Our main observation concerns closed geodesics on surfaces M with a smooth Finsler metric, i.e. a function F : TM → [0,∞) which is a norm on each tangent space TpM , p ∈ M , which is smooth outside of the zero section in TM , and which is strictly convex in the sense that Hess(F ) is positive definite on TpM \ {0}. One calls a Finsler metric F symmetric if F (p,−v) = F (p, v) for all v ∈ TpM . ...

We consider the broadcasting problem in sensor networks where the nodes have no prior knowledge of their neighbourhood. We describe several Area-based Beaconless Broadcasting Algorithms (ABBAs). In 2D, on receiving the packet (together with geographic coordinates of the sender), each node calculates the ratio P of its perimeter, along the circle of transmission radius, that is not covered by th...

We provide constant factor approximation algorithms for covering the nodes of a graph using trees (rooted or unrooted), under the objective function of minimizing the weight of the maximum weight tree, subject to an upper bound on the number of trees used. These problems are related to location routing and traveling salesperson problems.

Covering the solid lattice with a finite-element mesh produces a coarse-grained system of mesh nodes as pseudoatoms interacting through an effective potential energy that depends implicitly on the thermodynamic state. Use of the pseudoatomic Hamiltonian in a Monte Carlo simulation of the two-dimensional Lennard-Jones crystal yields equilibrium thermomechanical properties (e.g., isotropic stress...

Sharing resources on a world-wide scale is a current research topic. Nowadays, peerto-peer architecture is considered as a scalable solution to this issue. However, a lot of problems to extend this architecture for data storage remain open. When information is not highly replicated, localization of nodes storing relevant data becomes essential to avoid covering completely the network. To this p...

This paper presents LiFTinG, the first protocol to detect freeriders, including colluding ones, in gossip-based content dissemination systems with asymmetric data exchanges. LiFTinG relies on nodes tracking abnormal behaviors by cross-checking the history of their previous interactions, and exploits the fact that nodes pick neighbors at random to prevent colluding nodes from covering each other...

In this article a survey on algorithms used for recovery of failure nodes in wireless sensor network has presented. Node recovery is a technique used to recover the failure of most used active nodes in WSN, when it becomes crucial to repair these nodes from failure and also from the situation where some part of covering area gets out of control and sight of the networks. The information flow ge...

We consider the replica placement problem: given a graph with clients and nodes, place replicas on a minimum set of nodes to serve all the clients; each client is associated with a request and maximum distance that it can travel to get served and there is a maximum limit (capacity) on the amount of request a replica can serve. The problem falls under the general framework of capacitated set cov...