Euclidean movement minimization
- 204 Downloads
We consider a class of optimization problems called movement minimization on euclidean plane. Given a set of \(m\) nodes on the plane, the aim is to achieve some specific property by minimum movement of the nodes. We consider two specific properties, namely the connectivity (Con) and realization of a given topology (Topol). By minimum movement, we mean either the sum of all movements (Sum) or the maximum movement (Max). We obtain several approximation algorithms and some hardness results for these four problems. We obtain an \(O(m)\)-factor approximation for ConMax and ConSum and extend some known result on graphical grounds and obtain inapproximability results on the geometrical grounds. For the Topol problems (where the final decoration of the nodes must correspond to a given configuration), we find it much simpler and provide FPTAS for both Max and Sum versions.
KeywordsMovement minimization NP-hardness Approximation algorithms
- Basagni S, Carosi A, Petrioli C, Phillips CA (2008b) Moving multiple sinks through wireless sensor networks for lifetime maximization. In: MASS, pp. 523–526Google Scholar
- Basagni S, Carosi A, Petrioli C (2009) Heuristics for lifetime maximization in wireless sensor networks with multiple mobile sinks. In: ICC’09. IEEE International Conference on Communications, 2009, pp. 1–6Google Scholar
- Berman P, Demaine ED, Zadimoghaddam M (2011) O (1)-approximations for maximum movement problems. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Springer, Berlin, pp. 62–74Google Scholar
- Demaine ED, Hajiaghayi M, Marx D (2009b) Minimizing movement: fixed-parameter tractability. In: Algorithms-ESA 2009. Springer, pp. 718–729Google Scholar