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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)

- Maurits de Graaf, Alexander Schrijver
- J. Comb. Theory, Ser. B
- 1997

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)

- Maurits de Graaf, Alexander Schrijver
- J. Comb. Theory, Ser. B
- 1994

- Maurits de Graaf
- Ad Hoc Networks
- 2013

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)

- Mihaela Mitici, Jasper Goseling, Maurits de Graaf, Richard J. Boucherie
- 2013 IEEE Global Conference on Signal and…
- 2013

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)

- Tom Coenen, Maurits de Graaf, Richard J. Boucherie
- International Teletraffic Congress
- 2007

- Maurits de Graaf, Alexander Schrijver
- J. Comb. Theory, Ser. B
- 1997

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 analyze the Pareto front of the delay of collecting data from wireless devices located in the plane according to a Poisson process and the energy needed by the devices to transmit their observations. Fundamental bounds on the energy-delay trade-off over the space of all achievable scheduling strategies are provided.

—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)