Complexity and Approximation of a Geometric Local Robot Assignment Problem

O. Bonorden, B. Degener, B. Kempkes, P. Pietrzyk, in: Algorithmic Aspects of Wireless Sensor Networks, Springer, Berlin, Heidelberg, 2009, pp. 252–262.

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Book Chapter | Published | English
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Abstract
We introduce a geometric multi-robot assignment problem. Robots positioned in a Euclidean space have to be assigned to treasures in such a way that their joint strength is sufficient to unearth a treasure with a given weight. The robots have a limited range and thus can only be assigned to treasures in their proximity. The objective is to unearth as many treasures as possible. We investigate the complexity of several variants of this problem and show whether they are in $\classP$ or are $\classNP$-complete. Furthermore, we provide a distributed and local constant-factor approximation algorithm using constant-factor resource augmentation for the two-dimensional setting with $\bigO(\log^*n)$ communication rounds.
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Book Title
Algorithmic Aspects of Wireless Sensor Networks
Page
252-262
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Bonorden O, Degener B, Kempkes B, Pietrzyk P. Complexity and Approximation of a Geometric Local Robot Assignment Problem. In: Algorithmic Aspects of Wireless Sensor Networks. Berlin, Heidelberg: Springer; 2009:252-262. doi:10.1007/978-3-642-05434-1_25
Bonorden, O., Degener, B., Kempkes, B., & Pietrzyk, P. (2009). Complexity and Approximation of a Geometric Local Robot Assignment Problem. In Algorithmic Aspects of Wireless Sensor Networks (pp. 252–262). Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-642-05434-1_25
@inbook{Bonorden_Degener_Kempkes_Pietrzyk_2009, place={Berlin, Heidelberg}, title={Complexity and Approximation of a Geometric Local Robot Assignment Problem}, DOI={10.1007/978-3-642-05434-1_25}, booktitle={Algorithmic Aspects of Wireless Sensor Networks}, publisher={Springer}, author={Bonorden, Olaf and Degener, Bastian and Kempkes, Barbara and Pietrzyk, Peter}, year={2009}, pages={252–262} }
Bonorden, Olaf, Bastian Degener, Barbara Kempkes, and Peter Pietrzyk. “Complexity and Approximation of a Geometric Local Robot Assignment Problem.” In Algorithmic Aspects of Wireless Sensor Networks, 252–62. Berlin, Heidelberg: Springer, 2009. https://doi.org/10.1007/978-3-642-05434-1_25.
O. Bonorden, B. Degener, B. Kempkes, and P. Pietrzyk, “Complexity and Approximation of a Geometric Local Robot Assignment Problem,” in Algorithmic Aspects of Wireless Sensor Networks, Berlin, Heidelberg: Springer, 2009, pp. 252–262.
Bonorden, Olaf, et al. “Complexity and Approximation of a Geometric Local Robot Assignment Problem.” Algorithmic Aspects of Wireless Sensor Networks, Springer, 2009, pp. 252–62, doi:10.1007/978-3-642-05434-1_25.

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