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Theoretical Complexity of Grid Cover Problems Used in Radar Applications

Author

Listed:
  • Yann Briheche

    (Thales Air Systems
    Laboratoire des Sciences du Numérique de Nantes, UMR CNRS 6004)

  • Frederic Barbaresco

    (Thales Air Systems)

  • Fouad Bennis

    (Laboratoire des Sciences du Numérique de Nantes, UMR CNRS 6004)

  • Damien Chablat

    (Laboratoire des Sciences du Numérique de Nantes, UMR CNRS 6004)

Abstract

Modern radars are highly flexible systems, relying on digital antennas to dynamically control the radar beam shape and position through electronic circuits. Radar surveillance is performed by sequential emission of different radar beams. Optimization of radar surveillance requires finding a minimal subset of radar beams, which covers and ensures detection over the surveillance space, among a collection of available radar beams with different shapes and positions, thus minimizing the required scanning time. Optimal radar surveillance can be modelled by grid covering, a specific geometric case of set covering where the universe set is laid out on a grid, representing the radar surveillance space, which must be covered using available subsets, representing the radar beams detection areas. While the set cover problem is generally difficult to solve optimally, certain geometric cases can be optimized in polynomial time. This paper studies the theoretical complexity of grid cover problems used for modelling radar surveillance, proving that unidimensional grids can be covered by strongly polynomial algorithms based on dynamic programming, whereas optimal covering of bidimensional grids is generally non-deterministic polynomially hard.

Suggested Citation

  • Yann Briheche & Frederic Barbaresco & Fouad Bennis & Damien Chablat, 2018. "Theoretical Complexity of Grid Cover Problems Used in Radar Applications," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 1086-1106, December.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:3:d:10.1007_s10957-018-1354-x
    DOI: 10.1007/s10957-018-1354-x
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    References listed on IDEAS

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    1. V. Chvatal, 1979. "A Greedy Heuristic for the Set-Covering Problem," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 233-235, August.
    2. Nimrod Megiddo, 1991. "On Finding Primal- and Dual-Optimal Bases," INFORMS Journal on Computing, INFORMS, vol. 3(1), pages 63-65, February.
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