infrastructures and/or overlays considered in this project are selected from different contexts, including communication networks (from Internet to sensor networks), and societal networks (from the Web to P2P networks).

Managed by University Paris Diderot, P. Fraigniaud leads this project.

Managed by University Paris Diderot, H. Fauconnier leads this project that grants H. Tran.

EULER is a 3-year STREP Project targeting Challenge 1 "Technologies and systems architectures for the Future Internet" of the European Commission (EC) Seventh Framework Programme (FP7). The project scope and methodology position within the FIRE (Future Internet Research and Experimentation) Objective ICT-2009.1.6 Part b: Future Internet experimentally-driven research .

The main objective of the EULER exploratory research project is to investigate new routing paradigms so as to design, develop, and validate experimentally a distributed and dynamic routing scheme suitable for the future Internet and its evolution. The resulting routing scheme(s) is/are intended to address the fundamental limits of current stretch-1 shortest-path routing in terms of routing table scalability but also topology and policy dynamics (perform efficiently under dynamic network conditions). Therefore, this project will investigate trade-offs between routing table size (to enhance scalability), routing scheme stretch (to ensure routing quality) and communication cost (to efficiently and timely react to various failures). The driving idea of this research project is to make use of the structural and statistical properties of the Internet topology (some of which are hidden) as well as the stability and convergence properties of the Internet policy in order to specialize the design of a distributed routing scheme known to perform efficiently under dynamic network and policy conditions when these properties are met. The project will develop new models and tools to exhaustively analyse the Internet topology, to accurately and reliably measure its properties, and to precisely characterize its evolution. These models, that will better reflect the network and its policy dynamics, will be used to derive useful properties and metrics for the routing schemes and provide relevant experimental scenarios. The project will develop appropriate tools to evaluate the performance of the proposed routing schemes on large-scale topologies (order of 10k nodes). Prototype of the routing protocols as well as their functional validation and performance benchmarking on the iLAB experimental facility and/or virtual experimental facilities such as PlanetLab/OneLab will allow validating under realistic conditions the overall behaviour of the proposed routing schemes.

More information at
http://

Laurent Viennot is a scientific editor of the )i(nterstices ( http://interstices.info/) vulgarization site initiated by Inria in collaboration with french universities and Cnrs. He has written an article on the differences between the web and internet.

Michel Habib is member of the steering committee of STACS (Symposium on Theoretical Aspects of Computer Science) and also of WG (International Workshop on Graph-Theoretic Concepts in Computer Science).

Michel Habib is in charge of a course entitled “graph algorithms”. Pierre Fraigniaud is in charge of the course “Algorithmique distribuée pour les réseaux”. Laurent Viennot is teaching “Networks and geometry“.

Yacine Boufkhad is teaching scientific computer science and networks (192 hours);

Fabien de Montgolfier is teaching foundation of computer science, algorithmics, and computer architecture (192 hours);

Fabien de Montgolfier is teaching P2P theory and application;

Michel Habib is in charge of two courses untitled: Search Engines; Parallelism and mobility, which includes peer-to-peer overlay networks.

Thomas Hugel
*Estimations de satisfaisabilité*Jury: Advisors
(Directeurs): Y. Boufkhad, M. Habib, Reviewers
(Rapporteurs): N. Creignou, L. Kirousis, Examiners
(Examinateurs): A. Durand, M. Mézard.

Hoang Anh Phan
*Equilibrage de charge et diffusion multicast dans
les systèmes pair-à-pair*Jury: Advisor (Directeur):
P. Fraigniaud, Reviewers (Rapporteurs): S. Tixeuil, D.
Trystram, Examiners (Examinateurs): F. Mathieu, L.
Viennot.

Hung Tran has begun its PhD since
january 2010
*Failure detection with Byzantine adversary*. His
advisors are Hugues Fauconnier and Carole Delporte.
Hung Tran has a grant from ANR VERSO Shaman.

Mauricio Soto
*Algorithmes de pair à pair et analyse de la
structure d'Internet*(Chile-France Allocation).

Heger Arfaoui
*Distributed Computational Complexity*

Hervé Baumann
*protocoles d'échange dans les réseaux
distribués*.

Xavier Koegler
*Population protocols*

Antoine Mamcarz
*Algorithmes de décomposition pour les grands
graphes*(CNRS grant)

Julien Clément is in PostDoc (november 2009-november 2011). He works on sensor network and has a grant from Région Ile de France.

George Giakkoupis works on small world algorithmic aspects and communication complexity.