Journal of Combinatorial Optimization

, Volume 34, Issue 4, pp 1237–1264 | Cite as

Online set multicover algorithms for dynamic D2D communications

  • Alan Kuhnle
  • Xiang Li
  • J. David Smith
  • My T. ThaiEmail author


Motivated by the dynamic resource allocation problem for device-to-device (D2D) communications, we study the online set multicover problem (OSMC). In the online set multicover, the set X of elements to be covered is unknown in advance; furthermore, the coverage requirement of each element \(x \in X\) is initially unknown. Elements of X together with coverage requirements are presented one at a time in an online fashion; and a feasible solution must be maintained at all times. We provide the first deterministic, online algorithms for OSMC with competitive ratios. We consider two versions of OSMC; in the first, each set may be picked only once, while the second version allows each set to be picked multiple times. For both versions, we present the first deterministic, online algorithms, with competitive ratios \(O( \log n \log m )\) and \(O( \log n (\log m + \log k) )\), repectively, where n is the number of elements, m is the number of sets, and k is the maximum coverage requirement. By simulation, we show the efficacy of these algorithms for resource allocation in the D2D setting by analyzing network throughput and other metrics, obtaining a large improvement in running time over offline methods.


Online algorithm Set multicover Optimization D2D communications Resource allocation 



This work partially supported by NSF CAREER 0953284, and NSF CNS-1443905.


  1. Alim MA, Pan T, Thai MT, Saad W (2017) Leveraging social communities for optimizing cellular device-to-device communications. IEEE Trans Wirel Commun 16(1):551–564CrossRefGoogle Scholar
  2. Alon N, Awerbuch B, Azar Y, Buchbinder N, Naor J (2009) The online set cover problem. SIAM J Comput 39:361–370MathSciNetCrossRefzbMATHGoogle Scholar
  3. Alon N, Gutner S, Azar Y (2009) Admission control to minimize rejections and online set cover with repetitions. ACM Trans Algorithms 6(1):11MathSciNetCrossRefzbMATHGoogle Scholar
  4. Buchbinder N, Naor J (2009) Online primal-dual algorithms for covering and packing problems. Math Oper Res 34(2):270–286MathSciNetCrossRefzbMATHGoogle Scholar
  5. Chia-Hao Yu et al (2011) Resource sharing optimization for device-to-device communication underlaying cellular networks. IEEE Trans Wirel Commun 10.8:2752–2763CrossRefGoogle Scholar
  6. Chin WH, Fan Z, Haines R (2014) Emerging technologies and research challenges for 5G wireless networks. IEEE Wirel Commun 21(2):106–112CrossRefGoogle Scholar
  7. Doppler K, Rinne M, Wijting C, Ribeiro CB, Hugl K (2009) Device-to-device communication as an underlay to LTE-advanced networks. IEEE Commun Mag 47(12):42–49CrossRefGoogle Scholar
  8. Fu H, Kim DI (2006) Analysis of throughput and fairness with downlink scheduling in WCDMA networks. IEEE Trans Wirel Commun 5(8):2164–2174CrossRefGoogle Scholar
  9. Kaufman B, Aazhang B (2008) Cellular networks with an overlaid device to device network. Signals Syst Comput. 2008 42nd Asilomar conference on. IEEEGoogle Scholar
  10. Krogfoss B, Hanson G, Vale RJ (2011) Impact of consumer traffic growth on mobile and fixed networks: business model and network quality impact. Bell Labs Tech J 16:105–120CrossRefGoogle Scholar
  11. Kuhnle A, Li X, Thai MT (2014) Online algorithms for optimal resource management in dynamic D2D communications. In: 10th international conference on mobile ad-hoc and sensor networks (IEEE MSN2014)Google Scholar
  12. Lee DH, Choi KW, Jeon WS, Jeong DG (2013) Resource allocation scheme for device-to-device communication for maximizing spatial reuse. In: Wireless communications and networking conference (WCNC). IEEE, pp 112–117Google Scholar
  13. López-Pérez D, Valcarce A, De La Roche G, Zhang J (2009) OFDMA femtocells: a roadmap on interference avoidance. IEEE Commun Mag 47(9)Google Scholar
  14. Nguyen NP, Xuan Y, Thai MT (2010) A novel method for worm containment on dynamic social networks. In: Military communications conference, 2010-MILCOM 2010. IEEE, pp 2180–2185Google Scholar
  15. Novlan TD, Ganti RK, Ghosh A, Andrews JG (2011) Analytical evaluation of fractional frequency reuse of OFDMA cellular networks. IEEE Trans Wirel Commun 10(12):4294–4305Google Scholar
  16. Osseiran Afif et al (2014) Scenarios for 5G mobile and wireless communications: the vision of the METIS project. IEEE Commun Mag 52.5:26–35CrossRefGoogle Scholar
  17. Vazirani VV (2003) Approximation algorithms. Springer, BerlinCrossRefGoogle Scholar
  18. Zander Jens, Mahonen Petri (2013) Riding the data tsunami in the cloud: myths and challenges in future wireless access. IEEE Commun Mag 51(3):145–151CrossRefGoogle Scholar
  19. Zulhasnine M, Huang C, Srinivasan A (2010) Efficient resource allocation for device-to-device communication underlaying LTE network. Proc IEEE WiMob 2010:368–375Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of Computer and Information Science and EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.Division of Algorithms and Technologies for Networks Analysis, Faculty of Information TechnologyTon Duc Thang UniversityHo Chi Minh CityVietnam

Personalised recommendations