Maurits de Graaf

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Let C1 , ..., Ck be a system of closed curves on a triangulizable surface S. The system is called minimally crossing if each curve Ci has a minimal number of selfintersections among all curves C$i freely homotopic to Ci and if each pair Ci , Cj has a minimal number of intersections among all curve pairs C$i , C$j freely homotopic to Ci , Cj respectively (i,(More)
Let G=(V, E) be an Eulerian graph embedded on a triangulizable surface S. We show that E can be decomposed into closed curves C1 , ..., Ck such that mincr(G, D)= i=1 mincr(Ci , D) for each closed curve D on S. Here mincr(G, D) denotes the minimum number of intersections of G and D$ (counting multiplicities), where D$ ranges over all closed curves D$ freely(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)
Mobile wireless ad-hoc networks 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 maximized. The(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)
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 life-time of the network. Our aim is a probabilistic analysis of this power assignment problem. We(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)