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dedicated to professor w. t. tutte on the occasion of his eightieth birthday Let C 1 , ..., C k be a system of closed curves on a triangulizable surface S. The system is called minimally crossing if each curve C i has a minimal number of self-intersections among all curves C$ i freely homotopic to C i and if each pair C i , C j has a minimal number of… (More)

—We consider wireless caches placed in the plane according to a homogeneous Poisson process. A data file is stored at the caches, which have limited storage capabilities. Clients can contact the caches to retrieve the data. The caches store the data according to one of the two data allocation strategies: partitioning & coding. We consider the Pareto front… (More)

dedicated to professor w. t. tutte on the occasion of his eightieth birthday Let G=(V, E) be an Eulerian graph embedded on a triangulizable surface S. We show that E can be decomposed into closed curves C 1 , ..., C k such that mincr(G, D)= k i=1 mincr(C i , D) for each closed curve D on S. Here mincr(G, D) denotes the minimum number of intersections of G… (More)

In large-scale distributed applications, a loosely-coupled event-based style of communication as in publish/subcribe systems eases the integration of autonomous, heterogeneous components. In a publish/subscribe system, content based routing-where routing is based on the content of the messages-is an alternative to address-based delivery. In this paper we… (More)

We consider the problem of retrieving a reliable estimate of an attribute monitored by a wireless sensor network, where the sensors harvest energy from the environment independently, at random. Each sensor stores the harvested energy in batteries of limited capacity. Moreover, provided they have sufficient energy, the sensors broadcast their measurements in… (More)

Keywords: Performance analysis Wireless sensor networks Energy harvesting Stochastic geometry Markov decision process Scheduling a b s t r a c t We consider the problem of retrieving a reliable estimate of an attribute from a wireless sensor network within a fixed time window and with minimum energy consumption for the sensors. The sensors are located in… (More)

A fundamental problem for wireless ad hoc networks is the assignment of suitable transmission powers to the wireless devices such that the resulting communication graph is connected. The goal is to minimize the total transmit power in order to maximize the lifetime of the network. Our aim is a probabilistic analysis of this power assignment problem. We… (More)