Journal of Combinatorial Optimization

, Volume 32, Issue 2, pp 354–367 | Cite as

Euclidean movement minimization

  • Nima Anari
  • MohammadAmin Fazli
  • Mohammad Ghodsi
  • MohammadAli Safari


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.


Movement minimization NP-hardness Approximation algorithms 


  1. Basagni S, Carosi A, Melachrinoudis E, Petrioli C, Wang ZM (2008a) Controlled sink mobility for prolonging wireless sensor networks lifetime. Wirel Netw 14(6):831–858CrossRefGoogle Scholar
  2. 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
  3. 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
  4. 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
  5. Burda Z, Jurkiewicz J, Krzywicki A (2004) Network transitivity and matrix models. Phys Rev E 69(2):026106CrossRefGoogle Scholar
  6. Callaway DS, Newman MEJ, Strogatz SH, Watts DJ (2000) Network robustness and fragility: percolation on random graphs. Phys Rev Lett 85(25):5468CrossRefGoogle Scholar
  7. Demaine ED, Hajiaghayi M, Mahini H, Sayedi-Roshkhar AS, Oveisgharan Shayan, Zadimoghaddam Morteza (2009a) Minimizing movement. ACM Trans Algorithms (TALG) 5(3):30MathSciNetzbMATHGoogle Scholar
  8. Demaine ED, Hajiaghayi M, Marx D (2009b) Minimizing movement: fixed-parameter tractability. In: Algorithms-ESA 2009. Springer, pp. 718–729Google Scholar
  9. Garey MR, Johnson DS, Tarjan RE (1976) The planar hamiltonian circuit problem is np-complete. SIAM J Comput 5(4):704–714MathSciNetCrossRefzbMATHGoogle Scholar
  10. Itai A, Papadimitriou CH, Szwarcfiter JL (1982) Hamilton paths in grid graphs. SIAM J Comput 11(4):676–686MathSciNetCrossRefzbMATHGoogle Scholar
  11. Kleinberg J (2007) Cascading behavior in networks: algorithmic and economic issues. Algorithmic Game Theory 24:613–632MathSciNetCrossRefzbMATHGoogle Scholar
  12. Philips TK, Panwar Shivendra S, Tantawi AN (1989) Connectivity properties of a packet radio network model. IEEE Trans Inf Theory 35(5):1044–1047CrossRefGoogle Scholar
  13. Valiant LG (1981) Universality considerations in vlsi circuits. IEEE Trans Comput 100(2):135–140MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Nima Anari
    • 1
  • MohammadAmin Fazli
    • 2
  • Mohammad Ghodsi
    • 2
    • 3
  • MohammadAli Safari
    • 2
  1. 1.Computer Science DivisionUniversity of California BerkeleyBerkeleyUSA
  2. 2.Department of Computer EngineeringSharif University of TechnologyTehranIran
  3. 3.Institute of Research in Fundamental Sciences (IPM)TehranIran

Personalised recommendations