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The Accuracy of One Polynomial Algorithm for the Convergecast Scheduling Problem on a Square Grid with Rectangular Obstacles

  • Adil Erzin
  • Roman Plotnikov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11353)

Abstract

In the Convergecast Scheduling Problem, it is required to find in the communication graph an oriented spanning aggregation tree with a root in a base station and the arcs oriented to the root and to build a conflict-free min-length schedule for aggregating data along the arcs of the aggregation tree. This problem is NP-hard in general, however, if the communication graph is a unit square grid in each node of which there is a sensor and in which a data packet is transmitted along any edge during a one-time slot, the problem is polynomially solvable. In this paper, we consider a communication graph in the form of a square grid with rectangular obstacles impenetrable by the messages. In our previous paper, we proposed a polynomial algorithm for constructing a feasible schedule and intensive numerical experiment allowed us to make a hypothesis that the algorithm constructs an optimal solution. In this paper, we present a counterexample and prove that the proposed algorithm constructs a schedule of length at most one time round longer than the optimal schedule.

Notes

Acknowledgments

The research of A.I. Erzin is partly supported by the Russian Foundation for Basic Research, Projects 16-07-00552 and by the program of fundamental scientific researches of the SB RAS No. I.5.1. (project 0314-2016-0014). The research of R.V. Plotnikov is partly supported by the Russian Foundation for Basic Research, Project 16-37-60006.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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