A note on the data-driven capacity of P2P networks

We consider two capacity problems in P2P networks. In the first one, the nodes have an infinite amount of data to send and the goal is to optimally allocate their uplink bandwidths such that the demands of every peer in terms of receiving data rate are met. We solve this problem through a mapping from a node-weighted graph featuring two labels per node to a max flow problem on an edge-weighted bipartite graph. In the second problem under consideration, the resource allocation is driven by the availability of the data resource that the peers are interested in sharing. That is a node cannot allocate its uplink resources unless it has data to transmit first. The problem of uplink bandwidth allocation is then equivalent to constructing a set of directed trees in the overlay such that the number of nodes receiving the data is maximized while the uplink capacities of the peers are not exceeded. We show that the problem is NP-complete, and provide a linear programming decomposition decoupling it into a master problem and multiple slave subproblems that can be resolved in polynomial time. We also design a heuristic algorithm in order to compute a suboptimal solution in a reasonable time. This algorithm requires only a local knowledge from nodes, so it should support distributed implementations. We analyze both problems through a series of simulation experiments featuring different network sizes and network densities. On large networks, we compare our heuristic and its variants with a genetic algorithm and show that our heuristic computes the better resource allocation. On smaller networks, we contrast these performances to that of the exact algorithm and show that resource allocation fulfilling a large part of the peer can be found, even for hard configuration where no resources are in excess.Comment: 10 pages, technical report assisting a submissio

Morphologie des ensembles ordonnés (répercussions algorithmiques)

Cette thèse traite de l'étude morphologique et algorithmique des ordres finis. Dans un premier temps, on étudie la notion de St-série décomposition qui induit une famille partitive sur ses éléments constituée de trois sous-ensembles, dont deux, non vides, engendrent un sous-ordre décomposable par composition série, tandis que l'autre ensemble induit une antichaîne. On obtient ainsi une caractérisation inductive des ordres d'intervalles. Dans un second temps, on s'intéresse à la classe des ordres chaîne dominés, i.e. des ordres admettant une famille partitive constituée de deux ensembles, l'un induisant une chaîne et l'autre induisant un stable dans leur graphe de couverture. Dans un troisième temps, on considère la notion d'extension respectueuse d'un ordre, c'est-à-dire que l'on étudie le non abritement d'un ordre dans un ordre cible à travers la préservation de cette caractéristique sur les extensions de l'ordre cible.This thesis deals with morphologic and algorithmic studies of finite posets. Firstly, we are interested in the notion of St-serie decomposition, that is a generalization of serie decomposition. A St-serie decomposition of an order induces a partition of its elements in three subsets. Two of them, which must be none void, give a suborder decomposable by serie composition, and the last one induces an antichain. This decomposition permits to have an inductive characterization of interval orders. Secondly, we investigate the class of chain dominated orders, those orders have a partitions of its elements in two subsets, one inducing a chain and the other inducing a stable set in their covering graph. Finally, we consider the notion of faithfull extension of an order, that is we study the none embedding of this order into a guest order through the preservation of this characteristic on the extensions of the guest orders.NANTES-BU Sciences (441092104) / SudocSudocFranceF

Inductive Characterizations of Finite Interval Orders and Semiorders

International audienc

Query range problem in wireless sensor networks

International audienceWireless sensor networks with multiple users extracting data directly from nearby sensors have many potential applications. An important problem in such a network is how to allocate the multi-hop query range for each user such that a certain global optimality is achieved. We introduce this problem and show it is NP-complete in its generic form. Distributed heuristic is proposed and evaluated with simulations. Interesting behaviors of the network when optimized with different global objectives are observed from the simulation results

Optimizing resource sharing in node-capacitated overlay networks

International audienceA frequently occurring problem in the field of distributed systems is to determine an allocation of a generic resource so that the demand of every node in the system is fulfilled. Node-capacitated graphs, i.e. graphs where the weight of a node corresponds to the amount of resources it can give to the system, provide an appealing model that can be readily applied to real-world applications, such as peer-to-peer and grid-based systems. In this paper, we propose a model for this problem and show that it can be reduced to a problem of maximizing a flow in a bipartite network. We then describe a distributed fault-tolerant algorithm which allows each peer to compute the allocation of its resources using only local knowledge. Finally, we show that computing the maximal flow in a bounded-degree graph is NP-complete, which means that optimizing resource sharing in bounded-degree overlays is still an open problem