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)
We present an average case analysis of the minimum spanning tree heuristic for the range assignment problem on a graph with power weighted edges. It is well-known that the worst-case approximation ratio of this heuristic is 2. Our analysis yields the following results: (1) In the one dimensional case (d = 1), where the weights of the edges are 1 with(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(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)
Mobile wireless communication systems often need to maximize their network lifetime (defined as the time until the first node runs out of energy). In the broadcast network lifetime problem, all nodes are sending broadcast traffic, and one asks for an assignment of transmit powers to nodes, and for sets of relay nodes so that the network lifetime is(More)
—We consider the problem of finding the Pareto front of the expected deployment cost of wireless caches in the plane and the expected retrieval cost of a client requesting data from the caches. The data is allocated at the caches according to partitioning and coding strategies. We show that under coding, it is optimal to deploy many caches with low storage(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)