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PTAS for routing-cost constrained minimum connected dominating set in growth bounded graphs

Author

Listed:
  • Lidong Wu

    (University of Texas at Dallas)

  • Hongwei Du

    (Harbin Institute of Technology, Shenzhen Graduate School)

  • Weili Wu

    (University of Texas at Dallas)

  • Yuqing Zhu

    (University of Texas at Dallas)

  • Ailan Wang

    (Taiyuan University of Technology)

  • Wonjun Lee

    (Korea University)

Abstract

Connected dominating set (CDS) has played an important role in building virtual backbone, which is used on unicast, multicast, and fault-tolerant routing in wireless sensor networks. In order to reduce traffic congestion and communication delay, a routing-cost constrained minimum CDS (ROC–CDS) has been studied extensively in the literature. In this paper, we present a PTAS for $$\alpha $$ α ROC–CDS where $$\alpha \ge 5$$ α ≥ 5 , that is, there exists a polynomial-time $$(1+\varepsilon )$$ ( 1 + ε ) -approximation for minimum CDS under constraint that for every pair of nodes u and v, $$m_{CDS}(u,v) \le m(u,v)$$ m CDS ( u , v ) ≤ m ( u , v ) where $$m(u,v)$$ m ( u , v ) denotes the number of intermediate nodes in the shortest path between u and v, and $$m_{CDS}(u,v)$$ m CDS ( u , v ) denotes the number of intermediate nodes of the shortest path between u and v through CDS produced by the approximation algorithm.

Suggested Citation

  • Lidong Wu & Hongwei Du & Weili Wu & Yuqing Zhu & Ailan Wang & Wonjun Lee, 2015. "PTAS for routing-cost constrained minimum connected dominating set in growth bounded graphs," Journal of Combinatorial Optimization, Springer, vol. 30(1), pages 18-26, July.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:1:d:10.1007_s10878-013-9626-8
    DOI: 10.1007/s10878-013-9626-8
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