Balls and Funnels: Energy Efficient Group-to-Group Anycasts

  • Jennifer Iglesias
  • Rajmohan Rajaraman
  • R. Ravi
  • Ravi SundaramEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)


We introduce group-to-group anycast (g2g-anycast), a network design problem of substantial practical importance and considerable generality. Given a collection of groups and requirements for directed connectivity from source groups to destination groups, the solution network must contain, for each requirement, an omni-directional down-link broadcast, centered at any node of the source group, called the ball; the ball must contain some node from the destination group in the requirement and all such destination nodes in the ball must aggregate into a tree directed towards the source, called the funnel-tree. The solution network is a collection of balls along with the funnel-trees they contain. g2g-anycast models DBS (Digital Broadcast Satellite), Cable TV systems and drone swarms. It generalizes several well known network design problems including minimum energy unicast, multicast, broadcast, Steiner-tree, Steiner-forest and Group-Steiner tree. Our main achievement is an \(O(\log ^4 n)\) approximation, counterbalanced by an \(\log ^{(2-\epsilon )}n\) hardness of approximation, for general weights. Given the applicability to wireless communication, we present a scalable and easily implemented \(O(\log n)\) approximation algorithm, Cover-and-Grow for fixed-dimensional Euclidean space with path-loss exponent at least 2.


Network design Wireless Approximation 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Jennifer Iglesias
    • 1
  • Rajmohan Rajaraman
    • 2
  • R. Ravi
    • 1
  • Ravi Sundaram
    • 2
    Email author
  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.Northeastern UniversityBostonUSA

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