Graph algorithms

Graph Decompositions

We study new decompositions schemes such as 2-join, skew partitions and others partition problems. These graph decompositions appeared in the structural graph theory and are the basis of some well-known theorems such as the Perfect Graph Theorem. For these decompositions there is a lack of efficient algorithms. We aim at designing algorithms working in $O\left(nm\right)$ since we think that this could be a lower bound for these decompositions.

Graph Search

We more deeply study multi-sweep graph searches. In this domain a graph search only yields a total ordering of the vertices which can be used by the subsequent graph searches. This technique can be used on huge graphs and do not need extra memory. We already have obtained preliminary results in this direction and many well-known graph algorithms can be put in this framework. The idea behind this approach is that each sweep discovers some structure of the graph. At the end of the process either we have found the underlying structure ( for example an interval representation for an interval graph) or an approximation of it (for example in hard discrete optimization problems). Application to exact computations of centers in huge graphs, to underlied combinatorial optimization problems, but also to networks arising in Biology.

Distributed computing

The distributed community can be viewed as the union of two sub-communities. This is true even in our team. Even though they are not completely disjoint, they are disjoint enough not to leverage each other’s results. At a high level, one is mostly interested in timing issues (clock drifts, link delays, crashes, etc.) while the other one is mostly interested in spatial issues (network structure, memory requirements, etc.). Indeed, one sub-community is mostly focusing on the combined impact of asynchronism and faults on distributed computation, while the other addresses the impact of network structural properties on distributed computation. Both communities address various forms of computational complexities, through the analysis of different concepts. This includes, e.g., failure detectors and wait-free hierarchy for the former community, and compact labeling schemes and computing with advice for the latter community. We have the ambitious project to achieve the reconciliation between the two communities by focusing on the same class of problems, the yes/no-problems, and establishing the scientific foundations for building up a consistent theory of computability and complexity for distributed computing. The main question addressed is therefore: is the absence of globally coherent computational complexity theories covering more than fragments of distributed computing, inherent to the field? One issue is obviously the types of problems located at the core of distributed computing. Tasks like consensus, leader election, and broadcasting are of very different nature. They are not yes-no problems, neither are they minimization problems. Coloring and Minimal Spanning Tree are optimization problems but we are often more interested in constructing an optimal solution than in verifying the correctness of a given solution. Still, it makes full sense to analyze the yes-no problems corresponding to checking the validity of the output of tasks. Another issue is the power of individual computation. The FLP impossibility result as well as Linial’s lower bound hold independently from the individual computational power of the involved computing entities. For instance, the individual power of solving NP-hard problems in constant time would not help overcoming these limits which are inherent to the fact that computation is distributed. A third issue is the abundance of models for distributed computing frameworks, from shared memory to message passing, spanning all kinds of specific network structures (complete graphs, unit-disk graphs, etc.) and or timing constraints (from complete synchronism to full asynchronism). There are however models, typically the wait-free model and the LOCAL model, which, though they do not claim to reflect accurately real distributed computing systems, enable focusing on some core issues. Our research program is ongoing to carry many important notions of Distributed Computing into a standard computational complexity.

A Peer-to-Peer approach to future content Distribution

Unexpectedly, the field of P2P applications is still growing and challenging issues remain worth studying.

New network models

The new models that have been proposed to take into account the evolution of network architecture and usage indicate new opportunities for P2P, like the possibility to have superscalable systems whose performance increases with the popularity. This surprising property, if it can be enforced, will give P2P an additional asset compared to the current situation. However, this results are still at an early stage, and it is planned to continue the study from a theoretical point of view, but also with experimentations with emulation and/or simulation of future networks on large grids.

P2P storage

The challenges of a persistent and robust distributed storage with respect to failures are nowadays relatively well understood. However, the results about instant availability are still not completely understood: how to give guarantees, in a P2P system where peers are not online 100% of the time, that a content will be available when its owner asks for it? Can we propose some allocation policy that ensures maximal availability with only a partial knowledge of online patterns? We believe that these issues, halfway between failure tolerance and opportunistic networks, are still promising.

Caching allocation

Today, most of content distribution is ensured by so-called Content Distribution Networks (CDNs). It is expected that caching techniques will remain a hot topic in the years to come, for instance through the studies related to Content Centric Networking, which is inspired by P2P content distribution paradigms, like using so-called chunks as the basic data exchange unit. Many challenges in this field are related to dimensioning and caching strategies. In GANG, we aim at conducting a study centered on the trade-offs between storage and bandwidth usage. Note that many studies have been/are realized on this topic, mostly rely on operational research methodology and offer solutions that can sometimes be difficult to use in practice. GANG uses a different approach, based on alternate modeling assumptions inherited from our previous achievments on bandwidth dimensioning. The goal of this complementary approach is to provide simple dimensioning guidelines while giving approximated, yet meaningful, performance evaluation.

Long term perspective on P2P content distribution

The success of YouTube-like delivery platforms (YouTube, DailyMotion...) does not come only from their technical performances, but from the ergonomy: these platforms allow to launch a video directly from one’s browser, without the usual burden that comes with traditional P2P applications (install a specific client, open incoming ports, find .torrent files . . . ). It is therefore important to keep working on basic P2P research, especially as many challenges are still open (see above), and new opportunities are likely to rise. First, advances in other fields may make P2P more interesting than other solutions –again. For instance, CCN protocols are designed to facilitate data dissemination. One could hope they open the way to CCN-assisted P2P protocols, where both the issues of ergonomy and network burden would be taken care of by design. Unpredictable events, such as emerging/closing centralized filesharing services, can also change the power balance very fast with effects that are still hard to determine. For all these reasons, GANG aims at improving its expertise in the field of decentralized content distribution, even if it is quite difficult at the fast evolving current time to tell if that expertise should apply on traditional P2P, CCN, Cloud... architectures, or on any hybridation of these.