Maurits de Graaf

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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)
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)
—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)
Wireless Sensor Networks (WSNs) are usually self-organized wireless ad hoc networks comprising of a large number of resource constrained sensor nodes. One of the most important tasks of these sensor nodes is systematic collection of data and transmits gathered data to a distant base station (BS). Hence network lifetime becomes an important parameter for(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)
We consider the problem of data estimation in a sensor wireless network where sensors transmit their observations according to decentralized and centralized transmission schedules. A data collector is interested in achieving a data estimation using several sensor observations such that the variance of the estimation is below a targeted threshold. We analyze(More)